To find the equilibrium constant (K) for the given reaction at 825 degrees Celsius, you need to use the equation:
ln(K) = (-ΔH°/RT) + (ΔS°/R)
Where:
- ΔH° is the standard enthalpy change for the reaction (-908 kJ)
- ΔS° is the standard entropy change for the reaction (1206 J/K)
- R is the ideal gas constant (= 8.314 J/(mol*K))
- T is the temperature in Kelvin (825°C + 273.15 = 1098.15 K)
Step 1: Convert ΔH° to J/mol:
ΔH° = -908 kJ = -908,000 J/mol
Step 2: Plug in the values into the equation:
ln(K) = (-908,000 J/mol) / (8.314 J/(mol*K) * 1098.15 K) + (1206 J/K) / (8.314 J/(mol*K))
Step 3: Simplify the equation:
ln(K) = -121.09 + 145.34
Step 4: Calculate the value of ln(K):
ln(K) = 24.25
Step 5: Solve for K:
K = e^(ln(K)) = e^(24.25)
Using a calculator, K ≈ 5.36 × 10^10
Therefore, the equilibrium constant (K) for the reaction at 825 degrees Celsius is approximately 5.36 × 10^10.