Question

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

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).

Find (a) the total number and (b) the total mass of protons in 34 mg of $N{H}_3$ at STP. Will the answer change if the temperature and pressure are changed?

Answer 1

Number of electrons present in 1 molecule of methane (C$H_4$)
{1(6) + 4(1)} = 10
Number of electrons present in 1 mole i.e., 6.023 × ${10}^{23}$ molecules of methane
= 6.022 × ${10}^{23}$ × 10 = 6.022 × ${10}^{24}$

(a) Number of atoms of 14C in 1 mole= 6.023 × ${10}^{23}$
Since 1 atom of 14C contains (14 – 6) i.e., 8 neutrons, the number of neutrons in 14 g of 14C is (6.023 × ${10}^{23}$ ) ×8. Or, 14 g of 14C contains (6.022 × ${10}^{23}$ × 8) neutrons.
Number of neutrons in 7 mg
$=\frac{6.022\times {10}^{23}\times 8\times 7mg}{1400mg}=2.4092\times {10}^{21}$
(b) Mass of one neutron = 1.67493 × ${10}^{–27}$ kg
Mass of total neutrons in 7 g of 14C
= (2.4092 × ${10}^{21}$ ) (1.67493 × ${10}^{–27}$ kg) = 4.0352 × ${10}^{–6}$ kg

(a) 1 mole of $N{H}_3$ = {1(14) + 3(1)} g of $N{H}_3$
= 17 g of $N{H}_3$
= 6.022× ${10}^{23}$ molecules of $N{H}_3$
Total number of protons present in 1 molecule of $N{H}_3$
= {1(7) + 3(1)}
= 10
Number of protons in 6.023 × ${10}^{23}$ molecules of $N{H}_3$
= (6.023 × ${10}^{23}$ ) (10)
= 6.023 × ${10}^{24}$
⇒ 17 g of $N{H}_3$ contains (6.023 × ${10}^{24}$ ) protons. Number of protons in 34 mg of $N{H}_3$
$=\frac{6022\times {10}^{24}\times 34mg}{17000mg}=1.2046\times {10}^{22}$
(b) Mass of one proton = 1.67493 × ${10}^{–27}$ kg
Total mass of protons in 34 mg of $N{H}_3$
= (1.67493 × ${10}^{–27}$ kg) (1.2046 × ${10}^{22}$ )
= 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.