For a reaction, H0 = 206 kJ/mol and S0 = 0.215 kJ/(K•mol). At what temperatures is this reaction spontaneous?A.At no temperatureB.At temperatures greater than 958 KC.At all temperaturesD.At temperatures less than 44 K
Question
For a reaction, H0 = 206 kJ/mol and S0 = 0.215 kJ/(K•mol). At what temperatures is this reaction spontaneous?A.At no temperatureB.At temperatures greater than 958 KC.At all temperaturesD.At temperatures less than 44 K
Solution
The spontaneity of a reaction can be determined using the Gibbs Free Energy equation:
ΔG = ΔH - TΔS
Where: ΔG is the change in Gibbs Free Energy ΔH is the change in enthalpy (or heat content) T is the temperature in Kelvin ΔS is the change in entropy (or disorder)
A reaction is spontaneous if ΔG is less than zero.
Given: ΔH = 206 kJ/mol ΔS = 0.215 kJ/(K•mol)
We need to find the temperature (T) at which ΔG = 0 (the threshold between spontaneity and non-spontaneity). We can set up the equation as follows:
0 = ΔH - TΔS T = ΔH / ΔS
Substituting the given values:
T = (206 kJ/mol) / (0.215 kJ/(K•mol)) T = 958 K
Therefore, the reaction is spontaneous at temperatures greater than 958 K. So, the correct answer is B. At temperatures greater than 958 K.
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