Open Question
What is ∆G° for the reaction CaO(s) + CO2(g) → CaCO3(s)?
19. Chemical Thermodynamics
Entropy Calculations
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A reaction has ΔrH = -107 kJ mol^-1 and ΔrS = 285 J K^-1 mol^-1. At what temperature is the change in entropy for the reaction equal to the change in entropy for the surroundings?
A
150 K
B
250 K
C
500 K
D
375 K
Verified step by step guidance1
Understand that the change in entropy for the reaction (ΔrS) and the change in entropy for the surroundings are related through the Gibbs free energy equation: ΔG = ΔH - TΔS, where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.
Recognize that the change in entropy for the surroundings is given by the equation ΔS_surroundings = -ΔH/T. We want to find the temperature at which ΔrS = ΔS_surroundings.
Set up the equation ΔrS = -ΔH/T. Substitute the given values: ΔrS = 285 J K^-1 mol^-1 and ΔH = -107 kJ mol^-1. Note that you need to convert ΔH from kJ to J by multiplying by 1000, so ΔH = -107,000 J mol^-1.
Rearrange the equation to solve for T: T = -ΔH/ΔrS. Substitute the values: T = -(-107,000 J mol^-1) / 285 J K^-1 mol^-1.
Calculate the temperature T using the rearranged equation. This will give you the temperature at which the change in entropy for the reaction equals the change in entropy for the surroundings.
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