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

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)

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