Q14 / 120 · VITEEE 2019 · Chemistry
At low pressure, the van der Waal's equation is reduced to
- Correct answerA$\mathrm{Z}=\frac{\mathrm{PV}_{\mathrm{m}}}{\mathrm{RT}}=1-\frac{\mathrm{a}}{\mathrm{VRT}}$
- B$\quad \mathrm{Z}=\frac{\mathrm{PV}_{\mathrm{m}}}{\mathrm{RT}}=1+\frac{\mathrm{b}}{\mathrm{RT}} \mathrm{P}$
- C$\quad \mathrm{PV}_{\mathrm{m}}=\mathrm{RT}$
- D$\quad \mathrm{Z}=\frac{\mathrm{PV}_{\mathrm{m}}}{\mathrm{RT}}=1-\frac{\mathrm{a}}{\mathrm{RT}}$
Solution
When pressure is low
$$
\left[\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^{2}}\right](\mathrm{V}-\mathrm{b})=\mathrm{RT}
$$
or $\quad \mathrm{PV}=\mathrm{RT}+\mathrm{Pb}-\frac{\mathrm{a}}{\mathrm{V}}+\frac{\mathrm{ab}}{\mathrm{V}^{2}}$
or $\frac{\mathrm{PV}}{\mathrm{RT}}=1-\frac{\mathrm{a}}{\mathrm{VRT}}$
$$
\begin{array}{l}
\mathrm{Z}=-\frac{\mathrm{a}}{\mathrm{VRT}} \\
\left(\because \frac{\mathrm{PV}}{\mathrm{RT}}=\mathrm{Z}\right)
\end{array}
$$
Hence, the correct answer is option: 'A'.