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

For a given reaction, ∆H = 35.5 kJ mol^–1 and ∆S = 83.6 J K^–1 mol^–1. The reaction is spontaneous at:
[Note: Assume that ∆H and ∆S  do not vary with temperature]

1. T > 425K
2. All temperatures
3. T > 298K
4. T < 425K

A gas is allowed to expand in a well-insulated container against a constant external pressure of 2.5atm from an initial volume of 2.50 L to a final volume of 4.50L. The change in internal energy U of the gas in joules will be:

The bond dissociation energies of X₂ , Y₂ and XY are in the ratio of 1 : 0.5 : 1. ∆H for the formation of XY is –200 kJ mol^–1. The bond dissociation energy of X₂ will be

The heat of combustion of carbon to CO₂ is –393.5 KJ/mol. The heat released upon the formation of 35.2 g of CO₂ from carbon and oxygen gas is:

The correct statement for a reversible process in a state of equilibrium is:
1. $∆$G = – 2.30RT log K
2. $∆$G = 2.30RT log K
3. $∆$G^o = – 2.30RT log K
4. $∆$G^o = 2.30RT log K

For the reaction:
\(\mathrm{X}_2 \mathrm{O}_4(l) \rightarrow 2 \mathrm{XO}_2(g)\)
with the given values \(\Delta U = 2.1 \, \text{kcal}\) and \(\Delta S = 20 \, \text{cal K}^{-1}\) at \(300 \, \text{K}\), what is the value of \(\Delta G\)?

1. +2.7 kcal
2. –2.7 kcal
3. +9.3 kcal
4. –9.3 kcal

In which of the following reactions, the standard reaction entropy change
$(∆S^0)$ is positive, and standard Gibb's energy change
$(∆G^0)$ decreases sharply with increasing temperature?