Question

At a constant pressure, the entropy of mixing of 1 mole of oxygen with 3 moles of nitrogen at 25 $^\circ$C is _ _ _ J K$^{-1}$. (rounded off to two decimal places)

Hint:

For ideal gas mixing, use mole fractions in $\Delta S_{\text{mix}} = -R\sum n_i\ln x_i$

Answer 1

Correct Answer: 18.7

Step 1: Entropy of mixing.
\[ \Delta S_{\text{mix}} = -R(n_1\ln x_1 + n_2\ln x_2) \]

Step 2: Mole fractions.
With one mole of oxygen and three of nitrogen, the fractions are 0.25 and 0.75.

Step 3: Evaluate.
\[ \Delta S_{\text{mix}} = -8.314[\ln 0.25 + 3\ln 0.75] \approx 18.70 \]

Step 4: Answer.
\[ \boxed{18.70 \text{ J K}^{-1}} \]