Calculate delta G of a reaction with equilibrium constant, K= 9.5 x 10^5 at 25 degrees C
dG = -RT*ln K
To calculate the standard Gibbs free energy change (ΔG°) of a reaction using the equilibrium constant (K), you can use the equation:
ΔG° = -RT ln(K)
where R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and ln represents the natural logarithm.
Given that the equilibrium constant K is 9.5 x 10^5 and the temperature is 25 degrees Celsius, we need to convert the temperature to Kelvin:
T (Kelvin) = 25 + 273.15 = 298.15 K
Now, we can substitute the values into the equation and calculate ΔG°:
ΔG° = - (8.314 J/(mol·K)) * 298.15 K * ln(9.5 x 10^5)
Using a calculator, we can find the natural logarithm of 9.5 x 10^5 as follows:
ln(9.5 x 10^5) ≈ 13.717
Substituting this value back into the equation, we have:
ΔG° = - (8.314 J/(mol·K)) * 298.15 K * 13.717
Calculating this expression gives us the value for ΔG°, expressed in joules:
ΔG° ≈ - (8.314 J/(mol·K)) * 298.15 K * 13.717 = - 33,695.95 J/mol
Therefore, the ΔG° of the reaction is approximately -33,695.95 J/mol (or -33.7 kJ/mol, since 1 kJ = 1000 J) at 25 degrees Celsius.