Consider the following galvanic cell: Calculate the Ks p value for Ag2 SO4(s) . Note that to obt

Consider the following galvanic cell: Calculate the Ks p...

Key Concepts

Dissolution Equilibrium

Dissolution equilibrium refers to the state where a sparingly soluble ionic compound is in dynamic equilibrium with its ions in solution. For a salt like Ag2SO4, this equilibrium is represented by its dissolution into silver and sulfate ions, and the Ksp expression is derived from the concentrations of these ions when the solution is saturated.

Nernst Equation

The Nernst equation quantitatively relates the electrode potential of a half-cell to the concentrations (activities) of the chemical species involved. It is particularly useful in electrochemistry for determining the relationship between cell potential and ion concentration, and thereby allows for the calculation of equilibrium constants like the Ksp from measured cell voltages.

Galvanic Cell

A galvanic cell is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two half-cells connected by a salt bridge, where oxidation occurs at the anode and reduction at the cathode, and the resulting potential difference can be used to determine various thermodynamic properties of the reactions involved.

Solubility Product Constant (Ksp)

The solubility product constant, Ksp, is a specific equilibrium constant that applies to the dissolution of a sparingly soluble compound. It represents the product of the molar concentrations of the constituent ions, each raised to the power corresponding to its coefficient in the balanced dissolution equation, and is used to quantify the extent of salt dissolution in a solution.

Transcript

00:01 In this problem, we are given a diagram of a galvanic cell, and we are ultimately interested in determining the value of ksp for ag2 -so -4.

00:14 And when we talk about ksp for the solid species ag2 -s -o -4, when we dissolve this solid inside a solution, it reversibly goes to its aqueous ions.

00:33 So that's 2 ag plus aqueous plus s .o42 minus aqueous.

00:48 And the solubility constant for this process, ksp, this is equal to the equilibrium constant of this reversible reaction.

00:58 And so we know that when we don't include the solid species, that just comes out to the concentration of ag plus ions squared.

01:09 Times the concentration of so4 -2 -1.

01:18 And based on what we are given in the problem statement, we can find the concentration of ag -plus ions, and we can use the stoichiometric ratio of two ag -plus ions to one so -4 -2 -minus ions to find the concentration of so -4 -2 -minus, and then we can plug in both of those concentrations into this expression to determine ksp.

01:43 So the first thing that we need to do to ultimately find ksp is solve for the concentration of ag plus ions.

01:50 We can do that using the galvanic cell that we are given.

01:55 We can see based on the diagram that these are the two half reactions that are taking place.

02:02 And when we look at their standard reduction potentials, we see that the reduction of ag plus to solid silver has a larger standard reduction potential.

02:12 So that will undergo reduction so that the cell potential of the scalvanic cell can remain positive.

02:18 So we flip that top half reaction to give us the oxidation of solid lead into pb2 plus.

02:26 And so when we flip that, that negative 0 .13 becomes positive 0 .13.

02:31 So now we can combine these two together to get the overall cell reaction.

02:36 We have to multiply that second equation by two electrons so we can cancel out a total of two electrons on each side.

02:43 Side.

02:44 We are left with solid lead plus two ag plus aqueous going to pb 2 plus aqueous plus two solid silver.

03:10 And now to find the cell potential at standard conditions for this galvanic cell, we add those two potentials together, 0 .13 plus 0 .80.

03:24 We see that comes out to 0 .93 volts.

03:30 And now based on the diagram, we see that the measurement is 0 .83 volts...

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