Question

Sodium carbonate, Na2CO3, can be made by heating sodium bicarbonate, NaHCO3, according to the following chemical equation:

2NaHCO3(s) → Na2CO3(s) + CO2(g) + H2O(g)
If ΔH° = 128.9 kJ/mol and ΔG° = 33.1 kJ/mol at 25 °C, estimate the minimum temperature above which

the reaction becomes spontaneous.

Answer 1

The reaction will be spontaneous, if dG becomes negative.

2NaHCO3(s) → Na2CO3(s) + CO2(g) + H2O(g)

Given that;
ΔH° = 128.9 kJ/mol ; ΔG° = 33.1 kJ/mol and T= 25°C= 298 K
First we calculate the dS as follows:
dG = dH - TdS
33.1 = 128.9 - (298K)(dS)
-95.8 = - (298K)(dS)
dS = + 0.321 kJ/K

now we find the temp where it is almost spontaneous means at equilibrium condition:

at equilibrium dG = 0
dG = dH - TdS
0 = 128.9 - (T)(0.321 kJ/K)
128.9 = (T)(0.321 kJ/K)
T = 401.5 K or 402 K or 129 °C

At 129°C this reaction becomes spontaneous.