Under standard conditions, the Gibbs free energy of the reactants G,std(reactants) in a reaction in the gas phase is 232.94 kJ and the Gibbs free energy of the products G,std(products) is 211.56 kJ. Calculate the value of the equilibrium constant for this reaction under standard conditions at 25degC.
dGrxn = dG products - dG reactants
Then dG = -RTlnK
To calculate the equilibrium constant (K) for a reaction using the Gibbs free energy values, you can use the formula:
ΔG° = -RT ln(K)
Where:
ΔG° = Change in Gibbs free energy under standard conditions
R = Gas constant (8.314 J/(mol*K) or 0.008314 kJ/(mol*K))
T = Temperature in Kelvin
K = Equilibrium constant
Given:
G,std(reactants) = 232.94 kJ
G,std(products) = 211.56 kJ
Temperature (T) = 25°C = 25 + 273.15 K = 298.15 K
First, we need to find the change in Gibbs free energy (ΔG°) between the reactants and products:
ΔG° = G,std(products) - G,std(reactants)
ΔG° = 211.56 kJ - 232.94 kJ
ΔG° = -21.38 kJ
Note that we have taken the negative value because the equation requires the change in Gibbs free energy to be negative.
Now, we can rearrange the formula to solve for K:
K = exp(-ΔG° / (RT))
Substituting the values:
K = exp(-(-21.38 kJ) / (0.008314 kJ/(mol*K) * 298.15 K))
Simplifying the equation:
K = exp(2574.04)
Calculating the value:
K ≈ 7.1454 x 10^111
Therefore, the equilibrium constant for this reaction under standard conditions at 25°C is approximately 7.1454 x 10^111.