In this article, we shall study to solve problems on the calculations of the number of electrons, protons, and neutrons in atoms, molecules, and species.

Example 01:

Calculate the charge and mass of 1 mole of electrons.

Solution:

1 mole of electron corresponds to 6.023 x 10²³ electrons

Mass of 1 electron = 9.1 x 10^-31 kg

Mass of one mole of electron = 9.1 x 10^-31 x 6.022 x 10²³ = 5.48 x 10^-7 kg

Charge of 1 electron = 1.602 x 10^-19 C

Charge on one mole of electron = 1.602 x 10^-19 x 6.022 x 10²³ = 9.65 x 10⁴ C

Ans: The mass of one mole of electrons is 5.48 x 10^-7 kg and the charge on one mole of electrons is 9.65 x 10⁴ C

Example 02:

Calculate the total number of electrons in 1 mole of ammonia (NH₃).

Solution:

Nitrogen (N):

Atomic number = Z = 7

Number of electrons = Atomic number = 7

Hydrogen (H):

Atomic number = Z = 1

Number of electrons in 1 atom of hydrogen = Atomic number = 1

Number of electrons in 3 hydrogen atoms = 1 x 3 = 3

Number of electrons in 1 molecule of ammonia = 7 + 3 = 10

1 mole of ammonia contains 6.022 x 10²³ molecules of ammonia

Number of electrons in 1 mole of ammonia = 10 x 6.022 x 10²³ = 6.022 x 10²⁴

Ans: The number of electrons in 1 mole of ammonia = 6.022 x 10²⁴

Example 03:

Calculate the total number of electrons in 1 mole of methane (CH₄).

Solution:

Carbon (C):

Atomic number = Z = 6

Number of electrons = Atomic number = 6

Hydrogen (H):

Atomic number = Z = 1

Number of electrons in 1 atom of hydrogen = Atomic number = 1

Number of electrons in 4 hydrogen atoms = 1 x 4 = 4

Number of electrons in 1 molecule of ammonia = 6 + 4 = 10

1 mole of ammonia contains 6.022 x 10²³ molecules of ammonia

Number of electrons in 1 mole of ammonia = 10 x 6.022 x 10²³ = 6.022 x 10²⁴

Ans: The number of electrons in 1 mole of ammonia = 6.022 x 10²⁴

Example 04:

Find the total number and the total mass of neutrons in 7 m of ¹⁴C. Mass of neutron = 1.675 x 10^-27 kg.

Given mass of carbon = 7 mg = 7 x 10^-3 g

Molecular mass of carbon = 14 g

Number of moles of carbon = (7 x 10^-3)/14 = 5 x 10^-4  mol

Number of carbon atoms in 7 mg of ¹⁴C = 5 x 10^-4 x 6.022 x 10²³ = 3.011 x 10²⁰

Number of neutrons in 1 atom of carbon = A – Z = 14 – 6 = 8

Number of neutrons in 7 mg of ¹⁴C = 8 x 3.011 x 10²⁰ = 2.4088 x 10²¹

Mass of 1 neutron = 1.675 x 10^-27 kg.

Mass of neutron in 7 mg of ¹⁴C = 1.675 x 10^-27 x 2.4088 x 10²¹

Mass of neutron in 7 mg of ¹⁴C = 4.0347 x 10^-6 kg

Example 05:

Find total number and total mass of proton in 34 mg of ammonia at STP. Will the answer change if temperature and pressure are changed?

Given mass of ammonia = 34 mg = 34 x 10^-3 g

Molecular mass of ammonia = 14 + 3 = 17 g

Number of moles of ammonia = (34 x 10^-3)/17 = 2 x 10^-3 mol

Nitrogen (N):

Atomic number = Z = 7

Number of protons = Atomic number = 7

Hydrogen (H):

Atomic number = Z = 1

Number of protons in 1 atom of hydrogen = Atomic number = 1

Number of protons in 3 hydrogen atoms = 1 x 3 = 3

Number of protons in 1 molecule of ammonia = 7 + 3 = 10

Number of molecules in 34 mg of ammonia = 2 x 10^-3 x 6.022 x 10²³ = 1.2044 x 10²¹

Number of protons in 34 mg of ammonia = 10 x 1.2044 x 10²¹= 1.2044 x 10²²

Mass of 1 proton = 1.673 x 10^-27 kg.

Mass of protons in 34 mg of ammonia = 1.673 x 10^-27 x 1.2044 x 10²²

Mass of protons in 34 mg of ammonia = 2.015 x 10^-5 kg

Due to change in temperature and pressure, there is no change in number of moles of the gas. Hence there is no effect o change of temperature and pressure.

Example 06:

Calculate the number of electrons which will together weigh 1 gram.

Mass of 1 electron = 9.1 x 10^-31 kg = 9.1 x 10^-28 g

Number of electrons in 1 gram = 1/(9.1 x 10^-28) = 1.098 x 10²⁷ electrons

Example 07:

2 x 10⁸ atoms of carbon are arranged side by side, calculate the radius of carbon atom, if the length of this arrangement is 2.4 cm

Diameter of carbon atom = 2.4/(2 x 10⁸) = 1.2 x 10^-8  cm

Radius of carbon atom = (1.2 x 10^-8)/2 = 6 x 10^-9 cm = 6 x 10^-11 m = 0.6 x 10^-10  m = 0.6 angstrom

Example 08:

Find the total number and total mass of neutrons in 18 mL of water. The specific gravity of water = 1.

Given volume of water = 18 mL = 18 x 10^-3 L

Mass of water = Volume x density = 18 x 10^-3 L x 1 kg/L = 18 x 10^-3 kg = 18 g

Molecular mass of water= 2 + 16 = 18 g

Number of moles of water = 18/18 = 1 mol

Oxygen (O):

Atomic number = Z = 8

Atomic mass number = A = 16

Number of neutrons = 16 – 8 = 8

Hydrogen (H):

Atomic number = Z = 1

Atomic mass of hydrogen = A = 1

Number of neutrons in 1 atom of hydrogen = 1 – 1 = 0

Number of neutrons in 2 hydrogen atoms = 0 x 2 = 0

Number of neutrons in 1 molecule of water = 8 + 0 = 8

Number of molecules in 18 mL of water = 1  x 6.022 x 10²³ = 6.022 x 10²³

Number of neutrons in 18 mL of water = 8 x 6.022 x 10²³= 4.8176 x 10²⁴

Mass of 1 neutron = 1.675 x 10^-27 kg.

Mass of neutrons in 18 mL of water = 1.675 x 10^-27 x 4.8176 x 10²⁴

Mass of neutrons in 18 mL of water = 8.0695 x 10^-3 kg

Due to change in temperature and pressure, there is no change in number of moles of the gas. Hence there is no effect o change of temperature and pressure.

Science > Chemistry > Atomic Structure > Problems on Calculation of Number of Electrons, Protons, and Neutrons

The post Problems on Calculation of Mass of Electrons, Protons, and Neutrons appeared first on The Fact Factor.

In this article, we shall study to solve problems based on the calculation of atomic number, atomic mass number, and neutron number

Atomic number (Z) :

The number of protons (positive charge) present in the nucleus of an atom of a particular element is called the atomic number of that element. It is denoted by letter ‘Z’.

Neutron number (N): 

The number of neutrons present in the nucleus of an atom is known as neutron number. It is denoted by ‘N’

Mass number (A): 

The total number of protons and neutrons present in the nucleus of an atom of the element is called mass number. The mass number is denoted as ‘A’.

A  =   Z + N

Example 01:

Calculate the number of electrons, protons, and neutrons in the following atoms.

Atomic Number = Z = 15

Atomic Mass Number = A = 31

Number of protons = atomic number = 15

Number of electrons = atomic number = 15

Neutron number = Number of neutrons = A – Z = 31 – 15 = 16

Number of nucleons = Atomic mass number = 31

Atomic Number = Z = 12

Atomic Mass Number = A = 24

Number of protons = atomic number = 12

Number of electrons = atomic number = 12

Neutron number = Number of neutrons = A – Z = 24 – 12 = 12

Number of nucleons = Atomic mass number = 24

Atomic Number = Z = 17

Atomic Mass Number = A = 37

Number of protons = atomic number = 17

Number of electrons = atomic number = 17

Neutron number = Number of neutrons = A – Z = 37 – 17 = 20

Number of nucleons = Atomic mass number = 37

Atomic Number = Z = 18

Atomic Mass Number = A = 40

Number of protons = atomic number = 18

Number of electrons = atomic number = 18

Neutron number = Number of neutrons = A – Z = 40 – 18 = 22

Number of nucleons = Atomic mass number = 40

Atomic Number = Z = 35

Atomic Mass Number = A = 80

Number of protons = atomic number = 35

Number of electrons = atomic number = 35

Neutron number = Number of neutrons = A – Z = 80 – 35 = 45

Number of nucleons = Atomic mass number = 80

Atomic Number = Z = 20

Atomic Mass Number = A = 40

Number of protons = atomic number = 20

Number of electrons = atomic number = 20

Neutron number = Number of neutrons = A – Z = 40 – 20 = 20

Number of nucleons = Atomic mass number = 40

Atomic Number = Z = 6

Atomic Mass Number = A = 13

Number of protons = atomic number = 6

Number of electrons = atomic number = 6

Neutron number = Number of neutrons = A – Z = 13 – 6 = 7

Number of nucleons = Atomic mass number = 13

Atomic Number = Z = 8

Atomic Mass Number = A = 16

Number of protons = atomic number = 8

Number of electrons = atomic number = 8

Neutron number = Number of neutrons = A – Z = 16 – 8 = 8

Number of nucleons = Atomic mass number = 16

Atomic Number = Z = 26

Atomic Mass Number = A = 56

Number of protons = atomic number = 26

Number of electrons = atomic number = 26

Neutron number = Number of neutrons = A – Z = 56 – 26 = 30

Number of nucleons = Atomic mass number = 56

Atomic Number = Z = 38

Atomic Mass Number = A = 88

Number of protons = atomic number = 38

Number of electrons = atomic number = 38

Neutron number = Number of neutrons = A – Z = 88 – 38 = 50

Number of nucleons = Atomic mass number = 88

Example 02:

Calculate the number of electrons, protons, and neutrons in the following species.

Atomic Number = Z = 15

Atomic Mass Number = A = 31

Number of protons = atomic number = 15

P^3- → P + 3 e^–

Number of electrons = 15 + 3 = 18

Number of neutrons = A – Z = 31 – 15 = 16

Number of nucleons = Atomic mass number = 31

Atomic Number = Z = 35

Atomic Mass Number = A = 80

Number of protons = atomic number = 35

Br^– → Br + e^–

Number of electrons = 35 + 1= 36

Number of neutrons = A – Z = 80 – 35 = 45

Number of nucleons = Atomic mass number = 80

Atomic Number = Z = 20

Atomic Mass Number = A = 40

Number of protons = atomic number = 20

Ca²⁺ → Ca – 2e^–

Number of electrons = 20 – 2= 18

Number of neutrons = A – Z = 40 – 20 = 20

Number of nucleons = Atomic mass number = 40

H₃PO₄

Hydrogen (H):

Atomic Number = Z = 1

Atomic Mass Number = A = 1

Number of protons per atom= atomic number = 1

Number of electrons per atom = Z = 1

Number of neutrons per atom = A – Z = 1 – 1 = 0

There are 3 hydrogen atoms in the molecule

Total number of protons in 3 hydrogens = 1 x 3 = 3

Total number of electrons in 3 hydrogens = 1 x 3 = 3

Total number of neutrons in 3 hydrogens = 0 x 3 = 0

Phosphorous (P):

Atomic Number = Z = 15

Atomic Mass Number = A = 31

Number of protons per atom= atomic number = 15

Number of electrons per atom = Z = 15

Number of neutrons per atom = A – Z = 31 – 15 = 16

There is 1 phosphorous atom in the molecule

Total number of protons in 1 phosphorous = 15 x 1 = 15

Total number of electrons in 1 phosphorous = 15 x 1 = 15

Total number of neutrons in 1 phosphorous = 16 x 1 = 16

Oxygen (O):

Atomic Number = Z = 8

Atomic Mass Number = A = 16

Number of protons per atom= atomic number = 8

Number of electrons per atom = Z = 8

Number of neutrons per atom = A – Z = 16 – 8 = 8

There are 4 oxygen atom in the molecule

Total number of protons in 4 oxygen= 8 x 4 = 32

Total number of electrons in 4 oxygen = 8 x 4 = 32

Total number of neutrons in 4 oxygen = 8 x 4 = 32

Ans:

Total number of protons in H₃PO₄ = 3 + 15 + 32 = 50

Total number of electrons in H₃PO₄ = 3 + 15 + 32 = 50

Total number of neutrons in H₃PO₄ = 0 + 16 + 32 = 48

NH₄⁺

Nitrogen (N):

Atomic Number = Z = 7

Atomic Mass Number = A = 14

Number of protons per atom= atomic number = 14

Number of electrons per atom = Z = 14

Number of neutrons per atom = A – Z = 14 – 7 = 7

Hydrogen (H):

Atomic Number = Z = 1

Atomic Mass Number = A = 1

Number of protons per atom= atomic number = 20

Number of electrons per atom = Z = 1

Number of neutrons per atom = A – Z = 1 – 1 = 0

There are 4 hydrogen atoms in the species

Total number of protons in 3 hydrogens = 1 x 4 = 4

Total number of electrons in 3 hydrogens = 1 x 4 = 4

Total number of neutrons in 3 hydrogens = 0 x 4 = 0

Total number of protons in NH₄⁺ = 7 + 4 = 11

NH₄⁺ → NH₄ – e^–

Total number of electrons in NH₄⁺ = 7 + 4 – 1 = 10

Total number of neutrons in NH₄⁺ = 7 + 4 = 11

ClO₃^–

Chlorine (Cl):

Atomic Number = Z = 17

Atomic Mass Number = A = 37

Number of protons per atom= atomic number = 17

Number of electrons per atom = Z = 17

Number of neutrons per atom = A – Z = 37 – 17 = 20

Oxygen (O):

Atomic Number = Z = 8

Atomic Mass Number = A = 16

Number of protons per atom= atomic number = 8

Number of electrons per atom = Z = 8

Number of neutrons per atom = A – Z = 16 – 8 = 8

There are 3 oxygen atom in the species

Total number of protons in 4 oxygen= 8 x 3 = 24

Total number of electrons in 4 oxygen = 8 x 3 = 24

Total number of neutrons in 4 oxygen = 8 x 3 = 24

Total number of protons in ClO₃^– = 17 + 24 = 41

ClO₃^– → ClO₃ + e^–

Total number of electrons in ClO₃^– = 17 + 24 + 1 = 42

Total number of neutrons in ClO₃^– = 20 + 24 = 44

Example 03:

Complete the table

Solution:

Zn

Atomic Number = Z = 30

Atomic Mass Number = A = 64

Number of protons = atomic number = 30

Number of electrons = atomic number = 30

Number of neutrons = A – Z = 64 – 30 = 34

Sr²⁺

Atomic Number = Z = 38

Atomic Mass Number = A = 90

Number of protons = atomic number = 38

Sr²⁺ → Sr – 2e^–

Number of electrons = 38 – 2 = 36

Number of neutrons = A – Z = 90 – 38 = 52

Te

Number of protons = 43

Number of Neutrons = N = 56

Atomic number =Number of protons = Z = 43

Atomic mass number = Z + N = 43 + 56 = 99

Number off electrons = Atomic number = 43

Br^–

Number of neutrons = N = 44

Number of electrons = 36

Br^– → Br + e^–

Number of protons = 36 – 1 = 35

Atomic Number = Number of protons = Z = 35

Atomic mass number = Z + N = 35 + 44 = 79

N

Number of neutrons = N = 7

Number of electrons = 7

Number of protons = 7

Atomic Number = Number of protons = Z = 7

Atomic mass number = Z + N = 7 + 7 = 14

Ca²⁺

Atomic Number = Z = 20

Number of neutrons = N = 20

Atomic Mass Number = Z + N = 20 + 20 = 40

Number of protons = atomic number = 20

Ca²⁺ → Ca – 2e^–

Number of electrons = 20 – 2 = 18

O

Atomic Number = Z = 8

Atomic Mass Number = A = 16

Number of protons = atomic number = 8

Number of electrons = atomic number = 8

Number of neutrons = A – Z = 16 – 8 = 8

The completed table is as follows:

Example 04:

The numbers of electrons, protons, and neutrons in a monoatomic species are equal to 36, 35, and 45 respectively. Assign proper symbol.

Solution:

Number of electrons = 36

Number of protons = Atomic number = Z = 35

Number of neutrons = N = 45

Atomic mass number = A = Z + N = 35 + 45 = 80

Charge on species = Z – Number of electrons = 35 – 36 = -1

The species is

Example 05:

The numbers of electrons, protons, and neutrons in a monoatomic species are equal to 18, 16, and 16 respectively. Assign proper symbol.

Solution:

Number of electrons = 18

Number of protons = Atomic number = Z = 16

Number of neutrons = N = 16

Atomic mass number = A = Z + N = 16 + 16 = 32

Charge on species = Z – Number of electrons = 16 – 18 = -2

The species is

Example 06:

Find the number of electrons in fluorine atom, fluorine molecule, and fluoride ion. The atomic number and mass number of fluorine are 9 and 19 respectively.

Solution:

Atomic number = Z = 9

Atomic mass number A = 19

Fluorine Atom (F):

Number of protons = Atomic number = 9

Number of Protons = Atomic number = 9

Number of electrons = Atomic number = 9

Number of neutrons = a – z = 19 – 9 =10

Fluorine Molecule (F₂):

There are 2 atoms in a molecule of fluorine

Number of protons in fluorine molecule= 9 x 2 = 18

Number of electrons in fluorine molecule= 9 x 2 = 18

Number of neutrons in fluorine molecule= 10 x 2 = 20

Fluoride Ion (F^–):

Number of Protons = Atomic number = 9

F^– → F + e^–

Number of electrons = 9 + 1 = 10

Number of neutrons = a – z = 19 – 9 =10

Example 07:

An isotope of atomic mass 24 had 12 neutrons in its nucleus. What is its atomic number? Represent the isotope in symbolic form.

Solution:

Atomic mass number = A = 24

Number of neutrons = N = 12

Number of protons = A – Z = 24 – 12= 12

Atomic number = Number of protons = Z = 12

The element is

Isotopes, Isotones, and Isobars

• Different atoms of the same element having the same atomic number but having different mass numbers are known as isotopes.
• Atoms of the different elements having a different atomic number but having the same mass numbers are known as isobars.
• Atoms of the different elements having the different atomic number, different mass number but having the same neutron number are known as isotones.

Example 08:

Write the complete symbol for the atom with the given atomic number (Z) and atomic mass (A):

• Z = 17 and A = 35

• Z = 92, A = 233

• Z = 4, A = 9

Example 09:

Give an isobar, an isotone, and an isotope of

Isobar
Isotone
Isotope

Science > Chemistry > Atomic Structure > Problems Based on Atomic Number, Mass Number, and Neutron Number

The post Problems Based on Atomic Number, Mass Number, and Neutron Number appeared first on The Fact Factor.

Mathematical relationships between volume, pressure, and temperature of a given mass of gas are referred to as Gas laws. In this article. we shall study Pressure-Temperature relation or Gay-Lussac’s law.

Gay-Lussac’s Law:

Statement:

At constant volume the pressure of a given mass of a gas increases or decreases by 1/273 of its pressure at 0^oC for every degree rise or fall in temperature.

Explanation:

Let P_o be the volume of a gas at 0 °C, Let this gas be heated through t °C, Let P_t be the volume of the gas at t °C. then,

Alternate Statement of Gay-Lussac’s law:

Thus at constant volume, the pressure of the certain mass of enclosed gas is directly proportional to the absolute temperature of the gas.

In general

This relation is called the pressure-temperature relation.

Graphical Representation:

A graph is drawn by taking the absolute temperature on the x-axis and pressure on the y-axis. The graph is as follows. This graph is also known as a P-T  diagram.

Numerical Problems:

Example 01:

A steel tank contains air at a pressure of 15 bar at 20 ^oC. The tank is provided with a safety valve which can withstand a pressure of 35 bar. Calculate the temperature to which the tank can be safely heated.

Solution:

Given: Initial pressure P₁ = 15 bar, Initial temperature = 20 ^oC = 20 + 273 = 293 K, Final pressure P₂ = 35 bar

To Find: Temperature up to which tank can be heated = T₂ =?

By Gay-Lussac’s Law

T₂ = (P₂ x T₁)/P₁ = (35 x 293)/15 = 683.67 K

T₂ = 683.67 – 273.15 = 410.15 ^oC

Ans: The tank can be heated up to 410.15 ^oC

Example 02:

An iron tank contains helium at a pressure of 2.5 atm at 25 ^oC. The tank can withstand a maximum pressure of 10 atm. The building in which the tank has been installed catches fire. Predict whether the tank will blow up first or melt if the melting point of iron is 1535 ^oC.

Solution:

Given: Initial pressure P₁ = 2.5 atm, Initial temperature = 25 ^oC = 25 + 273 = 298 K, Melting point of iron = T₂ = 1535 ^oC = 1535 + 273 = 1808 K

To Find: Final pressure = P₂ =?

By Gay-Lussac’s Law

P₂ = (T₂ x P₁)/T₁ = (1808 x 2.5)/298 = 15.16 atm

The pressure at the melting point is 15.16 atm, which is much more than the maximum pressure that the tank can withstand 10 atm. Hence the tank will blow up before reaching the melting point.

Ans: The tank will blow up before reaching the melting point.

Science > Chemistry > States of Matter > Charle’s Law

The post Pressure-Temperature Relation (Gay-Lussac’s law) appeared first on The Fact Factor.

All matter has physical and chemical properties. Extensive properties are those properties of a substance which depend on the amount of substance. They vary with the amount of the substance. Examples: Mass, weight, and volume. Intensive properties are those properties of a substance which do not depend on the amount of substance. Examples: colour, melting point, boiling point, electrical conductivity, and physical state at a given temperature.

Physical Properties of Substance:

Physical properties are characteristics that can be measured or observed without changing the composition of the substance under study. All samples of a pure substance have the same chemical and physical properties. Physical properties can be extensive or intensive. 

Mass

A mass is the amount of matter that is found in a substance. Mass is expressed in terms of kilograms (kg).

Density

Density is the measurement of mass with respect to and in a relationship with volume. The mass of a substance per its unit volume is called density. Density is expressed in kilograms per cubic metre (kg/m³). Mathematically

Density = Mass / Volume

The density depends on the temperature and pressure of the substance. The effect is prominent in cases of gases. The application of increasing temperature decreases its density because its volume increases with increasing temperatures, and the application of increasing pressure increases density because the volume decreases with increasing pressure.

Volume

Volume is the measurement of the quantity or amount of matter in a three dimensional space. It is the space occupied by the substance. Volume is expressed in cubic metres (m³).

Boiling Point:

The temperature at which a liquid changes its state to a gas at atmospheric pressure is called the boiling point of that liquid.  It is defined as the temperature at which the vapour pressure of the liquid becomes equal to the atmospheric pressure. This is the point at which both liquid and gaseous phase exists at equilibrium. The boiling point of the substance also varies with pressure and is specified at standard pressure.

The boiling point of a liquid is a characteristic property and can be treated as a criterion for the purity of liquid.  It increases with the increase in external pressure. Liquids having greater intermolecular forces have high boiling points.

Melting Point:

The temperature at which a solid changes its state to a liquid at atmospheric pressure is called the melting point of that solid. This is the point at which both liquid and solid phase exists at equilibrium. The melting point of the substance also varies with pressure and is specified at standard pressure.

The melting point of a liquid is a characteristic property and can be treated as a criterion for the purity of a solid.  It increases with the increase in external pressure. Solids having greater intermolecular forces have high melting points.

Conductivity

Conductivity is the measure of a substance’s ability, or lack of ability, to conduct electricity or heat. Some matter has a high level of conductivity and other matter has a high level of resistance to the conduction of electricity.

Heat Capacity

Simply stated, heat capacity is the amount of heat that must be added or taken away from a substance to achieve a certain temperature. Heat capacity is also referred to as thermal capacity and the amount of heat that is added or taken away is measured in terms of joules per kelvin.

Deliquescence:

Deliquescence refers to the property of a substance to absorb water from the air to dissolve itself and form an aqueous solution. Materials showing deliquescence are termed deliquescent. In order to be deliquescent, a substance must both absorb a large amount of water and be sufficiently soluble to dissolve in it. Examples: Sodium hydroxide, potassium hydroxide, anhydrous potassium chloride, anhydrous magnesium chloride, anhydrous ferric chloride show deliquescence.

Hygroscopicity:

Hygroscopicity is the tendency of a solid substance to absorb moisture from the surrounding atmosphere and are converted into hydroxides or hydrates. Anhydrous copper sulphate, quick lime (CaO), anhydrous sodium carbonate, etc. are hygroscopic in nature.

Efflorescence:

Efflorescence is a spontaneous loss of water by a hydrated salt, which occurs when the aqueous vapor pressure of the hydrate is greater than the partial pressure of the water vapour in the air. Washing soda (Na₂CO₃·10H₂O), Glauber’s salt or sodium sulphate (Na₂SO₄·10H₂O), Ferrous sulphate (FeSO₄·7H₂O), potash alum (K₂SO₄· Al₂(SO₄)₃.24H₂O) show efflorescence.

Mechanical Properties of Substance:

Strength:

It is the property of a material which opposes the deformation or breakdown of material in presence of external forces or load. Engineering materials must have the suitable mechanical strength to be capable to work under different mechanical forces or loads. It is shown by solids.

Toughness:

Toughness is the ability of a material to absorb energy and gets plastically deformed without fracturing. For good toughness, materials should have good strength as well as ductility. To be tough, the material should be capable to withstand both high stress and strain. It is shown by solids.

Elasticity:

Within elastic limit, the solid completely regains its original shape, size or volume after removal of deforming force, then the property is called elasticity. Steel, copper, aluminium show elastic behaviour.

Plasticity:

If a body is stressed beyond elastic limit, and it does not regain original shape, size, and volume after removal of deforming force, then the property is called plasticity. These substances can be given required shape very easily. Example: Plaster of paris

Hardness:

It is the ability of a material to resist permanent shape change due to external stress. There are various measures of hardness – Scratch Hardness, Indentation Hardness, and Rebound Hardness. Scratch Hardness is the ability of materials to oppose the scratches to the outer surface layer due to external force. It is shown by solids.

It is measured on Mohs’ scale. The Mohs’ scale of mineral hardness is a qualitative ordinal scale that characterizes the scratch resistance of different minerals through the ability of a harder material to scratch a softer material. It was created by the German geologist and mineralogist Friedrich Mohs in 1812.

On Moh’s scale hardness of a diamond is maximum (10) and that of talk is minimum (1). If a material can scratch topaz but can’t scratch corundum, then it possesses hardness equal to 8.

Brittleness:

The brittleness of a material indicates that how easily it gets fractured when it is subjected to a force or load. The solids of non-metal are generally brittle in nature. The brittleness of the material is temperature-dependent. Some metals which are ductile at normal temperature become brittle at low temperature. Hardness and brittleness are inverse properties. The harder the substance, the more brittle it is. It is shown by solids.

Malleability:

Malleability is a property of solid materials which indicates that how easily a material gets deformed under compressive stress. Malleability is often categorized by the ability of the material to be formed in the form of a thin sheet by hammering or rolling. This mechanical property is an aspect of the plasticity of the material. The malleability of material is temperature-dependent. With the rise in temperature, the malleability of material increases. This is the characteristic property of metals. Copper, aluminium, gold, silver show malleability. Gold is the most malleable metal.

Ductility:

Ductility is a property of a solid material indicates that how easily a material gets deformed under tensile stress. Ductility is often categorized by the ability of a material to get stretched into a wire by pulling or drawing. This mechanical property is also an aspect of the plasticity of material and is temperature-dependent. With the rise in temperature, the ductility of material increases. This is a characteristic property of metals. Copper, aluminium, gold, silver show ductility. Platinum is the most ductile metal.

Creep:

Creep is the property of a material that indicates the tendency of a material to move slowly and deform permanently under the influence of external mechanical stress. It results due to long time exposure to large external mechanical stress within the limit of yielding. Creep is more severe in materials that are subjected to heat for a long time.

Resilience:

Resilience is the ability of material to absorb the energy when it is deformed elastically by applying stress and release the energy when stress is removed. Proof resilience is defined as the maximum energy that can be absorbed without permanent deformation. The modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without permanent deformation.

Fatigue:

Fatigue is the weakening of a material caused by the repeated loading of the material. When a material is subjected to cyclic loading, and loading greater than a certain threshold value but much below the strength of the material (ultimate tensile strength limit or yield stress limit), microscopic cracks begin to form at grain boundaries and interfaces. Eventually, the crack reaches a critical size. This crack propagates suddenly and the structure gets fractured.

Chemical Properties of Substance:

Chemical properties are characteristics that can only be measured or observed as matter transforms into a particular type of matter. The tendency of matter to react chemically with other substances is known as reactivity.

Reactivity:

The tendency of matter to combine chemically with other substances is known as reactivity. Certain materials like chlorine, potassium, sodium, etc. are highly reactive, whereas others like gold, platinum, etc. are extremely inactive.

Flammability:

The tendency of matter to burn is referred to as flammability. As matter burns, it reacts with oxygen and transforms into various substances. Example: wood, paper, etc. are flammable. Petrol, ethyl alcohol are highly flammable.

Toxicity:

Toxicity refers to the extent to which a chemical element or a combination of chemicals may harm an organism. Methyl alcohol, methyl isocyanate are highly toxic.

Reactivity with Acids and Bases:

A substance’s ability to react with an acid or a base is a chemical property.

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In this article, we shall study the factors affecting the rate of a chemical reaction and the Arrhenius equation.

Factors Affecting the Rate Of Reaction:

The Concentration of Reactants:

The number of collisions and hence the activated collisions between the reactant molecules increase with the increase in concentration. According to the collision theory, the rate of a reaction should increase with the increase in the concentration since the rate is directly proportional to the collision frequency.

Pressure:

The number of collisions increases with an increase in the partial pressures of gases. Hence the rate of a reaction involving gaseous reactants increases with an increase in partial pressures. However, it has no effect on reactions involving reactants in liquid or solid phases.

It is important to keep in mind that the partial pressures of reactants can be increased by increasing the pressure of the overall system. However, the partial pressures do not increase when an inert gas or a non-reacting gas is added to the reaction mixture at constant volume.

Temperature:

The average kinetic energy increases with increase in absolute temperature. Hence the number of molecules with energy greater than the threshold energy also increases.

As a result, the number of effective collisions between reactant molecules also increases. Therefore, usually, it is observed that the rate of reaction increases with increase in temperature.

Catalyst:

The catalyst is a substance which changes the rate of a reaction without being consumed or without undergoing any chemical change during the reaction.

In case of reversible reactions, the catalyst lowers the activation energies of both forward and backward reactions to the same extent and helps in attaining the equilibrium quickly.

Some substances may decrease the rate of a reaction. These are generally referred to as negative catalysts or inhibitors. They interfere with the reaction by forming relatively stable complexes, which require more energy to break up. Thus the speed of the reaction is reduced.

Nature of Reactants:

The rate of a reaction depends on the nature of bonding in the reactants. Usually, the ionic compounds react faster than covalent compounds.

The reactions between ionic compounds in water occur very fast as they involve the only exchange of ions, which were already separated in aqueous solutions during their dissolution.

Whereas, the reactions between covalent compounds take place slowly because they require energy for the cleavage of existing bonds.

The Orientation of Reacting Species:

The reaction between the reactants occurs only when they collide in the correct orientation in space. Greater the probability of collisions between the reactants with proper orientation, greater is the rate of reaction.

The orientation of molecules affects the probability factor, p. The simple molecules have more ways of proper orientations to collide. Hence their probability factor is higher than that of complex molecules.

The orientation factor also affects the interaction between reactants and catalysts. For example in case of biological reactions, which are catalyzed by enzymes, the biocatalysts. The enzymes activate the reactant molecules (or substrates) at a particular site on them. These sites are called active sites and have definite shape and size. The size, stereochemistry, and orientation of substrates must be such that they can fit into the active site of the enzyme. Then only the reaction will proceed. This is also known as lock and key mechanism. The enzymes lose their activity upon heating or changing the pH or adding certain chemical reagents. This is due to deformation of the configuration of the active site.

Surface Area of Reactant:

The rate of a reaction increases with increase in the surface area of solid reactant if any used. The surface of a solid can be increased by grinding it to a fine powder.

This is also true with the solid catalysts, which are usually employed in finely powdered form while carrying out a chemical reaction.

The Intensity of Light:

The rate of some photochemical reactions, which occur in presence of light, increases with increase in the intensity of suitable light used.

With the increase in the intensity, the number of photons in light also increases. Hence number of reactant molecules get energy by absorbing more number of photons and undergo a chemical change.

Nature of Solvent:

The solvent may affect the rate in many ways as explained below:

The solvents are used to dissolve the reactants and while doing so they help in providing more interactive surface between reactant molecules which may be otherwise in different phases or strongly bonded in the solid phase.

Usually, solvents help in breaking the cohesive forces between ions or molecules in the solid state. The polar molecules tend to dissolve more in polar solvents with more dielectric constants and react faster in them. Whereas nonpolar molecules prefer nonpolar solvents.

In case of diffusion controlled reactions, the viscosity of the solvent plays a major role. The rate decreases with increase in the viscosity of the solvent.

Effect of Change of Temperature on the Rate of Reaction:

The average kinetic energy increases with increase in absolute temperature. Hence the number of molecules with energy greater than the threshold energy also increases.

As a result, the number of effective collisions between reactant molecules also increases. Therefore, usually, it is observed that the rate of reaction increases with increase in temperature.

The two distribution graphs are shown below for a lower temperature T₁ and a higher temperature T₂. The area under each curve represents the total number of molecules whose energies fall within the particular range.

The shaded regions indicate the number of molecules which are sufficiently energetic to meet the requirements dictated by the two values of E_a that are shown.

It is clear from these graphs that the fraction of molecules whose kinetic energy exceeds the activation energy increases quite rapidly as the temperature is raised. This the reason that virtually all chemical reactions (and all elementary reactions) proceed more rapidly at higher temperatures.

Arrhenius Equation:

Arrhenius came up with an equation that demonstrated that rate constants of different kinds of chemical reactions varied with temperature. This equation indicates a rate constant that has a proportional relationship with temperature. For example, as the rate constant increases, the temperature of the chemical reaction generally also increases. The result is given below:

Where k is rate constant, Ea the activation energy, T the absolute temperature of the reaction and R is universal gas constant. A is called frequency factor or pre-exponential factor and proportional to the frequency of collisions between reacting molecules. A is independent of the absolute temperature T.

Equations (1), (2) and (3) are different forms of Arrhenius equation. A and Ea are called Arrhenius parameters.

Arrhenius Equation and Temperature Variation:

The relation between rate constant k and the absolute temperature T of the reaction is given by

For two different temperatures say T₁ and T₂ we have

Determination of Activation Energy:

We have

By knowing Values of K₁ and K₂ at temperatures T₁ and T₂ using experiments, the value of activation energy can be calculated.

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The occurrence of a bimolecular chemical reaction can be explained on the basis of collision theory.

The Collision of Reacting Molecules:

Consider a bimolecular general reaction

A  + B  →   C

In order for a chemical reaction to take place, the molecules of reactants A and B must collide. The rate of a chemical reaction depends on the rate of collision between the molecules. As the concentration and temperature increase, the rate of reaction also increases.

The Energy of Activation:

The collision between the molecules in a chemical reaction provides the kinetic energy needed to break the necessary bonds so that new bonds can be formed.  If the kinetic energy is not sufficient the bond between the reactants will not be broken and thus new bonds will not be formed. This required energy is called activation energy.

The activation energy (E_act) is defined as the minimum kinetic energy required for the molecular collision to lead to the reaction.

Thus reaction to take place the kinetic energy of colliding molecules should be greater than the activation energy.

The Orientation of Reacting Molecules:

The minimum kinetic energy (energy of activation) does not mean successful collision leading to the reaction.

For successful collision leading to the reaction, the colliding molecules must be so oriented relative to each other that the group reacting or bonds to be shifted are relatively close. This criterion is not essential for simple molecules but it becomes very much essential for complex molecules.

Potential Energy Barrier:

Consider a bimolecular general reaction

B  + AC   →   BA   +    C

During the collision the electron distribution about the three nuclei A, B and C changes in such a way that the new bond B-A strengthens at the same time the old bond A-C weakens. A stage is reached when all the three nuclei are weakly linked together. This state is called activated complex or transition state.

B   +   AC   →     B—-A —-C

The transition state is an unstable transitory complex of the highest energy state through which the reactants must pass on the way to products.  It decomposes spontaneously to form products.

To achieve this configuration, atoms require energy to overcome the repulsion between B and AC that have filled shells of electrons. This energy comes from kinetic energy due to the collision of reacting molecules and gets converted into potential energy in the activated complex. Thus transition state has the highest energy state. In an energy profile diagram (E.P.D.), the highest energy point (Peak) corresponds to the transition state.

Thus reactant molecules have to climb up the barrier to get converted into products.

Mathematical Treatment to Collision Theory:

Consider a bimolecular general reaction

B  + AC    →    BA   +    C

It is a second-order reaction. Hence the rate of collision is given by

Rate of collision = Z [AC] [B]

Where Z = frequency of collision.

The reaction rate is given by

Rate of reaction = P x f x Rate of collision

Where P is the fraction of collisions with proper orientations of colliding molecules. f is a fraction of molecules with sufficient kinetic energy.

Rate of reaction = P x f x Z [AC] [B]  …… (1)

Burt the rate of second-order reaction is given by

Rate of reaction = k [AC] [B] …… (2)

From (1) and (2) we have

k = P.f.Z

By Arrhenius equation we have

Where A = P.Z and called as frequency factor or pre-exponential factor.

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In this article, we shall study the molecularity of reaction and catalysis.

The Concept of Elementary Reactions:

Many reactions that follow a simple rate law are actually taking place in series of steps. These reactions are called complex reactions. Each step in a complex reaction is called elementary reaction. Thus complex reaction can be broken down into the elementary reactions.

An elementary reaction is defined as a reaction that takes place in a single step and can’t be broken down further into simplest chemical reactions.

Illustration:

Consider complex reaction

3 ClO^–_(aq)  →  ClO₃^–_(aq) + 2Cl^–_(aq)

Actually, this reaction takes place in two steps. Thus there are two elementary reactions.

Step-1:

2 ClO^–_(aq)  →  ClO₂^–_(aq) +  Cl^–_(aq)    (Bimolecular reaction)

Step – 2:

ClO₂^–_(aq)  +  ClO^–_(aq)  →  ClO₃^–_(aq) +  Cl^–_(aq)    (Bimolecular reaction)

The sum of the two reactions gives the overall reaction.

Molecularity of Elementary Reactions:

The molecularity of an elementary reaction is defined as the number of reaction molecules taking part in the reaction.

Example of Unimolecular Reaction:

O_3(g)  →  O_2(g) +  O_(g) 

C₂H₅I_(g)  →  C₂H_4(g) +  HI_(g) 

Example of Bimolecular Reaction:

O_3(g)  +  O_(g)  →  2O_2(g)

2NO_2(g)  → 2NO_(g)   +  O_2(g)

Distinguishing Between Molecularity and Order of Reaction:

Molecularity of a Reaction:

• The molecularity of a reaction is defined as the number of reaction molecules taking part in the reaction.
• Molecularity is always a whole number.
• It is a theoretical property indicating the number of molecules involved in each act leading to the reaction.
• It does not change with experimental conditions.
• It is the property of elementary reaction and has no meaning for a complex reaction.

Order of a Reaction:

• The overall order of the reaction is defined as the sum of the exponents to which the concentration terms in the rate law are raised.
• order of reaction may be an integer, fraction, or zero.
• It is a purely experimental property indicating the dependence of the observed reaction rate on the concentration of the reactants.
• It may change with experimental conditions.
• It is the property of both elementary and complex reactions.

Multistep Reactions:

A multistep reaction is a reaction involving two or more steps. Consider the reaction

A       →     C

It consists of two steps.

First step:         A    →    B

Second step:    B    →   C

In the above reaction, B is intermediate. The Intermediate is the product of the first step and reactant of the second step.

Reaction Intermediates:

The additional species other than the reactants or products formed in the mechanism during the progress of a reaction is called reaction intermediate.

Characteristics of Intermediate:

• They may be stable or unstable.
• The number of Intermediates in a reaction =  The number of Steps  –   1
• Thus reaction involving two steps will have one intermediate and one step reaction will have no intermediate.
• The intermediates appear in mechanism but do not appear in overall reaction because they are produced in one step and consumed in another step.
• The concentration of reaction intermediates is very small, hence cannot be determined easily.
• The rate of reaction is independent of the concentration of intermediates.
• The life period of reaction intermediates is very small hence they cannot be isolated.

Catalysis:

Catalyst and its Effect on the Rate of Reaction:

A catalyst is a substance, added to the reactants, that increases the rate of reaction without itself being consumed in the reaction

Example: In preparation of O₂ from KClO₃ in laboratories MnO₂ is used as a catalyst.

Characteristics of Catalyst:

• The catalyst does not appear in an overall reaction because they are consumed in one step and regenerated in another step.
• A catalyst lowers the activation energy of a reaction.
• In presence of a catalyst the height of the energy barrier decreases. Thus the number of molecules the possess the minimum kinetic energy increases.
• Chemically, the catalyst remains unchanged during a reaction.
• Catalyst does not change the quantity of the product.
• A catalyst is specific, which means different chemical reactions may have a different catalyst.
• Just a small amount needed to achieve a big increase in the rate of reaction.
• More amount of catalyst used can further increase the rate of reaction.
• A catalyst in powder form can further increase the rate of reaction.
• A catalyst may undergo a physical change in a reaction.

Distinguishing Between Catalyst and Reaction Intermediate:

Catalyst:

• A catalyst is a substance, added to the reactants, that increases the rate of the reaction without itself being consumed in the reaction.
• A catalyst increases the rate of a reaction.
• A catalyst is present at the start of the reaction.
• A catalyst is consumed in one step and regenerated in the subsequent step.
• The concentration of catalyst may appear in rate law.
• Catalysts are stable under ordinary conditions.

Intermediate:

• The additional species other than the reactants or products formed in the mechanism during the progress of a reaction is called reaction intermediate.
• Intermediate has no effect on the rate of reaction.
• An intermediate exist during the mechanism of the reaction.
• An intermediate is produced in one step and consumed in the subsequent step.
• The concentration of intermediate does not appear in rate law.
• Intermediates are highly unstable and ha a short life.

Note:

Both catalyst and intermediate do not appear in overall reaction.

Rate Determining Step (R.D.S.)

In a multistep reaction, rate of overall reaction depends upon the rate of the slowest step.  This slowest step is called rate determining step.

Example : Consider substitution reaction

R-X       +      Y        →      R-Y     +      X

Substrate   Reagent       Product    Living group

This reaction takes place as  follows

First Step:

R – X   →   R⁺  +     : X^–

Second Step:

R⁺  +   : Y^–  →   R  Y

In above case rate of overall reaction depends on the rate of the first step. Hence the first step is labelled as R.D.S.

The overall reaction cannot take place faster than the rate of rate determining step. Hence RDS step determines rate of overall reaction. As RDS is elementary reaction, the rate law can be determined from its stoichiometric equation. In rate law the exponents are equal to the coefficient of balanced equation for the step.

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In this article, we shall study the analytical treatment to the zero-order reaction, and the rate of zero-order reaction.

Order of Reaction:

The overall order of the reaction is defined as the sum of the exponents to which the concentration terms in the rate law are raised.

Let us consider a general reaction

aA  + bB  → Products

The rate law can be written as

Rate = K  [A]^x [B]^y …………… (1)

Thus the overall order of the reaction is (x + y).

Zero Order Reaction:

Integrated Law for Zero-Order Reaction:

A reaction whose rate is independent of the concentration of reactants is called a zero-order reaction.

Let us consider a general reaction

Let [A]_o be initial concentration of A (i.e at t = 0)  and be final concentration of A (i.e at t = t)

Integrating both sides of above equation

This relation is known as integrated law for zero-order reaction.

Expression for the Integrated Rate Constant:

From equation (1) we have

This is an expression of the integrated rate constant for the zero-order reaction.

Unit of Integrated Rate Constant:

The unit of  integrated rate constant is  mol dm^-3 t^-1 ( mol dm^-3 s^-1 or  mol dm^-3 min^-1,  mol dm^-3hr^-1)

Half-Life of Zero Order Reaction:

The half-life of a reaction is defined as the time required for the reactant concentration to fall to one half of its initial value. Thus for t = t_1/2,   [A]_t  = ½[A]_o

The  integrated rate constant for the zero-order reaction is given by

This is an expression of the half-life of a zero-order reaction.

Graphical Representation of Zero Order Reaction in Different Ways:

The graph of rate of reaction against time:     

The differential rate law for the zero-order reaction is

Thus the graph of the rate of reaction versus time is a straight line parallel to the time axis.

The graph of Rate of reaction against Initial Concentration:  

The differential rate law for the zero-order reaction is

Thus the rate is independent of the concentration of reactants. Hence Thus the graph of the rate of reaction versus concentration of reactants is a straight line parallel to concentration axis.

The graph of Concentration of the reactants against time:

The differential rate law for the zero order reaction is

[A]_t  = – kt + [A]_o

It is of the form y = mx + c. Thus the graph of concentration at instant versus time is a straight line with y-intercept. [A]_o. The slope of the straight line is – k.

Examples of Zero-order Reaction

• Decomposition of NH₃ on a hot platinum surface:

• Decomposition of Nitrous oxide in presence of platinum as a catalyst:

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In this article, we shall study the order of reaction and the analytical treatment to the first-order reaction, and the rate of the first-order reaction.

Order of Reaction:

The overall order of the reaction is defined as the sum of the exponents to which the concentration terms in the rate law are raised.

Let us consider a general reaction

aA  + bB  → Products

The rate law can be written as

Rate = K  [A]^x [B]^y …………… (1)

Thus the overall order of reaction is (x + y).

Example:

In the reaction, 

NO_2(g)   +   CO_(g)  →  NO_(g)   + CO_2(g)

The rate of reaction is experimentally found to proportional

to [NO₂]² and independent of [CO]. Thus x = 2 and y = 0

Thus the rate law of reaction is

Thus the overall order of the reaction is 2.

Characteristics of Order of Reaction:

• Order of reaction represents the number of atoms, ions and molecules whose concentration influence the rate of reaction.
• Order of the reaction is defined as the sum of the exponents to which the concentration terms in the rate law are raised. Thus it is not dependent on the stoichiometric coefficients in a balanced chemical reaction.
• Values of x and y are determined experimentally. The values of x and y in the rate law are not necessarily equal to the stoichiometric coefficients of reactants. Thus the order of reaction can be decided by performing experiment only.
• Order of reaction is defined in terms of concentration of reactants only and not of products.
• Order of reaction may be integer, fraction or zero.

Reactions with No Order:

If the rate of reaction cannot be expressed in the form, Rate, then the reaction has no order and term order should not be used for such reactions.

Example:

Clear Concept of Stoichiometric Coefficients of Balanced Chemical Equations and Exponents in Rate Law:

Let us consider a general reaction

aA  + bB  → Products

The stoichiometric coefficients of A and B are a and b.

Let us assume that the rate of reaction depends on [A]^x and [B]^y

The rate law is written as

Rate = K  [A]^x [B]^y …………… (1)

The values of x and y for the reaction are found experimentally. The values of x and y may be integer, fraction or zero.

First Order Reactions:

Integrated Rate Law For First Order Reaction:

The equations which are obtained by integrating the differential rate laws and which gives the direct relationship between the concentrations of the reactants and time is called integrated rate laws. A reaction whose rate depends on the single reactant concentration is called the first-order reaction.

Let us consider a general reaction

Let [A]_o be initial concentration of A (i.e at t = 0)  and [A]_t be the final concentration of A (i.e at t = t)

Integrating both sides of above equation

This relation is known as exponential integrated law for first order reaction.

The Expression for the Integrated Rate Constant for First Order Reaction:

This is an expression for the integrated rate constant for the first order reaction.

The expression for the integrated rate constant in terms of initial concentration for First Order Reaction:

Let a mol dm^-3 be the initial concentration of A (i.e at t = 0) and at some instant ‘t’ the decrease in concentration is x mol dm^-3.  (i.e at t = t). Thus   [A]_o = a and  [A] = a – x

Substituting in equation (2) we have

This is an expression for the integrated rate constant for the first order reaction in terms of initial concentration.

Unit of  the Integrated Rate Constant for the First Order Reaction:

The integrated rate constant for the first order reaction is given by

The quantity [A]_o / [A]  is a pure ratio. Hence it has no unit. Thus the unit of  integrated rate constant is per unit time (s^-1 or  min^-1 , hr^-1 )

Half-Life of First Order Reaction:

The half-life of a reaction is defined as the time required for the reactant concentration to fall to one half of its initial value. Thus for t = t1/2,  [A] = ½ [A]_o

The  integrated rate constant for the first order reaction is given by

This is an expression for the half-life of the first-order reaction.

Graphical Representation of Half-Life:

A graph is drawn by plotting time as a multiple of half-life on the x-axis and the concentration of reactant in terms of original concentration on the y-axis at that instant. The graph is as follows.

The graph shows that it is an exponential process. Thus this process will never complete. i.e. the graph will never touch x-axis.

Note: Such graph is shown by the disintegration of a radioactive element. The radioactive elements obey decay law.

Graphical Representation of the First Order Reaction in Different Ways:

The graph of Rate of reaction against time:     

The differential rate law for the first order reaction is

It is of the form y = mx + c. Thus the graph of rate reaction versus concentration at an instant  is a straight line passing through the origin (since c = 0). The slope of the straight line is k.

The graph of Concentration of the reactants of against time:

The exponential rate law for the first order reaction is [A]_t = [A]_o e^-kt

Thus it is an exponential process. Thus this process will never complete. i.e. the graph will never touch x-axis.

The graph of Concentration of the reactants against time:

This equation is of form y = mx + c. Thus the graph of  log₁₀[A]_t  versus time is a straight line with y-intercept log₁₀[A]₀.

The graph of log₁₀([A]₀/ [A]_t) against time:

This equation is of form y = mx + c. Where c = 0. Thus the graph of  log₁₀([A]₀/ [A]_t) versus time is  a straight line passing through the origin

Examples of First-order Reactions:

Pseudo First Order Reaction:

The reactions that have higher order true rate law are found to behave as the first order are called pseudo-first order reactions.

Examples of Pseudo First Order Reactions:

• Hydrolysis of methyl acetate:

CH₃COOCH_3(aq)  + H₂O_(l) → CH₃COOH_(aq)) + CH₃OH_(aq)

The true rate law of reaction must be

Rate = K'[CH₃COOCH₃][H₂O]

Thus it seems that the rate of reaction is dependent on two reactants.

But the concentration [H₂O]  is constant (say k’’)

Rate = K’ K”[CH₃COOCH₃]

Hence,  Rate = K[CH₃COOCH₃]

Thus the reaction actually a first order reaction. Hence it is called as pseudo first order reaction.

• Hydrolysis of cane sugar (sucrose):

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In this article, we shall discuss the concept of chemical kinetics, rate of reactions, and types of reactions on the basis of their rates.

Rate of Reaction:

The branch of chemistry, which deals with the rate of chemical reactions, the factors affecting the rate of reactions and the mechanism of the reaction. is called chemical kinetics.

Importance of Chemical Kinetics:

• It gives an idea that how fast a reaction can occur. using which we know how quickly a medicine is able to work or what is the time required for completion of the reaction.
• In environmental chemistry, it is important to study the ozone balance in the upper atmosphere. The maintenance and depletion of the ozone layer depend on the relative rate of formation and destruction of ozone in the upper atmosphere.
• It is important in catalysis. It is used to solve industrial problems such as the development of catalysts to synthesize new materials.
• It has biological importance. In our body, large protein molecules called enzymes, increase the rate of biological reactions.
• It is important in the food industry. It is used to determine the factors which spoil the food and the rate at which the food is getting spoilt. Hence the probable expiry date or best before the date can be determined.
• The fast setting ceramic material is used for the material for dental fillings.
• It is used to determine the rate at which steel rusts.
• It is used to study the rate at which fuel burns in an automobile engine.

Classification of Chemical Reactions on the Basis of the Rate of the Reaction:

Fast/Instantaneous Reactions (Type – I):

The chemical reaction which completes in less than 1ps (one pieco second) (10^-12 s) time, is known as the fast reaction. It is practically impossible to measure the speed of such reactions. The reason for a very fast rate of such reaction is that no chemical bonds are to be broken among the reactants.

e.g., ionic reactions. Organic substitution reactions, neutralization reaction.

Very Slow Reactions (Type – II):

Chemical reactions which complete in a long time from some minutes to some years are called slow reactions. The rates of such reactions are hardly of any physical importance.

e.g. rusting of iron, transformation of carbon into diamond etc.

Moderately Slow Reactions:

Chemical reactions which are intermediate between slow and fast reactions are called moderately slow reactions.

These reactions proceed at a moderate speed which can be measured easily. Mostly these reactions are in molecular nature.

Note:

The rate of chemical reaction can be changed by changing the conditions under which they occur.

Rate of a Reaction:

The rate of a chemical reaction may be defined as the change in concentration of designated species (reactant or product) per unit time. The rate can be measured qualitatively or quantitatively.

Qualitative Rate: The qualitative rate is based on certain visual parameters such as disappearance of reactants, colour change, effervescence etc.

Quantitative Rate: The quantitative rate is based on the rate of decrease in the concentration of any one reactant or the rate of increase in the concentration of any one product.

Average Rate of Reaction:

The average rate of reaction is defined as the change in concentration of reactant or product divided by the time interval over which the change occurs.

Consider a general reaction

Positive sign indicates that the concentration of B is increasing. It is to be noted that the rate of reaction is always positive.

The rate of reaction is expressed in terms of moles per litre per unit time (mol L^-1t^-1) or molar per unit time (Mt^-1). If time is measured in a second then the unit is moles per litre per second (mol L^-1s^-1) or molar per second (Ms^-1). In terms of partial pressure (for gaseous reactions) units is atmosphere per unit time. The average rate of reaction depends on the time interval chosen.

Average Rates of Some Reactions:

Example – 1:

In this case, stoichiometric coefficients of the reactants and products are same, the rate of the reaction is

Example – 2:

In this case, stoichiometric coefficients of H₂, N₂ and NH₃ are  1, 3 and 2 respectively. Hence the rate of the reaction is

Example – 3:

In this case, stoichiometric coefficients of N₂O₅, NO₂ and O₂ are  2, 4 and 1 respectively. Hence the rate of the reaction is

General Example:

aA  + bB  → cC   +   dD

In this case, stoichiometric coefficients of A, B, C and D are a, b, c and d respectively. Hence the rate of the reaction is

Instantaneous of Rate of a Reaction:

The rate of a reaction at a specific instant is called an instantaneous rate.

If the average rate of reaction is calculated for a shorter and shorter interval of time, a rate at a specific instant can be obtained. The instantaneous rate at the beginning of a reaction is called the initial rate of the reaction.

Consider a general reaction

Example – 1:

In this case, stoichiometric coefficients of H₂, N₂ and NH₃ are  1, 3 and 2 respectively. Hence the rate of the reaction is

General Example:

aA  + bB  → cC   +   dD

In this case, stoichiometric coefficients of A, B, C and D are a, b, c and d respectively. Hence the rate of the reaction is

Note:

In chemical kinetics, we deal only with the instantaneous rate of reaction only. Hence the instantaneous rate of reaction is referred as the rate of reaction only.

Graphical Representation of Instantaneous and Average Rate of Reaction in terms of Reactants:

Graphical Representation of Instantaneous and Average Rate of Reaction in terms of Products:

Determination of Rate of Reaction:

Determination of Average Rate of Reaction:

A graph is drawn by taking a concentration of species (reactant or product) on y-axis and time on the x-axis.

The average rate of reaction at time t can be obtained by the change in concentration (C₂ – C₁) of species (reactant or product) in the time interval t1 and t2. (t1 and t2 are equidistant from t) Then the average rate of reaction is calculated using following formula.

Determination of Instantaneous Rate of Reaction:

A graph is drawn by taking the concentration of species (reactant or product) on y-axis and time on the x-axis.

The instantaneous rate of reaction at time t can be obtained by drawing a tangent at time t and finding its slope at that point. The slope of the tangent to the curve at that point gives an instantaneous rate of reaction.

Reaction Life Time:

It is defined as the time taken by a reaction to proceed to 98% of completion. Shorter the life time, faster is the reaction. It is used to compare the rate of reactions.

Rate Laws and Rate Constant:

Law of Mass Action:

This law was given by Goldberg and Waage in 1864. It states that “at a given temperature, the rate of reaction at a particular instant is proportional to the product of the active masses of the reactants at that instant raised to powers which are numerically equal to the numbers of their respective molecules in the stoichiometric equation describing the reaction.”

Explanation:

Consider general reaction

aA  + bB  → cC  +  dD

By law of mass action

Rate ∝  [A]^a [B]^b

∴   Rate = K  [A]^a [B]^b

Rate Law:

The rate of chemical reaction is found to be proportional to the molar concentrations of the reactants raised to simple powers.

Let us consider a general reaction

aA  + bB  → Products

Let us assume the rate of reaction depends on[A]^x and [B]^y.

Thus, Rate ∝  [A]^x [B]^y

Rate = K  [A]^x [B]^y …………… (1)

But instantaneous rate of reaction is given by

This relation is known as the differential rate law or simply rate law. Where k is a constant called specific reaction rate constant or simply rate constant.

Definition:

The rate law is defined as an experimentally determined equation that expresses the rate of a chemical reaction in terms of molar concentrations of the reactants.

Rate Constant:

By rate law we have,  Rate = K  [A]^x [B]^y

If [A] = 1 and [B] = 1, Then

Rate = k = Rate Constant

The rate constant is defined as the rate of reaction would have if all the concentrations were set equal to unity.

Characteristics of Rate Constant:

• The values of the rate constant give an idea about the speed of the reaction. Greater the value of the rate constant, faster is the reaction.
• Each reaction has a definite value of the rate constant at a particular temperature.
• The value of the rate constant depends on temperature.
• The value of rate constant is independent of the concentration of reacting species.
• The value of rate constant depends on nature of reactant, the presence of catalyst, solvent and pH of a solution.
• The unit of rate constant depends on the order of the reaction. In general unit of rate constant is

Where n is the order of reaction.

Notes:

• The value of x and y in the rate law are not necessarily equal to the stoichiometric coefficients (a and b) of  A and B.
• Values of x and y are determined experimentally.

Example to Illustrate Rate Law:

Example:

In the reaction, NO_2(g)   +   CO_(g)  →  NO_(g)   + CO_2(g)

The rate of reaction is experimentally found to proportional

to [NO₂]² and independent of [CO]. Thus x = 2 and y = 0

Thus the rate law of reaction is

Applications of Rate Law:

• The rate law can be used to estimate the rate of a reaction for any given composition of the reaction mixture.
• It can be used to estimate the concentration of reactants and products at any time during the course of reaction.\
• The rate law is useful for prediction of the mechanism of a complex reaction.

Characteristics of Rate of Reaction:

• It is the speed at which the reactants are converted into products at any instant of time.
• It is dependent on the concentrations of the reactant species at that instant.
• As the reaction proceeds the rate of reaction decreases.

Characteristics of Rate Constant:

• It is constant of proportionality in rate law expression.
• It is independent of the concentration of reactants.
• It is constant throughout the reaction i.e. it is independent of the progress of the reaction.

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