Expansion of 1 mole of ideal gas is taking place from 2 litre to … - Vidyadip

MCQ

Expansion of $1$ $mole$ of ideal gas is taking place from $2$ $litre$ to $8$ $litre$ at $300\,K$ against $1$ $atm$ pressure. Calculate $\Delta {S_{total}}$ in $J\,K^{-1}\,mol^{-1}$

(given $R = \frac{{8.3\,J}}\,{{mol - K}}$, $1$ $lit$ -$atm$ $=$ $100$ $J$ $ln$ $2$ $=$ $0.693$)

A
$11.5$
B
$13.5$
✓
$9.5$
D
$22.5$

✓

Answer

Correct option: C.

$9.5$

c
$\Delta S_{\text {sys }}=R \ln \frac{V_{2}}{V_{1}}=8.3 \ln 4$

$=8.3 \times 2 \times 0.693$

$=11.5\,\mathrm{J} / \mathrm{mol}-\mathrm{K}$

$\Delta S_{\text {surr. }}=\frac{-q_{\text {sys }}}{T}=\frac{-P_{\text {ext }}\left(V_{2}-V_{1}\right)}{T}$

$=-\left(\frac{(8-2)}{300}\right) \times 100=-2 \frac{\mathrm{J}}{\mathrm{mol}-\mathrm{K}}$

$\Delta S_{\text {Total }}=11.5-2=9.5 \,\frac{\mathrm{J}}{\mathrm{mol}-\mathrm{K}}$

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