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