To determine the temperature above which the reaction
2A+B→C becomes spontaneous, we can use the Gibbs free energy equation:
ΔG=ΔH−TΔS
The reaction becomes spontaneous when
is negative. Therefore, we need to find the temperature at which
changes from positive to negative. We set
to zero to find the threshold temperature:
0=ΔH−TΔS
Substituting the given values of
ΔH=400kJ mol−1=400,000J mol−1 (since 1 kJ = 1000 J) and
ΔS=0.2kJ mol−1K−1=200J mol−1K−1 , we get:
0=400,000J mol−1−T(200J mol−1K−1)
Solving for
, we have:
T=200J mol−1K−1400,000J mol−1
T=2000K
Therefore, the reaction will become spontaneous above
2000K . This means that at temperatures higher than 2000 K, the reaction tends towards product formation without the need for external energy to drive the process.
