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Ch.15 - Chemical Equilibrium
Chapter 15, Problem 99

The reaction of iron(III) oxide with carbon monoxide is important in making steel. At 1200 K, Kp = 19.9 for the reaction Fe2O3(s) + 3 CO(g) ⇌ 2 Fe(l) + 3 CO2(g). What are the equilibrium partial pressures of CO and CO2 if CO is the only gas present initially, at a partial pressure of 0.978 atm?

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1
Identify the balanced chemical equation: Fe2O3(s) + 3 CO(g) ⇌ 2 Fe(l) + 3 CO2(g). Note that solids and liquids do not appear in the expression for Kp.
Write the expression for the equilibrium constant Kp: Kp = (P_CO2^3) / (P_CO^3), where P_CO2 and P_CO are the equilibrium partial pressures of CO2 and CO, respectively.
Set up an ICE (Initial, Change, Equilibrium) table to track the changes in partial pressures. Initially, P_CO = 0.978 atm and P_CO2 = 0 atm.
Define the change in partial pressure of CO as -3x and the change in partial pressure of CO2 as +3x, where x is the change in moles of CO2 formed.
Substitute the equilibrium expressions from the ICE table into the Kp expression: 19.9 = ((3x)^3) / ((0.978 - 3x)^3). Solve for x to find the equilibrium partial pressures of CO and CO2.

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 products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction provided, Kp = 19.9 indicates that at equilibrium, the ratio of the partial pressures of the gaseous products (CO2) to the reactants (CO) is fixed, allowing us to calculate the equilibrium concentrations based on initial conditions.
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Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is disturbed by a change in concentration, temperature, or pressure, the system will adjust to counteract the disturbance and restore a new equilibrium. In this reaction, the initial presence of CO will shift the equilibrium position as the reaction proceeds, affecting the partial pressures of CO and CO2.
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Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. In this context, the initial partial pressure of CO is given as 0.978 atm, and as the reaction progresses towards equilibrium, the changes in the partial pressures of CO and CO2 must be calculated to satisfy the equilibrium constant expression, allowing us to determine their final values at equilibrium.
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