Consider the reaction: CO(g) + H2O(g) ⇌ CO2(g) + H2(g) Kp = 0.0611 at 2000 K. A reaction mixture initially contains a CO partial pressure of 1344 torr and a H2O partial pressure of 1766 torr at 2000 K. Calculate the equilibrium partial pressures of each of the products.

Verified step by step guidance

Convert the initial partial pressures from torr to atm by dividing each by 760, since 1 atm = 760 torr.

Set up an ICE (Initial, Change, Equilibrium) table to track the changes in partial pressures of each species. Let the change in pressure for CO and H2O be \(-x\), and for CO2 and H2 be \(+x\).

Write the expression for the equilibrium constant \(K_p\) in terms of partial pressures: \(K_p = \frac{P_{CO_2} \cdot P_{H_2}}{P_{CO} \cdot P_{H_2O}}\).

Substitute the equilibrium expressions from the ICE table into the \(K_p\) expression and solve for \(x\).

Calculate the equilibrium partial pressures by substituting \(x\) back into the expressions for each species: \(P_{CO} = P_{CO, initial} - x\), \(P_{H_2O} = P_{H_2O, initial} - x\), \(P_{CO_2} = x\), and \(P_{H_2} = x\).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (Kp)

The equilibrium constant (Kp) is a numerical value that expresses the ratio of the partial pressures of the products to the reactants at equilibrium for a given reaction at a specific temperature. For the reaction CO(g) + H2O(g) ⇌ CO2(g) + H2(g), Kp = 0.0611 indicates that at equilibrium, the products' partial pressures are relatively low compared to the reactants, reflecting the position of equilibrium.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract the change and restore a new equilibrium. In this context, if the initial concentrations of CO and H2O are high, the reaction will shift towards the products to reach equilibrium, affecting the partial pressures of CO2 and H2.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. In this reaction, the total pressure is the sum of the partial pressures of CO, H2O, CO2, and H2. To find the equilibrium partial pressures of the products, one must apply the initial conditions and the equilibrium constant to calculate how much of each gas is present at equilibrium.