Estimate the temperature of the reaction?

Question

Consider the reaction:

ZnO(s) + H2(g) = Zn(s) + H2O(g)

ΔH ΔG

------------------ ----------------------

ZnO(s) -348kJ/mol -318 kJ/mol

H2O(g) -242kJ/mol -228 kJ/mol

From these data, estimate the temperature at which the equilibrium constant for this reaction is approximately unity. The answer is 1900 K. How to do it?

Answer 1

........    ....ΔH ...   ...   ...   ΔG

ZnO(s) -348kJ/mol,,,,    -318 kJ/mol

H2O(g) -242kJ/mol....   -228 kJ/mol

ZnO(s) + H2(g) = Zn(s) + H2O(g)

find dG reaction = prod - reactants

dG = -228 - (-318) = 90 kJ

find dH reaction = prod - reactants

dH = -242 - (-348) = +106 kJ

find dS at these standard conditions where it is at 298Kelvin:

dG = dH -TdS

90 = 106 - (298)dS

dS = -16 / -298 = 0.05369 kj/K

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traditionally when we answer your question we use the assumption that the dS & the dH will  remain constant @ the new temp.

From these data, estimate the temperature at which the equilibrium constant for this reaction is approximately unity ( which is their way of saying  that it is at equilibrium):

dG = dH - TdS   which at equilibrium becomes

zero = dH - tdS

0 = 106kJ - T (0.05369 kj/K)

106kJ   =  T (0.05369 kj/K)

T = 106kJ  / (0.05369 kj/K)

T = 1974 K