Calculate the standard entropy $S_{\mathrm{T}}^{∘}$ of 1 mol of water at 20 °C and 1 bar. The molar heat capacity, C_p, of water is 75.3 J K^-1 mol^-1 and $S_{298}^{∘}$ is 69.9 J K^-1 mol^-1.

Question

Quizplus · Accepted Answer

We can use the equation:
$$\Delta S = \int_{298K}^{293.15K} \dfrac{C_P}{T}dT$$
We know that the molar heat capacity is $C_P=C_V+R$, and at constant pressure $C_P = 75.3$ JK$^{-1}$mol$^{-1}$.
Thus, we have:
$$\Delta S = \int_{298K}^{293.15K} \dfrac{75.3+8.314}{T}dT$$
$$\Delta S = 75.3\ln\dfrac{293.15}{298}+8.314\ln\dfrac{293.15}{298}$$
$$\Delta S = -1.63$$
Therefore, $S_{\mathrm{T}}^{∘} = S_{298}^{∘} + \Delta S = 68.7$ J K$^{-1}$mol$^{-1}$.

Calculate the Standard Entropy ST∘S_{\mathrm{T}}^{∘}ST∘​ Of 1 Mol of Water at 20 °C and 1

Calculate the Standard Entropy $S_{\mathrm{T}}^{∘}$ Of 1 Mol of Water at 20 °C and 1