For a phase change, H0 = 2 kJ/mol and S0 = 0.017 kJ/(K•mol). What are G and the spontaneity of the phase change at 500 K?A.G = 10.5 kJ; nonspontaneousB.G = -6.5 kJ; spontaneousC.G = 10.5 kJ; spontaneousD.G = -6.5 kJ; nonspontaneous
Question
For a phase change, H0 = 2 kJ/mol and S0 = 0.017 kJ/(K•mol). What are G and the spontaneity of the phase change at 500 K?A.G = 10.5 kJ; nonspontaneousB.G = -6.5 kJ; spontaneousC.G = 10.5 kJ; spontaneousD.G = -6.5 kJ; nonspontaneous
Solution
To solve this problem, we need to use the Gibbs free energy equation:
ΔG = ΔH - TΔS
where: ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy (H0 in the question), T is the absolute temperature in Kelvin, ΔS is the change in entropy (S0 in the question).
Given in the problem, we have ΔH = 2 kJ/mol, ΔS = 0.017 kJ/(K•mol), and T = 500 K.
Substituting these values into the equation, we get:
ΔG = 2 kJ/mol - 500 K * 0.017 kJ/(K•mol) = 2 kJ/mol - 8.5 kJ/mol = -6.5 kJ/mol
The sign of ΔG determines the spontaneity of the reaction. If ΔG is negative, the reaction is spontaneous. If ΔG is positive, the reaction is non-spontaneous.
So, the answer is B. ΔG = -6.5 kJ/mol; the phase change is spontaneous.
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