Equal masses in grams of $\mathrm{H}_2, \mathrm{~N}_2, \mathrm{Cl}_2$, and $\mathrm{O}_2$, are enclosed in…
Equal masses in grams of $\mathrm{H}_2, \mathrm{~N}_2, \mathrm{Cl}_2$, and $\mathrm{O}_2$, are enclosed in cylinders separately. If these gases expand isothermally and reversibly by $10 \mathrm{dm}^3$ at $300 \mathrm{~K}$, the work done by gas is maximum for
$\mathrm{H}_2$
$\mathrm{N}_2$
$\mathrm{Cl}_2$
$\mathrm{O}_2$
Solution
$\mathrm{W}_{\max }=-2.303 \mathrm{nRT} \log _{10} \frac{\mathrm{V}_2}{\mathrm{~V}_1}$
Hence, $\mathrm{W}_{\max } \infty \mathrm{n}$ (Given: R, T, $\mathrm{V}_2, \mathrm{~V}_1=$ Constant)
$\therefore \quad \mathrm{W}_{\max } \propto \frac{1}{\mathrm{M} . \mathrm{W} .}$ (Given: equal mass)
Hence, lower the molecular mass, greater is the work done. Among the given, $\mathrm{H}_2$ has the lowest molecular mass.