Hydrolysis of sucrose is given by the following reaction

Sucrose + H₂O $\rightleftharpoons$ Glucose + Fructose

If the equilibrium constant (K_c) is 2$\times$10¹³ at 300 K, the value of ${∆}_r{G}^{⊝}$ at the same temperature will be:

1. 8.314 J mol^-1 K^-1$\times$300 K$\times$ln (2$\times$10¹³)

2. 8.314 J mol^-1 K^-1$\times$300 K$\times$ln (3$\times$10¹³)

3. -8.314 J mol^-1 K^-1$\times$300 K$\times$ln (4$\times$10¹³)

4. -8.314 J mol^-1 K^-1$\times$300 K$\times$ln (2$\times$10¹³)

A process among the following shows decrease in entropy is :

1. $2\mathrm{H}\left(\mathrm{(g}\right)$)$\to$ ${\mathrm{H}}_2\left(\mathrm{(g)}\right)$

2. Evaporation of water

3. Expansion of a gas at a constant temperature

4. Sublimation of solid to gas

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 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

Given the reaction: 
X₂O₄(l) → 2XO₂(g) 
ΔU = 2.1 kcal, ΔS = 20 cal K^–1 at 300 K 
The value of ΔG is:
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?

Standard entropies of X₂, Y₂ and XY₃ are 60, 40 and 50JK^-1mol^-1 respectively. For the reaction 
$\frac{1}{2}{\mathrm{X}}_2$ $+$ $\frac{3}{2}{\mathrm{Y}}_2$ $$ $\leftrightharpoons$ ${\mathrm{XY}}_3$ $;$ $∆\mathrm{H}$ $=$ $-30$ $\mathrm{kJ}$ to be at equilibrium, the temperature should be:

1. 750 K

2. 1000 K

3. 1250 K

4. 500 K

For vaporization of water at 1 atmospheric pressure, the values of ∆H and ∆S are 40.63 kJ mol^–1 and 108.8 JK^–1 mol^–1, respectively. The temperature when Gibbs energy change (∆G) for this transformation will be zero, is:

1. 393.4 K

2. 373.4 K

3. 293.4 K

4. 273.4 K