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 ${}^{14}C$.
(Assume that mass of a neutron =$1.675\times {10}^{-27}kg$).

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

Answer 1

(i) Total number of electrons present in 1 methane molecule $=6+4=10$.

Total number of electrons resent in 1 mole of methane $=10\times 6.023\times {10}^{23}=6.023\times {10}^{24}$ electrons.

The number of neutrons is equal to the difference in the mass number and atomic number.
It is equal to $\d

isplaystyle 14-6=8 $.

(ii)(a) The number of neutrons present in 7 mg of C-14 is
$\frac{6.023\times {10}^{23}\times 8}{14}\times 7\times {10}^{10-3}=2.4088\times {10}^{21}$ neutrons.

(b) Total mass of neutrons in 7 mg of C-14 is $2.4088\times {10}^{21}\times 1.675\times {10}^{-27}4.035\times {10}^{-6}$ kg.

(iii)(a)Number of protons present in 1 molecule of ammonia $=7+3=10$.

Number of molecules present in 34 mg of ammonia is $\frac{6.023\times {10}^{23}\times 34\times {10}^{-3}}{17}=1.2044\times {10}^{21}$.

Total number of protons present in 34 mg of ammonia$=10\times 1.2044\times {10}^{21}=1.2044\times {10}^{22}$

(b) Total mass of protons present in 34 mg of ammonia at STP is $1.6726\times {10}^{-27}\times 1.204\times {10}^{22}=2.0138\times {10}^{-5}$ kg.

When temperature and pressure are changed, there is no difference in the answer.