Question

Oxygen is heated from 300 K to 600 K at a constant pressure of 1 bar. The molar heat capacity in $J{K}^{-1}mo{l}^{-1}$ for $O_2$ is $C_P=25.5+13.6\times {10}^{-3}T-42.5\times {10}^{-7}{T}^2$. What is the increases in molar entropy?

• A. $21.296J{k}^{-1}mo{l}^{-1}$
• B. $212.96J{k}^{-1}mo{l}^{-1}$
• C. $2129.6J{k}^{-1}mo{l}^{-1}$
• D. None of these

Answer 1

Answer: (A)

$21.296J{k}^{-1}mo{l}^{-1}$

The increases in molar entropy is given by the expression.

$\Delta S=\frac{n{C}_{P}dT}{T}$

Substitute values in the above expression.

$\Delta S=1\times {\int }_{300}^{600}(\frac{25.5+13.6\times {10}^{-3}T-42.5\times {10}^{-7}{T}^2)}{T}dT$

$\Delta S=1\times {\int }_{300}^{600}(\frac{25.5}{T}+13.6\times {10}^{-3}-42.5\times {10}^{-7}T)dT$

$\Delta S=2.303\times 25.5log2+13.6\times {10}^{-3}\times 300-42.5\times {10}^{-7}\frac{({600}^2-{300}^2)}{2}$

$\Delta S=21.29J{K}^{-1}mo{l}^{-1}$

Hence, the increases in molar entropy is $21.29J{K}^{-1}mo{l}^{-1}$.