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

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

Step-by-step explanation:

The expression for the standard change in free energy is:

`\Delta G=\Delta H-T* \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* \Delta S`

`-29815\Delta S=-9580`

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

So, For reaction to be spontaneous,
`\Delta G<0`

Thus, For minimum temperature:-

`\Delta H-T* \Delta S=0`

`128.9-T* 0.32131=0`

`T=(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.