Chapter 19: Problem 71
From the following information, calculate the solubility product of
Short Answer
Expert verified
The solubility product of is approximately .
Step by step solution
01
Understand the Concepts
The solubility product, denoted as , is an equilibrium constant for a solid substance dissolving in an aqueous solution. In this scenario, we want to determine for . The provided half-reactions and standard electrode potentials will help us calculate this value.
02
Write the Relevant Equations
We have two half-reactions: 1. 2. . We need the net equation for the dissolution of into and ions: .
03
Determine the Cell Potential
To find the , we need to use the Nernst equation, which relates the cell potential to the equilibrium constant ( ). Identify the anode and cathode reactions:- Reaction 1 is the anode with .- Reaction 2 is the cathode with .Calculate the overall cell potential: .
04
Calculate the Solubility Product
Use the equation , where (the number of moles of electrons), (Faraday's constant), (universal gas constant), and is the temperature (usually 298 K for standard conditions). Rework to find : . Substitute the known values to get . Evaluating this gives .
05
Compute and Verify the Value
Calculate the value based on the expression from the previous step: . Recheck calculations to ensure accuracy.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Electrochemistry
Electrochemistry involves the study of chemical processes that cause electrons to move. This movement is what creates electricity. In an electrochemical reaction, two half-reactions occur; one involves oxidation (loss of electrons) and the other reduction (gain of electrons). These reactions take place in two separate electrodes known as the anode and the cathode. The pushing or pulling of electrons across these electrodes is measured as an electric potential. Electrochemistry is central to processes like battery operation and electroplating.
Understanding electrochemistry helps us connect chemical reactions and the electrical energy they produce or consume. This is vital in various real-world applications, including energy storage and electrolysis.
Understanding electrochemistry helps us connect chemical reactions and the electrical energy they produce or consume. This is vital in various real-world applications, including energy storage and electrolysis.
Nernst Equation
The Nernst equation helps link the electrical potential of a cell to its chemical properties. This vital equation is where: in electrochemical reactions.
-
is the cell potential under non-standard conditions. -
is the standard cell potential. -
is the gas constant. -
is the temperature in Kelvin. -
is the number of moles of electrons. -
is Faraday's constant. -
is the reaction quotient.
Half-Reaction
A half-reaction is a part of the overall redox reaction, focusing on either the oxidation or reduction part. Each half-reaction shows the transfer of electrons. For example:
- Oxidation half-reaction:
- Reduction half-reaction:
Standard Electrode Potential
The standard electrode potential is the voltage developed by a cell under standard conditions (1 M concentration, 1 atm pressure, and usually at 25°C). It's a measure of the tendency of a chemical species to be reduced, and it's essential in comparing the reactivity of different electrodes. For example, the standard electrode potential for:
is 0.80 V is 0.07 V