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

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

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

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

For a given reaction, ∆H = 35.5 kJ mol^–1 and ∆S = 83.6 J K^–1 mol^–1. The reaction is spontaneous at:
(Assume that ∆H and ∆S  do not vary with temperature)
1. T > 425K
2. All temperatures
3. T > 298K
4. T < 425K

The bond dissociation energies of $X_2 , Y_2$ 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:
1. –315 KJ
2. +315 KJ
3. –630 KJ
4. +630 KJ

Which of the following statements is correct for the spontaneous adsorption of a gas?

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

From the following bond energies:
H—H bond energy: 431.37 kJ mol^-1 
C=C bond energy: 606.10 kJ mol^-1 
C—C bond energy: 336.49 kJ mol^-1 
C—H bond energy: 410.50 kJ mol^-1 
Enthalpy for the reaction, 

will be:

If \(Q\), \(E\), and \(W\) denote respectively the heat added, the change in internal energy, and the work done in a closed cycle process, then:

Under the isothermal condition, a gas at \(300 \mathrm{~K}\) expands from \(0.1 \mathrm{~L}\) to \(0.25 \mathrm{~L}\) against a constant external pressure of 2 bar. The work done by the gas is:
1. \(30 ~\mathrm {J} \)
2. \(-30 ~\mathrm{J} \)
3. \(5~ \mathrm{kJ}\)
4. \(25~ \mathrm{J}\)