A voltaic cell is constructed that is based on the following reaction: Sn2+(aq) + Pb(s) → Sn(s) + Pb2+(aq) (b) If the anode half-cell contains SO4^2- = 1.00 M in equilibrium with PbSO4(s), what is the Ksp of PbSO4?

Verified step by step guidance

Identify the components of the voltaic cell: The anode is where oxidation occurs, and the cathode is where reduction occurs. In this reaction, Pb(s) is oxidized to Pb2+(aq), and Sn2+(aq) is reduced to Sn(s).

Write the half-reactions for the oxidation and reduction processes: Oxidation: Pb(s) → Pb2+(aq) + 2e^- Reduction: Sn2+(aq) + 2e^- → Sn(s)

Understand the equilibrium condition in the anode half-cell: PbSO4(s) is in equilibrium with Pb2+(aq) and SO4^2-(aq). The solubility product constant (Ksp) for PbSO4 can be expressed as:

K_{sp} = [Pb

²⁺][SO₄^2-]

Use the given concentration of SO4^2- to find the concentration of Pb2+: Since the concentration of SO4^2- is 1.00 M, and assuming PbSO4 is sparingly soluble, the concentration of Pb2+ will be equal to the solubility of PbSO4 in this solution.

Calculate the Ksp of PbSO4: Substitute the concentration values into the Ksp expression to find the solubility product constant.

K_{sp} = [Pb

²⁺][SO₄^2-]

Key Concepts

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

Voltaic Cell

A voltaic cell, or galvanic cell, is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. In this type of cell, oxidation occurs at the anode and reduction at the cathode, allowing for the flow of electrons through an external circuit. Understanding the components and functioning of a voltaic cell is essential for analyzing electrochemical reactions.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. Ksp provides insight into the extent to which a compound can dissolve in solution, which is crucial for determining the solubility of PbSO4 in this context.

Equilibrium and Le Chatelier's Principle

Equilibrium in a chemical reaction refers to the state where the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. Le Chatelier's Principle states that if a system at equilibrium is disturbed, it will shift in a direction that counteracts the disturbance. This principle is important for understanding how changes in concentration, such as the addition of SO4^2-, affect the solubility and Ksp of PbSO4.

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Textbook Question

A voltaic cell is constructed that is based on the following reaction: Sn²⁺(aq) + Pb(s) → Sn(s) + Pb²⁺(aq) (a) If the concentration of Sn²⁺ in the cathode half-cell is 1.00 M and the cell generates an emf of +0.22 V, what is the concentration of Pb²⁺ in the anode half-cell?

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During a period of discharge of a lead–acid battery, 402 g of Pb from the anode is converted into PbSO₄(s). (b) How many coulombs of electrical charge are transferred from Pb to PbO₂?