An electrochemical cell consists of a standard hydrogen electrode and a copper metal electrode.

An electrochemical cell consists of a standard hydrogen...

Key Concepts

Half-Cell Reactions

Half-cell reactions describe the individual oxidation and reduction processes occurring at the electrodes in an electrochemical cell. Understanding these reactions is necessary to determine which electrode undergoes oxidation and which undergoes reduction, and to calculate the cell potential by combining the individual electrode potentials.

Cell Potential Calculation

The overall cell potential is determined by taking the difference between the potentials of the cathode and the anode. This calculation often involves using the measured or standard electrode potentials along with adjustments using the Nernst equation to account for non-standard conditions, such as those due to ion concentrations controlled by solubility equilibria.

Saturated Solutions and Ion Concentration

In a saturated solution, the solute has reached its maximum concentration at a given temperature, and any additional solute remains undissolved. The equilibrium between the dissolved ions and the undissolved solid is characterized by the Ksp, allowing calculation of the concentration of ions present in the solution.

Solubility Product (Ksp)

The solubility product (Ksp) governs the solubility of sparingly soluble compounds in solution. It quantifies the product of the equilibrium concentrations of the ions, each raised to the power matching their coefficient in the equation. This constant is crucial when determining the ion concentration in a saturated solution, which directly impacts the electrode potential.

Nernst Equation

The Nernst equation is essential for calculating the electrode potential under non-standard conditions. It adjusts the standard electrode potential by factoring in the temperature, the number of electrons transferred in the reaction, and the activities or concentrations of the reacting species, offering a realistic depiction of how potential varies with conditions.

Standard Electrode Potential

Standard electrode potentials provide a reference by which the voltage of a half-cell reaction is measured under standard conditions (typically 1 M concentration, 1 atm pressure, and 25°C). These values are used as benchmarks to calculate the overall cell potential in an electrochemical cell when combined with the Nernst equation.

Electrochemical Cell

An electrochemical cell is a system that converts chemical energy into electrical energy through redox reactions. It comprises two electrodes immersed in electrolyte solutions, with each electrode serving as a site for oxidation or reduction. The overall cell potential is determined by the difference in these electrode potentials, driving the flow of electrons in the external circuit.

Transcript

00:01 In this problem, we are told that we have these two half reactions taking place within an electrochemical cell, and we want to determine what the overall cell potential is at 25 degrees celsius.

00:11 We are at non -standard conditions for the compartment of the cell that contains the copper metal, and so we first need to calculate what the cell potential is, and then relate that to the cell potential at standard conditions for the standard hydrogen, road half reaction in order to determine the overall cell potential.

00:35 So we are given a value for the solubility equilibrium constant ksp for cu -o -h -2.

00:42 So we can begin by writing out the solubility reaction of that corresponds to.

00:47 So we have c -u -o -h -2 as a solid, and it reversibly dissociates into c -u -2 -plus aqueous ions, and 2 oh minus aqueous ions.

01:09 And so we can write out the equilibrium expression that this corresponds to, which would be equal to the solubility equilibrium constant ksp.

01:19 Based on the aqueous species, that would just be equal to the concentration of cu2 plus times the concentration of oh minus squared.

01:31 We have values for ksp, and we are told that the concentration of naoh is 0 .10 molar, so that corresponds to the concentration of oh minus ions.

01:42 So we have everything that we need to solve for the concentration of co2 plus in the copper electrode compartment of this electrochemical cell.

01:52 So we can solve that by rearranging this equation to say that the concentration of co2 plus is equal to ksp divided by the concentration of oh2, minus squared.

02:11 And now we just plug in what we are given in the problem.

02:14 We were told that ksp is equal to 1 .6 times 10 to the negative 19.

02:22 And we divide this by that 0 .10 molar concentration of n -a -o -h, and we square it.

02:33 And so the concentration of cu to plus ions in aqueous solution comes out to 1 .6.

02:43 Times 10 to the negative 17th molar in that copper electrode portion of the electrochemical cell...

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