To determine the temperature at which a reaction becomes spontaneous, we can 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 spontaneous reaction, ΔG must be negative. We can rearrange the equation to solve for the temperature at which this occurs:
ΔG = -RTln(K)
where: R is the gas constant (8.314 J/(mol·K)), K is the equilibrium constant.
Since we are given ΔH and ΔS, we can calculate ΔG at any given temperature using the equation ΔG = ΔH - TΔS.
Setting ΔG to zero, we can find the temperature at which the reaction becomes spontaneous:
0 = ΔH - TΔS
Rearranging the equation, we have:
TΔS = ΔH
T = ΔH/ΔS
Substituting the given values:
T = (+163.6 kJ) / (+75.8 J/K)
Note: We need to convert kilojoules (kJ) to joules (J):
T = (+163.6 kJ × 1000 J/kJ) / (+75.8 J/K)
T ≈ 2156.2 K
Therefore, above approximately 2156.2 Kelvin (K), the reaction is expected to become spontaneous given the values of ΔH = +163.6 kJ and ΔS = +75.8 J/K.