Question

(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 the 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 1

(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 of 14C contains i.e., 8 neutrons, the number of neutrons in 14 g of 14C is (6.023 × 10²³) ×8. Or, 14 g of 14C contains (6.022 × 10²³ × 8) neutrons.
Number of neutrons in 7 mg
=\(\frac{6.022\times 10^{23}\times8\times 7\,mg}{1400\,mg}\)= 2.4092 × 10²¹
(b) Mass of one neutron = 1.67493 × 10²⁷ kg
Mass of total neutrons in 7 g of 14C
= (2.4092 × 10²¹) (1.67493 × 10²⁷ kg) = 4.0352 × 10⁶ 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 = \(\frac{6.022\times 10^{23}\times8\times 7\,mg}{17000\,mg}\) = 1.2046 × 10²²
(b) Mass of one proton = 1.67493 × 10²⁷ kg
The total mass of protons in 34 mg of NH₃ = (1.67493 × 10²⁷ kg) (1.2046 × 10²² ) = 2.0176 × 10⁵ 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 are changed.