Final answer:
Without the change in entropy (ΔS) for the reaction, it is not possible to calculate the new equilibrium constant at 662 K from a given equilibrium constant at 298 K and the change in enthalpy (ΔH°rxn). In general, for exothermic reactions, increasing the temperature typically results in a decrease in the equilibrium constant.
Step-by-step explanation:
The equilibrium constant for a chemical reaction can be determined from the standard free energy change using the relationship ΔG° = -RT ln K, where ΔG° is the standard free energy change, R is the gas constant, T is the temperature in Kelvin, and K is the equilibrium constant. Given the change in enthalpy (ΔH°rxn) is -33.1 kJ/mol and the equilibrium constant (K) is 5.0×10³ at 298 K, we can use the Van't Hoff equation λln(K2/K1) = -ΔH°/R (λ(T2−T1)/T2T1) to find the new equilibrium constant at 662 K. Unfortunately, we do not have the change in entropy (ΔS) for the reaction, which is necessary to perform this calculation.
Without ΔS, a direct calculation is not possible. However, generally speaking, if a reaction has a negative ΔH and K increases with temperature, it implies that the reaction is exothermic, and according to the Le Chatelier's principle, higher temperature will shift the equilibrium towards the reactants, theoretically decreasing the value of K.