$(i)$ 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 $NH_3$. Will the answer change if the temperature and pressure are changed?

$(i)$ Number of electrons in $1$ molecule of methane $(CH_4) = 6 + 4(1) = 10$.
Number of electrons in $1$ mole $(6.022 \times 10^{23} \text{ molecules}) = 6.022 \times 10^{23} \times 10 = 6.022 \times 10^{24}$.
$(ii)$ $(a)$ $1$ atom of $^{14}C$ contains $(14 - 6) = 8$ neutrons.
Number of neutrons in $14 \, g$ of $^{14}C = 6.022 \times 10^{23} \times 8$.
Number of neutrons in $7 \, mg$ $(0.007 \, g) = \frac{6.022 \times 10^{23} \times 8 \times 0.007}{14} = 2.4088 \times 10^{21}$.
$(b)$ Mass of neutrons $= (2.4088 \times 10^{21}) \times (1.675 \times 10^{-27} \, kg) = 4.0347 \times 10^{-6} \, kg$.
$(iii)$ $(a)$ $1$ mole of $NH_3 = 17 \, g = 6.022 \times 10^{23}$ molecules.
Protons in $1$ molecule of $NH_3 = 7 + 3(1) = 10$.
Number of protons in $34 \, mg$ $(0.034 \, g) = \frac{6.022 \times 10^{23} \times 10 \times 0.034}{17} = 1.2044 \times 10^{22}$.
$(b)$ Mass of protons $= (1.2044 \times 10^{22}) \times (1.6726 \times 10^{-27} \, kg) \approx 2.0145 \times 10^{-5} \, kg$.
The number of subatomic particles is independent of temperature and pressure; hence,the values remain unchanged.