At what temperature (in K) does the following reaction become spontaneous, if Δ𝐻∘ = 311.1 kJ/mol and Δ𝑆∘ = 707.3 J/mol*K?
Question
At what temperature (in K) does the following reaction become spontaneous, if Δ𝐻∘ = 311.1 kJ/mol and Δ𝑆∘ = 707.3 J/mol*K?
Solution
The reaction becomes spontaneous when ΔG° < 0. The formula for ΔG° is ΔG° = ΔH° - TΔS°.
To find the temperature at which the reaction becomes spontaneous, we set ΔG° = 0 and solve for T:
0 = ΔH° - TΔS° T = ΔH° / ΔS°
Substituting the given values:
T = (311.1 kJ/mol) / (707.3 J/mol*K)
Note that we need to convert kJ to J because the units must match. 1 kJ = 1000 J, so:
T = (311.1 * 1000 J/mol) / (707.3 J/mol*K) T = 439.9 K
So, the reaction becomes spontaneous at a temperature of approximately 440 K.
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