Four voltaic cells are set up. In each, one half-cell...

Four voltaic cells are set up. In each, one half-cell contains a standard hydrogen electrode. The second half-cell is one of the following: (i) $\mathrm{Cr}^{3+}(\text { aq, } 1.0 \mathrm{M}) | \mathrm{Cr}(\mathrm{s})$ (ii) $\mathrm{Fe}^{2+}(\text { aq, } 1.0 \mathrm{M}) | \mathrm{Fe}(\mathrm{s})$ (iii) $\mathrm{Cu}^{2+}(\mathrm{aq}, 1.0 \mathrm{M}) | \mathrm{Cu}(\mathrm{s})$ (iv) $\mathrm{Mg}^{2+}(\mathrm{aq}, 1.0 \mathrm{M}) | \mathrm{Mg}(\mathrm{s})$ (a) In which of the voltaic cells does the hydrogen electrode serve as the cathode? (b) Which voltaic cell produces the highest potential? Which produces the lowest potential?

Four voltaic cells are set up. In each, one half-cell contains a standard hydrogen electrode. The second half-cell is one of the following:
(i) $\mathrm{Cr}^{3+}(\text { aq, } 1.0 \mathrm{M}) | \mathrm{Cr}(\mathrm{s})$
(ii) $\mathrm{Fe}^{2+}(\text { aq, } 1.0 \mathrm{M}) | \mathrm{Fe}(\mathrm{s})$
(iii) $\mathrm{Cu}^{2+}(\mathrm{aq}, 1.0 \mathrm{M}) | \mathrm{Cu}(\mathrm{s})$
(iv) $\mathrm{Mg}^{2+}(\mathrm{aq}, 1.0 \mathrm{M}) | \mathrm{Mg}(\mathrm{s})$
(a) In which of the voltaic cells does the hydrogen electrode serve as the cathode?
(b) Which voltaic cell produces the highest potential? Which produces the lowest potential?

Key Concepts

Voltaic Cell

A voltaic cell is an electrochemical cell that generates electrical energy from spontaneous redox reactions occurring between its two half-cells. Each half-cell consists of an electrode in contact with an electrolyte, and the cell's overall voltage is determined by the difference in the standard electrode potentials of the two electrodes.

Standard Electrode Potential

The standard electrode potential is a measure of the tendency of a chemical species to be reduced by gaining electrons under standard conditions. It is expressed in volts relative to the standard hydrogen electrode, which is assigned a potential of 0 V. Comparing these potentials allows us to predict the direction of electron flow in a cell.

Electrode Designation (Anode and Cathode)

In any electrochemical cell, the cathode is the electrode at which reduction occurs and the anode is where oxidation takes place. The electrode with the higher (more positive) reduction potential will tend to act as the cathode, while the other serves as the anode. Determining which electrode plays which role is crucial for establishing the cell’s operation and calculating its voltage.

Redox Reaction and Half-Cell Reactions

Redox reactions involve the transfer of electrons between species, where reduction (gain of electrons) occurs at the cathode and oxidation (loss of electrons) occurs at the anode. Each half-cell reaction can be analyzed using its standard electrode potential to determine the cell's overall reaction and electromotive force.

Cell EMF Calculation and Comparison

The electromotive force (EMF) of a cell is calculated by taking the difference between the reduction potentials of the cathode and anode. Comparing the standard reduction potentials of different electrodes, such as those involved in the given problem, helps determine which configuration produces the highest or lowest cell voltage and which electrode will serve as the cathode in the cell.

Transcript

0:00 All right.

00:01 Hello.

00:01 Today we're going to be dealing with these four half reactions and how they will react in the presence of a hydrogen electrode or a reference electrode.

00:10 Now, hydrogen electrode is special because it has a zero potential.

00:14 We use it as a reference compared to other electrodes.

00:17 So for our first consideration, we want to know with which of these four reactions will hydrogen be the cathode? now, if this is the cathode, that means that it is getting reduced, which means that the other substances are being oxidized.

00:35 So, if we consider our e not total is going to be, if hydrogen is getting reduced, it's e not hydrogen minus our e not metal.

00:50 Right? and we need our e not total to be positive for the reaction to occur, which means that our e not total, are if this is zero, right? that means that our e not metal should be less than zero, right? that way the negative will be positive.

01:10 And that applies to here, here, and here.

01:14 Or in essence, the three chemicals, though, the three half reactions that'll act as an anode and make hydrogen act as a cathode are cr3 plus, sorry, technical difficulties.

01:28 Cr3 plus, fe2 plus, and mg2 plus.

01:37 Perfect.

01:39 Now we want to look at which cell will produce the highest potential.

01:45 So we have two considerations, either hydrogen as an anode or hydrogen as a cathode.

01:52 Now, the anode will only happen with copper, and that will have a total potential of 0 .337.

01:57 We know that because from our, because hydrogen is zero...

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