Question

if either of the reactions is nonspontaneous but can become spontaneous, at what temperature might it become spontaneous? round your answer to significant digits.

Answer 1

To determine the temperature at which a nonspontaneous reaction might become spontaneous, we use the equation ΔG = ΔH° - TΔS°. Setting ΔG to zero and solving for T gives us the temperature threshold. In this case, the reaction becomes nonspontaneous at temperatures above approximately 463 K.

Step-by-step explanation:

If a nonspontaneous reaction is to become spontaneous, its Gibbs free energy change (ΔG) must become negative. The relationship between ΔG, enthalpy change (ΔH°), and entropy change (ΔS°) is given by the equation ΔG = ΔH° - TΔS°.

A reaction that is nonspontaneous at one temperature may become spontaneous at another temperature if the enthalpy and entropy changes promote such a condition. For the reaction where ΔH° is -91.8 kJ/mol and ΔS° is -198.1 J/K per mole, we can predict at what temperature the sign of ΔG would change from positive to negative, thus making the reaction spontaneous.

To find the temperature at which the reaction becomes spontaneous, we set ΔG° equal to zero and solve for T: 0 = ΔH° - TΔS° → T = ΔH°/ΔS°.

Converting ΔH° to J/mol (since ΔS° is in J), we have -91800 J/mol divided by -198.1 J/K​ per mole, which equals approximately 463 K. Therefore, the reaction becomes nonspontaneous at a temperature higher than 463 K.