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Ch.15 - Chemical Equilibrium
Chapter 15, Problem 75

For each of the following equilibria, write the equilibrium constant expression for Kc. Where appropriate, also write the equilibrium constant expression for Kp. (a) WO3(s) + 3 H2(g) ⇌ W(s) + 3 H2O(g) (b) Ag+(aq) + Cl-(aq) ⇌ AgCl(s) (c) 2 FeCl3(s) + 3 H2O(g) ⇌ Fe2O3(s) + 6 HCl(g) (d) MgCO3(s) ⇌ MgO(s) + CO2(g)

Verified step by step guidance
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Step 1: Understand the concept of equilibrium constant expressions. For a general reaction aA + bB ⇌ cC + dD, the equilibrium constant expression for Kc is given by: Kc = [C]^c [D]^d / [A]^a [B]^b, where [X] denotes the concentration of species X.
Step 2: For reactions involving gases, the equilibrium constant can also be expressed in terms of partial pressures, Kp. The relationship between Kc and Kp is given by: Kp = Kc(RT)^Δn, where Δn is the change in moles of gas (moles of gaseous products - moles of gaseous reactants), R is the ideal gas constant, and T is the temperature in Kelvin.
Step 3: For reaction (a) WO3(s) + 3 H2(g) ⇌ W(s) + 3 H2O(g), write the Kc expression considering only the gaseous species: Kc = [H2O]^3 / [H2]^3. Since there is a change in moles of gas (Δn = 0), Kp = Kc.
Step 4: For reaction (b) Ag+(aq) + Cl-(aq) ⇌ AgCl(s), write the Kc expression considering only the aqueous species: Kc = 1 / [Ag+][Cl-]. Since there are no gaseous species, Kp is not applicable.
Step 5: For reaction (c) 2 FeCl3(s) + 3 H2O(g) ⇌ Fe2O3(s) + 6 HCl(g), write the Kc expression considering only the gaseous species: Kc = [HCl]^6 / [H2O]^3. Calculate Δn for Kp: Δn = 6 - 3 = 3, and use the relationship Kp = Kc(RT)^3.

Key Concepts

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

Equilibrium Constant (Kc and Kp)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. Kc is used for reactions in terms of molarity (concentration), while Kp is used for reactions involving gases and is expressed in terms of partial pressures. The relationship between Kc and Kp can be established using the ideal gas law, particularly when the number of moles of gas changes during the reaction.
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Phase of Reactants and Products

In equilibrium expressions, only the concentrations or partial pressures of gaseous and aqueous species are included; solids and liquids do not appear in the expression. This is because their activities are defined as 1, meaning they do not affect the equilibrium position. Understanding the phases of the reactants and products is crucial for correctly writing the equilibrium constant expressions.
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Stoichiometry in Equilibrium Expressions

The coefficients of the balanced chemical equation play a vital role in forming the equilibrium constant expression. For each species in the reaction, its concentration or pressure is raised to the power of its coefficient in the balanced equation. This stoichiometric relationship is essential for accurately calculating Kc and Kp, as it reflects the proportionality of the reactants and products at equilibrium.
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