Given that GRxn = 474.4 kJ, calculate the equilibrium constant for the following
equilibrium at 25.0 C.
2 H2O(l) ⇌ H2(g) + O2(g)
dG = -RTlnK
Substitute and solve for K.
Remember to substitute G in J, R is 8.314, and T must be in kelvin.
To calculate the equilibrium constant (K) at a given temperature, we can use the equation:
ΔG° = -RT ln(K)
Where:
- ΔG° is the standard Gibbs free energy change.
- R is the ideal gas constant (8.314 J/mol·K or 0.008314 kJ/mol·K).
- T is the temperature in Kelvin.
- K is the equilibrium constant.
First, we need to convert the temperature from degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15 = 25.0 + 273.15 = 298.15 K
Next, rearrange the equation to solve for K:
K = e^(-ΔG°/RT)
Now we can substitute the known values into the equation:
K = e^(-474.4 kJ / (0.008314 kJ/mol·K × 298.15 K))
Calculating this expression will give us the equilibrium constant at 25.0 °C.
To calculate the equilibrium constant (K) for a given reaction, we can use the equation:
ΔG° = -RTln(K)
Where:
- ΔG° is the standard free energy change for the reaction.
- R is the gas constant which has a value of 8.314 J/(mol·K).
- T is the temperature in Kelvin.
- ln is the natural logarithm.
Given that ΔG°Rxn = 474.4 kJ, we need to convert it to J as the gas constant is in J/mol·K. Therefore:
ΔG°Rxn = 474.4 kJ * 1000 J/kJ = 474,400 J
Since the temperature is given at 25.0 °C, we need to convert it to Kelvin:
T = 25.0 °C + 273.15 = 298.15 K
Now we can calculate the equilibrium constant using the equation:
ΔG°Rxn = -RTln(K)
Rearranging the equation to solve for K, we have:
K = e^(-ΔG°Rxn / RT)
Now we can substitute the values:
K = e^(-474,400 J / (8.314 J/(mol·K) * 298.15 K))
Calculating this value will give us the equilibrium constant (K) for the reaction 2 H2O(l) ⇌ H2(g) + O2(g) at 25.0 °C.