Below what temperature does the following reaction become nonspontaneous? 2HNO₃(aq) + NO(g) → 3NO₂(g) + H₂O(l) Δ_rH = +136.5 kJ; Δ_rS = +287.5 J K^-1 mol^-1

Question

Quizplus · Accepted Answer

To determine the temperature at which the reaction becomes nonspontaneous (i.e. when ΔG = 0), we can use the equation:
ΔG = ΔH - TΔS
where ΔH and ΔS are the enthalpy and entropy changes of the reaction, T is the temperature in Kelvin, and ΔG represents the change in Gibbs free energy.

At the temperature where ΔG equals 0, the reaction is at equilibrium and no longer spontaneous. Solving for T:
ΔG = 0 = ΔH - TΔS
T = ΔH/ΔS

Substituting the given values:
T = (+136.5 kJ) / (+287.5 J/K mol)
Note that we need to convert kJ to J and divide by the molar units to cancel out the units of mol:
T = (+136500 J) / (+287.5 J/K mol)
T = 475 K

Therefore, at 475 K (approx. 201°C or 393°F), the reaction becomes nonspontaneous. Choice (C) is the correct answer.

Below What Temperature Does the Following Reaction Become Nonspontaneous? 2HNO3(aq)

Below What Temperature Does the Following Reaction Become Nonspontaneous? 2HNO₃(aq)