Final answer:
For the reaction CH4(g) + CO2(g) ⇌ 2CO(g) + 2H2(g) at 825 K, the Kc value can be calculated using the equation Kp = Kc(RT)^2, which gives a Kc value of 5.92.
Step-by-step explanation:
To find the value of Kc for the given reaction at a temperature of 825 K, we must use the relationship between Kp and Kc, which is given by the equation Kp = Kc(RT)Δn, where Δn is the change in moles of gas in the reaction, R is the ideal gas constant, and T is the temperature in Kelvin.
For the reaction CH4(g) + CO2(g) ⇌ 2CO(g) + 2H2(g), the change in moles of gas, Δn, is (2 + 2) - (1 + 1) = 2. The ideal gas constant, R, is 0.0821 L·atm/K·mol. Given that Kp = 4.0×102 and the temperature, T, is 825 K, we can solve for Kc.
Plugging these values into the equation gives us:
Kc = Kp / (RT)Δn
Kc = 4.0×102 / (0.0821 L·atm/K·mol × 825 K)2
After calculating the value, we find that Kc for the reaction at 825 K is 5.92.