The following reaction has the following standard thermodynamic parameters:
Reaction: C(g) + D(g)----> E(g)
Delta H rxn=-26.1kJ/mol and
Delta S rxn=-69.8J/(mol*K).
Calculate the temperature at which the reaction becomes nonspontaneous.
dG = dH- TdS
Set dG to zero and solve for T. That gives you the T for equilibrium, any move less than that moves in the non-spontaneous direction.
To calculate the temperature at which the reaction becomes nonspontaneous, we need to use the Gibbs free energy equation:
ΔG = ΔH - TΔS
where:
ΔG is the change in Gibbs free energy
ΔH is the change in enthalpy
T is the temperature in Kelvin
ΔS is the change in entropy
To determine the temperature at which the reaction becomes nonspontaneous, ΔG should be equal to zero. This occurs when the reaction is at equilibrium, meaning it is neither spontaneous nor nonspontaneous.
So, setting ΔG = 0, we can rearrange the equation:
0 = ΔH - TΔS
Now, let's solve for T:
TΔS = ΔH
T = ΔH / ΔS
Substituting the given values:
T = (-26.1 kJ/mol) / (-69.8 J/(mol*K))
Note that we need to convert kilojoules (kJ) to joules (J) and multiply by 1000 to convert J/(mol*K) to J/(J*K):
T = (-26.1 kJ/mol) / (-69.8 J/(mol*K)) * 1000 J/kJ
Calculating the numerical value:
T = 374.499 K
Therefore, the temperature at which the reaction becomes nonspontaneous is approximately 374.5 K.