Calculate the equilibrium constant, k a reaction with delta G= -32.5 kj/mol at 25 degrees C
dG = -RTlnK
Remember to change dG to J/mol
Use R = 8.314
T = 298 K
To calculate the equilibrium constant (K) of a reaction using the Gibbs free energy change (ΔG), we can use the following equation:
ΔG = -RT ln(K)
Where:
ΔG is the Gibbs free energy change (in joules),
R is the gas constant (8.314 J/mol·K),
T is the temperature in Kelvin,
ln is the natural logarithm function,
K is the equilibrium constant.
First, we need to convert the given ΔG from kilojoules per mole to joules per mole:
ΔG = -32.5 kJ/mol = -32.5 × 1000 J/mol = -32,500 J/mol
Next, we need to convert the temperature from degrees Celsius to Kelvin. The conversion formula is:
T(K) = T(°C) + 273.15
T(°C) = 25°C
T(K) = 25 + 273.15 = 298.15 K
Now, we can substitute the values into the equation:
-32,500 J/mol = -8.314 J/mol·K × 298.15 K × ln(K)
Simplifying the equation:
ln(K) = -32,500 J/mol / (-8.314 J/mol·K × 298.15 K)
ln(K) = 15.61
To solve for K, we can take the inverse natural logarithm of both sides:
K = e^(ln(K))
Using a scientific calculator or a programming language, we can calculate the value:
K ≈ e^(15.61) = 457,545.55
Therefore, the equilibrium constant (K) for the reaction is approximately 457,545.55.