A galvanic cell is based on the following half-reactions at...

A galvanic cell is based on the following half-reactions at $25^{\circ} \mathrm{C} :$ $$\begin{array}{c}{\mathrm{Ag}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}} \\ {\mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}}\end{array}$$ Predict whether $\mathscr{E}_{\text{cell}}$ is larger or smaller than $\mathscr{E}^{\circ}_{\text{cell}}$ for the following cases. a. [Ag1] 5 1.0 a. $\left[\mathrm{Ag}^{+}\right]=1.0 M,\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]=2.0 M,\left[\mathrm{H}^{+}\right]=2.0 \mathrm{M}$ b. $\left[\mathrm{Ag}^{+}\right]=2.0 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]=1.0 M,\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}$

A galvanic cell is based on the following half-reactions at $25^{\circ} \mathrm{C} :$
$$\begin{array}{c}{\mathrm{Ag}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}} \\ {\mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}}\end{array}$$
Predict whether $\mathscr{E}_{\text{cell}}$ is larger or smaller than $\mathscr{E}^{\circ}_{\text{cell}}$ for the following cases.
a. [Ag1] 5 1.0
a. $\left[\mathrm{Ag}^{+}\right]=1.0 M,\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]=2.0 M,\left[\mathrm{H}^{+}\right]=2.0 \mathrm{M}$
b. $\left[\mathrm{Ag}^{+}\right]=2.0 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]=1.0 M,\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}$

Key Concepts

Reaction Quotient and Concentration Effects

The reaction quotient (Q) is the ratio of the concentrations (or activities) of the products to those of the reactants at any point in time. In the context of the Nernst equation, deviations in Q from unity (the standard state) indicate how far a system is from standard conditions. Varying the concentrations of the reactants and products alters Q, which in turn influences the cell potential; thus, understanding this relationship is critical for predicting whether the actual cell potential will be greater or smaller than the standard cell potential.

Nernst Equation

The Nernst equation quantitatively relates the electrode potential to its standard electrode potential, temperature, the number of electrons transferred, and the reaction quotient (which reflects the concentrations of reactants and products). This equation is essential in predicting how deviations from standard conditions, such as changes in concentration, affect the cell potential, thereby providing insight into non-standard operational behavior of the cell.

Standard Electrode Potential

Standard electrode potentials are measured under standard conditions (typically 1 M concentration, 1 atm pressure, and 25°C) and provide a reference for comparing the tendency of different redox couples to gain or lose electrons. They are intrinsic properties of the half-reactions and indicate how readily a half-cell will be reduced, serving as a baseline for calculating the overall cell potential.

Redox Half-Reactions

Redox half-reactions represent the separate processes of oxidation and reduction that occur at the electrodes of a galvanic cell. Each half-reaction shows the transfer of electrons, with one species losing electrons (oxidation) and another gaining electrons (reduction). Understanding these half-reactions is crucial for constructing the overall cell reaction and analyzing the flow of electrons in an electrochemical system.

Galvanic Cell

A galvanic cell is an electrochemical cell that derives electrical energy from spontaneous redox reactions occurring at its two electrodes. In these cells, oxidation and reduction reactions take place in separate half-cells, with electrons flowing through an external circuit from the anode (site of oxidation) to the cathode (site of reduction). This concept underpins much of electrochemistry, linking chemical energy to electrical energy.

Transcript

00:01 In this problem, we are given the two half reactions that take place in a galvanic cell, and we are also given different conditions for the concentrations of the aqueous species, and we want to predict whether the cell potential at non -standard conditions would be greater than or less than the cell potential at standard conditions.

00:24 This means that we need to use the inerts equation shown here in order to compare the cell potential at standard and non -standard.

00:31 Standard conditions.

00:33 So one of the components of the nertsd equation is reaction quotient q.

00:39 We are given information about the species concentrations and parts a and b of this problem.

00:44 That will allow us to determine the value of q.

00:47 And then the nerns d equation, along with that value of q, will help us to determine whether e at non -standard conditions will be greater than or smaller than e at standard conditions.

00:59 So these are the two half reactions that we are given.

01:01 And we can look up the values of their standard reduction potentials in the table.

01:06 And we know that since this is a galvanic cell, that the overall cell potential has to be positive.

01:12 So therefore, we flip the reaction that has a smaller value for its standard reduction potential, and that would be the first half reaction involving silver since 0 .80 is less than 1 .78.

01:26 So we take that bottom half reaction and we keep it as it is, and we reverse that top reaction, and we see that we need to multiply that top half reaction by two to cancel out two electrons on either side.

01:41 And when we do that, we get the overall equation taking place in this galvanic cell.

01:47 And now based on this equation, we can write out the reaction quotient q.

01:51 We know that the reaction quotient only involves aqueous species, and therefore solid and liquid species are not involved.

01:58 In the numerator of the reaction quotient, we examine the products of the overall equation.

02:05 For the products, we have liquid water, and since that is not aqueous, we cannot have it in concentration units, so we do not include it.

02:13 We have aqueous ag plus with a coefficient of 2, so we take the concentration of ag plus and square it.

02:21 For the denominator of the reaction quotient, you look at the reactants.

02:26 We have solid silver, so that does not.

02:29 Factor into the reaction quotient...

Please give Ace some feedback