What is K for a reaction if ∆G° = -347.2 kJ/mol at 25.00 °C? Give your answer to four significant figures. (R = 8.314 J/mol·K)
Answer (2)
To find the equilibrium constant (K) for a reaction when given the standard Gibbs free energy change Δ G ∘ at a specific temperature, we can use the following relation:
Δ G ∘ = − RT ln K
Where:
Δ G ∘ is the standard Gibbs free energy change in joules per mole (J/mol).
R is the universal gas constant, 8.314 J/(mol·K).
T is the temperature in Kelvin.
K is the equilibrium constant of the reaction.
Given: Δ G ∘ = − 347.2 kJ/mol = − 347200 J/mol ( s in ce w e n ee d t h e u ni t s in J / m o l )
Temperature T = 25. 0 ∘ C = 25 + 273.15 = 298.15 K
Now, rearrange the formula to solve for K :
ln K = − RT Δ G ∘
Substitute the given values:
ln K = − 8.314 × 298.15 − 347200
Calculate the value:
ln K = 8.314 × 298.15 347200 = 2477.5671 347200 ≈ 140.1134
Now, to find K , we need to calculate the exponential of both sides:
K = e 140.1134
Use a calculator to find K :
K ≈ 2.97 × 1 0 60
Therefore, the equilibrium constant K for the reaction is approximately 2.970 × 1 0 60 when expressed to four significant figures.
The equilibrium constant K for the reaction, given \Delta G^\\text{\circ} = -347.2 \, \text{kJ/mol} at 25.00 °C, is found to be approximately 2.970 × 1 0 60 . This is derived using the equation \Delta G^\\text{\circ} = -RT \, \ln K .
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