Final answer:
To find the value of the equilibrium constant Kc, we need to solve an expression that relates the concentrations of the reactants and products at equilibrium. Using the initial concentrations and the changes in concentration, we can set up an equation and solve for x. Then, we can use the value of x to calculate the concentrations of H₂(g) and CO(g) at equilibrium, and finally determine the value of Kc.
Step-by-step explanation:
The equilibrium constant, Kc, for a reaction can be determined by comparing the concentrations of the reactants and products in the equilibrium mixture. In this case, the reaction equation is H₂O(g) + CO(g) → H₂(g) + CO₂(g). The given initial concentrations are 1.113×10-² moles of water vapor, 1.301×10-² moles of CO(g), and 8.122×10-³ moles of CO₂(g) in the equilibrium mixture. To find the value of the equilibrium constant Kc, we need to calculate the concentrations of H₂(g) and CO(g) at equilibrium.
In order to do this, we assume that x moles of H₂(g) and CO(g) are formed at equilibrium. Therefore, the change in concentration of H₂(g) and CO(g) is +x, and the change in concentration of H₂O(g) and CO₂(g) is -x. Using the initial concentrations and the changes in concentration, we can set up an expression for Kc:
Kc = [H₂(g)]/[CO(g)][H₂O(g)]/[CO₂(g)]
Since the stoichiometric coefficients of H₂O(g) and CO₂(g) are both 1, their concentrations can be directly related to x. The concentrations of H₂(g) and CO(g) can be obtained by subtracting the change x from the initial concentrations. Plugging in the obtained concentrations, we get:
Kc = ([1.301×10-² - x][1.113×10-² - x])/([x][x])
To find the value of x, we need to solve this equation. Then, we can substitute the obtained x value into the expressions for [H₂(g)] and [CO(g)] to calculate their concentrations at equilibrium. Finally, we can plug the calculated concentrations into the expression for Kc to determine the value of Kc at the temperature of the vessel.