Final answer:
The equilibrium constant at a new temperature can be calculated using the van't Hoff equation, which involves the enthalpy change of the reaction, the initial equilibrium constant, the initial temperature, the final temperature, and the gas constant.
Step-by-step explanation:
When considering the equilibrium constant (K) at different temperatures for a reaction with a given enthalpy change (ΔHrxn), the van't Hoff equation is typically used. This equation relates the change in the equilibrium constant with temperature to the enthalpy change of the reaction. The van't Hoff equation is expressed as:
ln(K2/K1) = (ΔHrxn / R) (1/T1 - 1/T2)
Where:
Given the change in enthalpy (ΔHrxn) for a reaction is -32.4 kJ/mol and the equilibrium constant (K) is 5.0×103 at 298 K, to find the equilibrium constant at 684 K, we would rearrange the van't Hoff equation and solve for K2:
ΔHrxn in J/mol = -32.4 kJ/mol × 1000 J/kJ = -32400 J/mol
K1 = 5.0×103 at T1 = 298 K
So, ln(K2/5.0×103) = (-32400 J/mol / 8.314 J/mol·K) (1/298 K - 1/684 K)
After calculating the right-hand side, take the exponent to remove the natural logarithm, and then multiply by K1 to find K2 at the temperature of 684 K.