We have a sample of gas characterised by $\mathrm{P}, \mathrm{V}$ and $\mathrm{T}$ and another sample of gas…

We have a sample of gas characterised by $\mathrm{P}, \mathrm{V}$ and $\mathrm{T}$ and another sample of gas characterised by $2 \mathrm{P}, \mathrm{V} / 4$, and $2 \mathrm{~T}$. What is the ratio of the number of molecules in the first and second samples?
  1. $2: 1$
  2. $4: 1$
  3. $8: 1$
  4. $16: 1$

Solution

$\begin{array}{ll}\text { PVT } & 2 \mathrm{P}, \mathrm{V} / 4,2 \mathrm{~T}\end{array}$ $\mathrm{P}_{1} \mathrm{V}_{1}=\mathrm{n}_{1} \mathrm{RT}_{1} ; \quad \mathrm{P}_{2} \mathrm{V}_{2}=\mathrm{n}_{2} \mathrm{RT}_{2}$ $\frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\frac{\mathrm{P}_{1} \mathrm{V}_{1} / \mathrm{RT}_{1}}{\mathrm{P}_{2} \mathrm{V}_{2} / \mathrm{RT}_{2}}=\frac{\mathrm{P}_{1} \mathrm{V}_{1}}{\mathrm{T}_{1}} \times \frac{\mathrm{T}_{2}}{\mathrm{P}_{2} \mathrm{V}_{2}}$ $=\frac{\mathrm{PV}}{\mathrm{T}} \times \frac{2 \mathrm{T} \times 2}{2 \mathrm{P} \times \frac{\mathrm{V}}{4}}=4: 1$ ~

Asked in: MHT CET 2020 (20 Oct Shift 2)

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