Question

In a container 5 moles of $He$ gas are mixed with 4 moles of $H_2$ gas isothermally. Find out the entropy change in mixing for the system in $J{K}^{-1}$, given that $R=8.314Jmo{l}^{-1}{K}^{-1}$

• A. 20.89
• B. 51.04
• C. 98.88
• D. -66.89

Answer 1

The correct option is B 51.04

Entropy change due to Isothermal Mixing : Due to mixing of gases, entropy of the system Changes. Initially both the gases have the same temperature so mixing will not change the temperature. Isothermal mixing increases the entropy of the system.
$\Delta S_{system\left(mixing\right)}=\Delta S_{Gas1\left(duetomixing\right)}+\Delta S_{Gas2\left(duetomixing\right)}$

$\Delta S_{sys}=-n_{1}Rln\left({\chi }_1\right)-n_{2}Rln\left({\chi }_2\right)\Delta S_{sys}=-R\left[n_{1}ln\right({\chi }_1)+n_{2}ln({\chi }_2\left)\right]$

$1=He;2=H_2$

${\chi }_1=\frac{5}{5+4}=\frac{5}{9};{\chi }_2=\frac{4}{5+4}=\frac{4}{9}\Delta S=-8.314[5\times ln(\frac{5}{9})+4\times ln\frac{4}{9})]\Delta S=51.04J{K}^{-1}$