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Ch.15 - Chemical Equilibrium
All textbooksMcMurry 8th EditionCh.15 - Chemical EquilibriumProblem 4
Chapter 15, Problem 4

Sulfur dioxide reacts with oxygen in a step in the production of sulfuric acid. 2 SO2(g) + O2(g) ⇌ 2 SO3(g), Kc = 7.9 * 10^4 at 1800 K. For an equilibrium mixture in which [SO2] = 4.5 * 10^-3 M and [O2] = 1.5 * 10^-3 M, what is [SO3]? (LO 15.4) (a) [SO3] = 6.2 * 10^-7 M (b) [SO3] = 4.9 * 10^-2 M (c) [SO3] = 0.73 M (d) [SO3] = 2.4 * 10^-3 M

Verified step by step guidance
1
Step 1: Write the expression for the equilibrium constant, Kc, for the reaction: Kc = [SO3]^2 / ([SO2]^2 * [O2]).
Step 2: Substitute the given values into the Kc expression: Kc = 7.9 * 10^4, [SO2] = 4.5 * 10^-3 M, and [O2] = 1.5 * 10^-3 M.
Step 3: Rearrange the Kc expression to solve for [SO3]^2: [SO3]^2 = Kc * ([SO2]^2 * [O2]).
Step 4: Calculate [SO2]^2 and multiply it by [O2] to find the denominator value.
Step 5: Multiply the result from Step 4 by Kc to find [SO3]^2, then take the square root to find [SO3].

Key Concepts

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

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In this state, the system is dynamic, meaning that reactions continue to occur, but there is no net change in concentration. Understanding equilibrium is crucial for solving problems involving equilibrium constants (Kc) and concentrations.
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Equilibrium Constant (Kc)

The equilibrium constant (Kc) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is expressed as Kc = [products]^[coefficients] / [reactants]^[coefficients]. A large Kc value, such as 7.9 * 10^4, indicates that at equilibrium, the concentration of products is much greater than that of reactants, guiding the calculation of unknown concentrations.
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Concentration Calculations

Concentration calculations involve determining the molarity of substances in a solution, which is essential for applying the equilibrium expression. In this problem, the concentrations of SO2 and O2 are provided, and using the Kc value, one can rearrange the equilibrium expression to solve for the unknown concentration of SO3. This requires an understanding of stoichiometry and the relationships between reactants and products.
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Related Practice
Open Question
The equilibrium concentrations in a gas mixture at a particular temperature are 0.13 M H2, 0.70 M I2, and 2.1 M HI. What equilibrium concentrations are obtained at the same temperature when 0.20 mol of HI is injected into an empty 500.0-mL container?
Open Question
What is the equilibrium expression for the reaction of iron metal with water vapor? (LO 15.2 and 15.6) 2 Fe(s) + 3 H2O(g) ⇌ Fe2O3(s) + 3 H2(g)
Open Question
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
Textbook Question
The reaction A21g2 + B21g2 ∆ 2 AB1g2 has an equilib- rium constant Kc = 9. The following figure represents a reaction 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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Open Question
If Kc = 7.5 * 10^-9 at 1000 K for the reaction N2(g) + O2(g) ⇌ 2 NO(g), give the value of Kc at 1000 K for the reaction 2 N2(g) + 2 O2(g) ⇌ 4 NO(g)
Open Question
The gas-phase reaction 2 SO2(g) + O2(g) ⇌ 2 SO3(g) has an equilibrium constant Kc = 5.8 * 10^3 at 600 °C. A mixture contains [SO2] = 0.10 M, [O2] = 0.100 M, and [SO3] = 0.200 M. Which statement is true about the reaction direction and equilibrium mixture? (LO 15.8, 15.9) (a) The mixture is at equilibrium and contains appreciable amounts of reactants and products. (b) The reaction will shift to make more product, and the equilibrium mixture contains appreciable amounts of reactants and products. (c) The reaction will shift to make more reactants, and the equilibrium mixture contains mostly product. (d) The reaction will shift to make more product, and the equilibrium mixture contains mostly reactant.