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Thermodynamics

Question
CBSEENCH11006271

For the reaction at 298 K
                  2 straight A plus straight B rightwards arrow straight C
increment straight H space equals space 400 space kJ space mol to the power of negative 1 end exponent space and space increment straight S space equals space 0.2 space kJ space straight K to the power of negative 1 end exponent mol to the power of negative 1 end exponent.

At what temperature will the reaction become spontaneous considering increment straight H space and space increment straight S to be constant over the temperature range?

Solution

According to Gibb's Helmholtz equation,
                     space increment straight G space minus space increment straight H space minus space straight T increment straight S
At equilibrium,
                increment straight G space equals space 0
space space space space space 0 space equals space increment straight H space minus space straight T increment straight S
or space space space straight T space equals space fraction numerator increment straight H over denominator increment straight S end fraction space space space space space space space space space space space space space... left parenthesis 1 right parenthesis
 Here space space increment straight H space equals space 400 space kJ space mol to the power of negative 1 end exponent
space space space space space space space space space space increment straight S space equals space 0.2 space kJ space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent
Substituting the values in equation (1), we get
          straight T space equals space fraction numerator 400 space kJ space mol to the power of negative 1 end exponent over denominator 0.2 space kJ space straight K to the power of negative 1 end exponent mol to the power of negative 1 end exponent end fraction space equals space 2000 space straight K
Above this temperature, ∆G will be negative and reaction becomes spontaneous.