Question

100 mL of a gas at NTP was heated with tin. Tin got converted into stannous sulphide and hydrogen was left. This hydrogen when passed over hot CuO produced 0.081 g water. If the vapor density of the gas is 17, then the number of atoms it contains in its formula is:

Answer 1

Hint: Here, first we have to write the given reaction taking atoms of hydrogen and sulphur as a and b respectively. Then, we have to calculate the value of a (hydrogen atoms in the gas) and then using the formula of ${\rm{Vapor}}\;{\rm{density}} = 2 \times {\rm{molar}}\,{\rm{mass}}$, we have to calculate the b (sulphur atoms in the gas).

Complete step by step answer:
Given that, at NTP 100 mL of a gas was heated with tin. In this reaction tin converted to stannous sulphide and hydrogen was left. On passing the hydrogen over hot CuO, 0.081 g water was produced.

As the reaction of the gas with tin produces stannous sulphur and hydrogen, the gas must contain hydrogen and sulphur. Let’s take the number of hydrogen atoms in the gas as a and the number of sulphur atoms in the gas is b. So, the chemical reaction for the given reaction is,
$H_{a}S_{b}+bSn\rightarrow bSnS+\frac{a}{2}H_{2}\overset{CuO}{\rightarrow}\dfrac{a}{2}H_{2}O$
So, the above reaction indicates that moles of hydrogen formed are equal to moles of water.
Therefore, ${\rm{Moles}}\,{\rm{of}}\,{{\rm{H}}_a}{{\rm{S}}_b} = \dfrac{a}{2}{\rm{moles}}\,{\rm{of}}\,{{\rm{H}}_{\rm{2}}} = \dfrac{a}{2}{\rm{moles}}\,{\rm{of}}\,{{\rm{H}}_{\rm{2}}}{\rm{O}}$
Therefore,
$\dfrac{{100}}{{22400}} = \dfrac{a}{2} \times \dfrac{{0.081}}{{18}}$

$ \Rightarrow a = 1.98 \approx 2$
So, the number of hydrogen atoms in the gas is 2
Now, we have to calculate the molar mass of the using the formula,
Molar mass=vapor density$ \times $2
The vapour density of the gas is 17.
${\rm{Vapor}}\;{\rm{density}} \times 2 = {\rm{Molar}}\,{\rm{mass}}\,{\rm{of}}\,{{\rm{H}}_{\rm{2}}}{{\rm{S}}_b}$
$ \Rightarrow 17 \times 2 = 2 \times 1 + b \times 32$
$ \Rightarrow 34 - 2 = 32b$

$ \Rightarrow b = 1$
So, the number of hydrogen atoms in the gas is 1. Therefore, the formula of the gas is ${{\rm{H}}_{\rm{2}}}{\rm{S}}$.

Note:
Vapor density of a vapor or gas is defined as the number of times a given volume of gas is heavier than the same volume of hydrogen measured as weighed under the same pressure and temperature.