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)

Which of the following processes shows a decrease in entropy?

1. \(2 \text H \left(g\right)\rightarrow\text H_{2} \left(g\right)\)

2. Evaporation of water

3. Expansion of a gas at a constant temperature

4. Sublimation of a solid to a gas

For a given reaction, if ΔH = 35.5 kJ/mol and ΔS = 83.6 J/K·mol, at what temperature is the reaction spontaneous?
(Assume ΔH and ΔS remain constant with temperature.)

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

Find the thermodynamic condition required for a reaction to be spontaneous at all temperatures.