Final answer:
To calculate Kc from the given Kp at 1000 K for the reaction A(g)+2B(g) ⇌ 3C(g)+D(g), use the equation Kp = Kc(RT)^Δn, where Δn is the change in moles of gas, R is the gas constant, and T is the temperature.
Step-by-step explanation:
The question is asking to calculate the equilibrium constant in terms of concentrations (Kc) for the reaction A(g)+2B(g) ⇌ 3C(g)+D(g), given the equilibrium constant in terms of pressure (Kp) at a temperature of 1000 K.
The relationship between Kp and Kc is given by the equation Kp = Kc(RT)Δn, where Δn is the change in moles of gas (products minus reactants), R is the gas constant, and T is the temperature in Kelvin. In this case, Δn is 2 (3 + 1 - 1 - 2). Plugging in the values, the equation becomes Kp = Kc(0.08206)(1000)2. To isolate Kc, rearrange the equation to solve for Kc, resulting in Kc = Kp/[(RT)2].
Given that Kp is 10x atm, and substituting R (0.08206 L atm / (mol K)) and T (1000 K) into the equation, we can calculate the value of Kc which would be expressed as Kc = 10x / [(0.08206)(1000)]2.