What per cent of a sample of nitrogen must be allowed to escape if its temperature, pressure and volume are to be changed as given?

$$\begin{gathered} \frac{{\mathrm{p}}_1{\mathrm{V}}_1}{{\mathrm{T}}_1}=\frac{3\times 1.65}{546}=9.066\times {10}^{-3} \\ \frac{{\mathrm{p}}_2{\mathrm{V}}_2}{{\mathrm{T}}_2}=\frac{0.75\times 0.55}{273}=1.51\times {10}^{-3}<\frac{{\mathrm{p}}_1{\mathrm{V}}_1}{{\mathrm{T}}_1} \\ \text{ Hence, }{\mathrm{N}}_2\text{ gas in LHS should escape to make }\frac{{\mathrm{p}}_1{\mathrm{v}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{p}}_2{\mathrm{v}}_2}{{\mathrm{T}}_2}\text{. } \\ \therefore {\mathrm{V}}_1=\frac{{\mathrm{p}}_2{\mathrm{V}}_2\times {\mathrm{T}}_1}{{\mathrm{T}}_2\times {\mathrm{P}}_1}=\frac{0.75\times 0.55\times 546}{273\times 3}=0.275\mathrm{L} \\ \text{ Volume of }{\mathrm{N}}_2\text{ escaped }=1.65-0.275=1.375\mathrm{L} \\ \text{ Hence, fraction of }{\mathrm{N}}_2\text{ escaped }=\frac{1.375}{1.65}=0.8333 \end{gathered}$$