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
When DG is - the reaction is spontaneous, when + it is spontaneous the other direction, the mid-point is 0. Set DG = 0 and substitute DH and DS into the equation. Solve for T. Remember DH is given in kJ and DS is given in J(not kJ).
To calculate the temperature at which the reaction becomes nonspontaneous, we will 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
For a reaction to be spontaneous, ΔG must be negative. When ΔG is zero, the reaction is at equilibrium. So, to find the temperature at which the reaction becomes nonspontaneous, we need to set ΔG equal to zero and solve for T.
0 = ΔH - TΔS
Rearranging the equation, we get:
T = ΔH / ΔS
Now we can substitute the given values:
T = (-26,100 J/mol) / (-69.8 J/(mol*K))
Calculating the division:
T ≈ 373.5 K
Therefore, at approximately 373.5 Kelvin, the reaction becomes nonspontaneous.