Question

For a particular reaction, Δ H ∘ = 20.1 kJ/mol and Δ S ∘ = 45.9 J / (mol ⋅ K). Assuming these values change very little with temperature,

at what temperature does the reaction change from nonspontaneous to spontaneous in the forward direction? T = K

Answer 1

Answer: 438 K

Step-by-step explanation:

According to Gibbs equation:

`\Delta G=\Delta H-T\Delta S`

`\Delta G` = Gibb's free energy change

`\Delta H` = enthalpy change = 20.1 kJ/mol = 20100 J/mol

T = temperature

`\Delta S` = entropy change = 45.9 J/Kmol

A reaction is at equilibrium when
`\Delta G` = Gibb's free energy change is zero and becomes spontaneous when
`\Delta G` = Gibb's free energy change is negative.

`\Delta H=T\Delta S`

`20100=T* 45.9J/Kmol`

T=437.9K

Thus the temperature at which the reaction change from nonspontaneous to spontaneous in the forward direction is 438 K