A voltaic cell consists of a Pb / Pb^2+ half-cell and a Cu / Cu^2+ half-cell at 25^∘ C . The ini

A voltaic cell consists of a Pb / Pb^2+ half-cell and a Cu /...

A voltaic cell consists of a $\mathrm{Pb} / \mathrm{Pb}^{2+}$ half-cell and a $\mathrm{Cu} / \mathrm{Cu}^{2+}$ half-cell at $25^{\circ} \mathrm{C}$ . The initial concentrations of $\mathrm{Pb}^{2+}$ and $\mathrm{Cu}^{2+}$ are 0.0500 $\mathrm{M}$ and $1.50 \mathrm{M},$ respectively. $$ \begin{array}{l}{\text { a. What is the initial cell potential? }} \\ {\text { b. What is the cell potential when the concentration of } \mathrm{Cu}^{2+}} \\ {\text { has fallen to } 0.200 \mathrm{M} \text { ? }} \\ {\text { c. What are the concentrations of } \mathrm{Pb}^{2+} \text { and } \mathrm{Cu}^{2+} \text { when the cell }} \\ {\text { potential falls to } 0.35 \mathrm{v} \text { ? }}\end{array} $$

A voltaic cell consists of a $\mathrm{Pb} / \mathrm{Pb}^{2+}$ half-cell and a $\mathrm{Cu} / \mathrm{Cu}^{2+}$ half-cell at $25^{\circ} \mathrm{C}$ . The initial concentrations of $\mathrm{Pb}^{2+}$ and $\mathrm{Cu}^{2+}$ are 0.0500 $\mathrm{M}$ and $1.50 \mathrm{M},$ respectively.
$$
\begin{array}{l}{\text { a. What is the initial cell potential? }} \\ {\text { b. What is the cell potential when the concentration of } \mathrm{Cu}^{2+}} \\ {\text { has fallen to } 0.200 \mathrm{M} \text { ? }} \\ {\text { c. What are the concentrations of } \mathrm{Pb}^{2+} \text { and } \mathrm{Cu}^{2+} \text { when the cell }} \\ {\text { potential falls to } 0.35 \mathrm{v} \text { ? }}\end{array}
$$

Key Concepts

Reaction Quotient

The reaction quotient, denoted as Q, is a ratio that relates the concentrations of the products to those of the reactants at any point during a reaction. In the context of electrochemistry, Q is used within the Nernst equation to account for deviations from standard conditions, thereby influencing the observed cell potential.

Nernst Equation

The Nernst equation provides a quantitative relationship between the electrode potential of a half-cell and the concentrations (or activities) of the reacting species. It is used to determine the cell potential under non-standard conditions by incorporating the effect of reactant and product concentrations, temperature, and the number of electrons transferred in the reaction.

Concentration Effects on Cell Potential

Changes in ion concentration in an electrochemical cell directly affect the electrode potentials, as described by the Nernst equation. As the concentrations of the ions are altered due to the progression of the reaction or deliberate changes, the cell potential shifts accordingly. Understanding these effects is critical for analyzing and predicting the behavior of cells in varying conditions.

Voltaic Cell

A voltaic cell (or galvanic cell) is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two half-cells, each containing an electrode immersed in an electrolyte, where one electrode undergoes oxidation and the other reduction. These cells are fundamental devices for studying energy conversion and electron transfer mechanisms in chemistry.

Standard Reduction Potential

Standard reduction potentials are tabulated values that indicate the tendency of a chemical species to be reduced under standard conditions (1 M concentration, 1 atm pressure, 25°C). They serve as a reference for predicting the direction of electron flow in redox reactions and calculating the overall cell potential by comparing the potentials of the half-reactions occurring in the electrodes.

Transcript

00:01 Okay, so for the first question, it asks us what is the cell potential of this cell reaction.

00:16 And the equation we need to use to solve this is this equation, that is e equals to the standard state of the e minus 0 .592 divided by, sorry, which is the number of electrons transferred in this cell reaction.

00:37 And then times lachew.

00:39 Q here is the expression of the equilibrium expression of this cell reaction.

00:49 And now since we know, the standard cell potential should be the differences of these two half cell potential, which is 0 .34 voltage minus 0 .13 voltage minus 0 .13 voltage, and it is 0 .47 voltage.

01:18 Okay, and q here equals to the pb, the lead ions concentration divided by the copper ions concentration, okay? and of course, n equals to 2 in this question.

01:34 And by plugging all of these values you will find e should be 0 .51 voltage.

01:44 This is the first question.

01:49 And the second question is very similar, and it's also need to use this equation.

02:02 But differently, the copper concentration is changed to 0 .4.

02:13 And here again, by plugging these values, you have got the copper's constant, the final cell potential will be 0 .49 voltage.

02:27 Okay, and it should be noticed here, the lead ion's concentration didn't change in this question, it's still 0 .05 more.

02:39 The only thing changed is the copper's concentration, which is changed from 1 .5 more to 0 .2 more.

02:49 Okay, the last question i would say is the most difficult question among three.

02:56 And it told you that in the final state, that the cell potential is 0 .35 voltage...

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