Calculate the total number of electrons present in one mole of methane.

(i) Calculate the total number of electrons present in one mole of methane.
(ii) Find (a) the total number and (b) the total mass of neutrons in 7 mg of ¹⁴C. (Assume that mass of a neutron = 1.675 × 10^-27 kg).
(iii) Find (a) the total number and (b) the total mass of protons in 34 mg of NH₃ at STP.
Will the answer change if the temperature and pressure are changed?
Answer
(i) Number of electrons present in 1 molecule of methane (CH₄) {1(6) + 4(1)} = 10
Number of electrons present in 1 mole i.e., 6.023 × 10²³
molecules of methane = 6.022 × 10²³ × 10 = 6.022 × 10²⁴
(ii) (a) Number of atoms of ¹⁴C in 1 mole= 6.023 × 10²³
Since 1 atom of¹⁴C contains (14 - 6) i.e., 8 neutrons, the number of neutrons in 14 g of¹⁴C
 is (6.023 × 10²³) ×8. Or, 14 g of¹⁴C contains (6.022 × 10²³× 8) neutrons
Number of neutrons in 7 mg

= 2.4092 × 10²¹
(b) Mass of one neutron = 1.67493 × 10^-27 kg Mass of total neutrons in 7 g of ¹⁴C
= (2.4092 × 10²¹) (1.67493 × 10^-27 kg)
= 4.0352 × 10^-6 kg
(iii) (a) 1 mole of NH₃ = {1(14) + 3(1)} g of NH₃ = 17 g of NH₃
= 6.022× 10²³ molecules of NH₃
Total number of protons present in 1 molecule of NH₃ = {1(7) + 3(1)}
= 10
Number of protons in 6.023 × 10²³ molecules of NH₃ = (6.023 × 10²³) (10)

= 6.023 × 10²⁴
⇒ 17 g of NH₃ contains (6.023 × 10²⁴) protons.
Number of protons in 34 mg of NH3= 1.2046 × 10²²
(b) Mass of one proton = 1.67493 × 10^-27 kg Total mass of protons in 34 mg of NH ₃
= (1.67493 × 10^-27 kg) (1.2046 × 10²²)
= 2.0176 × 10^-5 kg
The number of protons, electrons, and neutrons in an atom is independent of temperature and pressure conditions. Hence, the obtained values will remain unchanged if the temperature and pressure is changed.