Question

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

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.

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.

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