Textbook Question
For the equilibrium Br2(𝑔) + Cl2(𝑔) ⇌ 2 BrCl(𝑔) at 400 K, 𝐾𝑐 = 7.0. If 0.25 mol of Br2 and 0.55 mol of Cl2 are introduced into a 3.0-L container at 400 K, what will be the equilibrium concentrations of Br2, Cl2, and BrCl?
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Ch.15 - Chemical Equilibrium
Chapter 15, Problem 55
Consider the reaction \( \text{CaSO}_4(\text{s}) \rightleftharpoons \text{Ca}^{2+}(\text{aq}) + \text{SO}_4^{2-}(\text{aq}) \) At 25 °C, the equilibrium constant is \( K_c = 2.4 \times 10^{-5} \) for this reaction. (a) If excess \( \text{CaSO}_4(\text{s}) \) is mixed with water at 25 °C to produce a saturated solution of \( \text{CaSO}_4 \), what are the equilibrium concentrations of \( \text{Ca}^{2+} \) and \( \text{SO}_4^{2-} \)? (b) If the resulting solution has a volume of 1.4 L, what is the minimum mass of \( \text{CaSO}_4(\text{s}) \) needed to achieve equilibrium?
Verified step by step guidance1
Step 1: Understand the reaction and equilibrium expression. The dissolution of calcium sulfate in water is represented by the equation: \( \text{CaSO}_4(\text{s}) \rightleftharpoons \text{Ca}^{2+}(\text{aq}) + \text{SO}_4^{2-}(\text{aq}) \). The equilibrium constant expression for this reaction is \( K_c = [\text{Ca}^{2+}][\text{SO}_4^{2-}] \).
Step 2: Set up the equilibrium concentrations. Since \( \text{CaSO}_4 \) is a solid, its concentration does not appear in the equilibrium expression. Let \( s \) be the solubility of \( \text{CaSO}_4 \) in mol/L. At equilibrium, \([\text{Ca}^{2+}] = s\) and \([\text{SO}_4^{2-}] = s\).
Step 3: Substitute into the equilibrium expression. Substitute the equilibrium concentrations into the expression for \( K_c \): \( K_c = s \times s = s^2 \). Given \( K_c = 2.4 \times 10^{-5} \), solve for \( s \) by taking the square root of both sides.
Step 4: Calculate the equilibrium concentrations. The equilibrium concentrations of \( \text{Ca}^{2+} \) and \( \text{SO}_4^{2-} \) are both equal to \( s \), the solubility of \( \text{CaSO}_4 \).
Step 5: Determine the minimum mass of \( \text{CaSO}_4 \) needed. Use the solubility \( s \) to find the number of moles of \( \text{CaSO}_4 \) in 1.4 L of solution. Then, convert moles to grams using the molar mass of \( \text{CaSO}_4 \).
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Equilibrium Constant (Kc)
The equilibrium constant, denoted as Kc, quantifies the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction. For the reaction given, Kc = [Ca²⁺][SO₄²⁻] / [CaSO₄], where solid CaSO₄ does not appear in the expression. A small Kc value, like 2.4 × 10⁻⁵, indicates that at equilibrium, the concentration of products is much lower than that of the reactants, suggesting that the reaction favors the formation of solid CaSO₄.
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03:20
Equilibrium Constant Expressions
Saturated Solution
A saturated solution is one in which the maximum amount of solute has been dissolved in a solvent at a given temperature, resulting in a dynamic equilibrium between the dissolved ions and the undissolved solute. In this case, when excess CaSO₄ is added to water, it will dissolve until the solution reaches saturation, where the concentrations of Ca²⁺ and SO₄²⁻ ions remain constant, governed by the equilibrium constant.
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Stoichiometry and Mass Calculations
Stoichiometry involves using the relationships between reactants and products in a chemical reaction to calculate quantities. In this scenario, once the equilibrium concentrations of Ca²⁺ and SO₄²⁻ are determined, the molarity can be converted to moles, and then to mass using the molar mass of CaSO₄. This allows for the calculation of the minimum mass of CaSO₄ needed to achieve the desired equilibrium concentrations in a specified volume of solution.
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Related Practice
Textbook Question
At 373 K, 𝐾𝑝 = 0.416 for the equilibrium 2 NOBr(𝑔) ⇌ 2 NO(𝑔) + Br2(𝑔) If the pressures of NOBr(𝑔) and NO(𝑔) are equal, what is the equilibrium pressure of Br2(𝑔)?
Textbook Question
At 218°C, 𝐾𝑐 = 1.2×10−4 for the equilibrium NH4SH(𝑠) ⇌ NH3(𝑔) + H2S(𝑔) Calculate the equilibrium concentrations of NH3 and H2S if a sample of solid NH4SH is placed in a closed vessel at 218°C and decomposes until equilibrium is reached.
Textbook Question
At 80°C, 𝐾𝑐 = 1.87×10−3 for the reaction PH3BCl3(𝑠) ⇌ PH3(𝑔) + BCl3(𝑔) (a) Calculate the equilibrium concentrations of PH3 and BCl3 if a solid sample of PH3BCl3 is placed in a closed vessel at 80°C and decomposes until equilibrium is reached.
Textbook Question
At 80°C, 𝐾𝑐 = 1.87×10−3 for the reaction PH3BCl3(𝑠) ⇌ PH3(𝑔) + BCl3(𝑔) (a) Calculate the equilibrium concentrations of PH3 and BCl3 if a solid sample of PH3BCl3 is placed in a closed vessel at 80°C and decomposes until equilibrium is reached. (b) If the flask has a volume of 0.250 L, what is the minimum mass of PH3BCl3(𝑠) that must be added to the flask to achieve equilibrium?