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

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