Given the data for the following reactions at 298 K: N2(g) + O2(g) ⇌ 2 NO(g) Kp = 4.4 * 10^-31 NO(g) + 1/2 O2(g) ⇌ NO2(g) Kp = 1.5 * 10^6, calculate the value of the equilibrium constant Kp at 298 K for the reaction N2(g) + 2 O2(g) ⇌ 2 NO2(g). (LO 15.3) (a) Kp = 6.6 * 10^-25 (b) Kp = 1.3 * 10^-24 (c) Kp = 9.9 * 10^-19 (d) Kp = 5.4 * 10^-28

Verified step by step guidance

Step 1: Identify the target reaction: N2(g) + 2 O2(g) ⇌ 2 NO2(g).

Step 2: Recognize that the target reaction can be obtained by combining the given reactions: N2(g) + O2(g) ⇌ 2 NO(g) and NO(g) + 1/2 O2(g) ⇌ NO2(g).

Step 3: Reverse the first reaction to get 2 NO(g) ⇌ N2(g) + O2(g), which changes its Kp to 1/(4.4 * 10^-31).

Step 4: Multiply the second reaction by 2 to get 2 NO(g) + O2(g) ⇌ 2 NO2(g), which squares its Kp to (1.5 * 10^6)^2.

Step 5: Combine the modified reactions to form the target reaction and multiply their Kp values to find the Kp for the target reaction.

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 concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is calculated using the partial pressures of gases involved in the reaction. A larger Kp indicates a greater tendency for products to form, while a smaller Kp suggests a preference for reactants.

Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative amounts of products and reactants present in a reaction at any point in time, not just at equilibrium. It is calculated in the same way as Kp but uses the current concentrations or partial pressures. Comparing Q to Kp helps determine the direction in which a reaction will proceed to reach equilibrium.

Manipulating Equilibrium Constants

When combining reactions to find the equilibrium constant for a new reaction, the equilibrium constants of the individual reactions can be manipulated. If a reaction is reversed, the equilibrium constant is inverted. If a reaction is multiplied by a coefficient, the equilibrium constant is raised to that power. This principle is essential for calculating Kp for complex reactions.

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Equilibrium Constant K

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Textbook Question

The reaction A21g2 + B21g2 ∆ 2 AB1g2 has an equilib- rium constant Kc = 9. The following figure represents areaction mixture that contains A2 molecules (red), B2 mol- ecules (blue), and AB molecules. What statement about the mixture is true? (LO 15.5)

(a) The mixture is at equilibrium, and there will be no net shift in reaction direction.(b) The reaction will shift toward the reactants to reach equilibrium.(c) The reaction will shift toward the products to reach equilibrium.(d) More information is needed to answer this question.

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