Question

3.0 moles of an ideal gas is expanded from 2.0 bar to 0.1 bar at constant temperature. The surroundings are at 1.0 atm and 300 K, and the expansion is against the constant external pressure of the surrounding. Mark the correct options:
Take R =$\frac{25}{3}J/molK$ , $ln2=0.7$

• A. $\Delta S_{surr}$ is negative
• B. This is a non-spontaneous process
• C. $|\Delta S_{tot}|=5J/K$
• D. $\Delta S_{sys}=-17.5J/K$

Answer 1

Answer: (A), (C)

The correct options are
A $\Delta S_{surr}$ is negative
C $|\Delta S_{tot}|=5J/K$

$△S_{\text{system}}=nRln\frac{p_1}{p_2}\text{Because}△T=0q=-w=p_{ext}△V△S_{\text{surr}}=\frac{-q}{T}$
We need to find $△S_{\text{Total}}$and figure out if the reaction is spontaneous.
$△S_{\text{system}}=nRln\frac{p_1}{p_2}\Rightarrow △S_{\text{system}}=3\times \frac{25}{3}\times ln2=17.5J/Kq=+p_{ext}△V\Rightarrow q=1\times {10}^5(\frac{1}{p_2}-\frac{1}{p_1})\times 3\times \frac{25}{3}\times 300\to q=\frac{1\times {10}^5}{1\times {10}^5}[\frac{1}{1}-\frac{1}{2}]\times 3\times \frac{25}{3}\times 300=3750J\therefore △S_{\text{surr}}=\frac{-q}{T}=\frac{-3750}{300}=-12.50J/K\therefore △S_{\text{total}}=17.5-12.5=5J/K>0$
Hence the change is spontaneous and irreversible.