Question

Sodium carbonate can be prepared by heating sodium bicarbonate. 2 NaHCO3(s) ----> Na2CO3(s) + CO2(g) + H2O(g). Given that DHo = 128.9 kJ and DSo = 321 J/K·mol for this reaction, at what temperature will K = 1?

Answer 1

T = 401.6 K

Step-by-step explanation:

Given reaction:

`NaHCO3(s) ----> Na2CO3(s) + CO2(g) + H2O(g)`

The thermodynamic parameters; ΔG°, ΔH° and ΔS° are related via the Gibbs -Helmholtz equation given as:

`\Delta G^(0)=\Delta H^(0)-T\Delta S^(0)----(1)`

For a given reaction, the gibbs free energy change ΔG° is related to the equilibrium constant K as:

`\Delta G^(0)=-RTln(K) ---(2)`

It is given that K = 1,

Therefore,

`\Delta G^(0)=-RTln(1) = 0`

Substituting for ΔG° in equation (1)

`0=\Delta H^(0)-T\Delta S^(0)`

`\Delta H = T\Delta S`

`T = \Delta H^(0)/\Delta S^(0)=(128.9 kJ)/(0.321 kj/mol-K)=401.6 K`