Spontaneity Entropy

For a sample of a perfect gas when its pressure is changed isothermally from P_i to P_f, the entropy change is given by:

1. $∆\mathrm{s}=\mathrm{nR}$ $\ln$ $\left(\frac{{\mathrm{p}}_{\mathrm{f}}}{{\mathrm{p}}_{\mathrm{i}}}\right)$

2. $∆\mathrm{s}=\mathrm{nR}$ $\ln$ $\left(\frac{{\mathrm{p}}_{\mathrm{i}}}{{\mathrm{p}}_{\mathrm{f}}}\right)$

3. $∆\mathrm{s}=\mathrm{nRT}$ $\ln$ $\left(\frac{{\mathrm{p}}_{\mathrm{f}}}{{\mathrm{p}}_{\mathrm{i}}}\right)$

4. $∆\mathrm{s}=\mathrm{RT}$ $\ln$ $\left(\frac{{\mathrm{p}}_{\mathrm{i}}}{{\mathrm{p}}_{\mathrm{f}}}\right)$

If for a certain reaction ${∆}_{r}H$ is 30 kJ mol^–1 at 450 K, the value of ${∆}_{r}S$ (in JK^–1 mol^–1) for which the same reaction will be spontaneous at the same temperature is:

1.	70	2.	–33
3.	33	4.	–70

In which of the following processes entropy increases?

A.	A liquid evaporates to vapour.
B.	Temperature of a crystalline solid lowered from to
C.
D.

Choose the correct answer from the options given below:

1.		2.
3.		4.