Question

Sodium carbonate can be made by heating sodium bicarbonate: 2NaHCO3(s) → Na2CO3(s) + CO2(g) + H2O(g) At 25°C, for this reaction, ΔH°rxn = 128.9 kJ/mol and ΔG°rxn = 33.1 kJ/mol. Above what minimum temperature will the reaction become spontaneous under standard state conditions?

Answer 1

Answer:

401.17 K is the minimum temperature at which the reaction will become spontaneous under standard state conditions.

Explanation:

The expression for the standard change in free energy is:

$\Delta G=\Delta H-T\times \Delta S$

Where,  

$\Delta G$ is the change in the Gibbs free energy.

T is the absolute temperature. (T in kelvins)

$\Delta H$ is the enthalpy change of the reaction.

$\Delta S$ is the change in entropy.

Given at:-

Temperature = 25.0 °C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15  

So,  

T₁ = (25.0 + 273.15) K = 298.15 K

$\Delta H$ = 128.9 kJ/mol

$\Delta G$ = 33.1 kJ/mol

Applying in the above equation, we get as:-

$33.1=128.9-298.15\times \Delta S$

$-29815\Delta S=-9580$

$\Delta S=-9580$ = 0.32131 kJ/Kmol

So, For reaction to be spontaneous, $\Delta G$

Thus, For minimum temperature:-

$\Delta H-T\times \Delta S=0$

$128.9-T\times 0.32131=0$

$T=\frac{128.9}{0.32131}=401.17\ K$

Hence, 401.17 K is the minimum temperature at which the reaction will become spontaneous under standard state conditions.