Determine the values of ΔG^∘ for the following reactions carried out in voltaic cells. (a) 2 Al(

Determine the values of ΔG^∘ for the following reactions...

Determine the values of $\Delta G^{\circ}$ for the following reactions carried out in voltaic cells. (a) $2 \mathrm{Al}(\mathrm{s})+3 \mathrm{Cu}^{2+}(\mathrm{aq}) \longrightarrow 2 \mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{Cu}(\mathrm{s})$ (b) $\mathrm{O}_{2}(\mathrm{g})+4 \mathrm{I}^{-}(\mathrm{aq})+4 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow$ $2 \mathrm{H}_{2} \mathrm{O}(1)+2 \mathrm{I}_{2}(\mathrm{s})$ (c) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})+14 \mathrm{H}^{+}(\mathrm{aq})+6 \mathrm{Ag}(\mathrm{s}) \longrightarrow$ $2 \mathrm{Cr}^{3+}(\mathrm{aq})+6 \mathrm{Ag}^{+}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{O}(1)$

Determine the values of $\Delta G^{\circ}$ for the following reactions carried out in voltaic cells.
(a) $2 \mathrm{Al}(\mathrm{s})+3 \mathrm{Cu}^{2+}(\mathrm{aq}) \longrightarrow 2 \mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{Cu}(\mathrm{s})$
(b) $\mathrm{O}_{2}(\mathrm{g})+4 \mathrm{I}^{-}(\mathrm{aq})+4 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow$
$2 \mathrm{H}_{2} \mathrm{O}(1)+2 \mathrm{I}_{2}(\mathrm{s})$
(c) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})+14 \mathrm{H}^{+}(\mathrm{aq})+6 \mathrm{Ag}(\mathrm{s}) \longrightarrow$
$2 \mathrm{Cr}^{3+}(\mathrm{aq})+6 \mathrm{Ag}^{+}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{O}(1)$

Key Concepts

Electron Transfer Number (n)

The electron transfer number (n) represents the total number of moles of electrons exchanged in a redox reaction. It is critical in calculations involving electrochemical cells because it directly links the chemical reaction to electrical work, as seen in the relationship ?G° = -nFE°, where n quantifies the reaction stoichiometry in terms of electrons transferred.

Standard Electrode Potential

Standard electrode potential (E°) is the measure of the individual potential of a reversible electrode at standard conditions relative to a standard hydrogen electrode. This concept is central to electrochemistry because the difference in electrode potentials between two half-cells (E°cell) determines the driving force for electron flow in a voltaic cell. These potentials are essential for calculating the overall cell potential and subsequently the free energy change.

Faraday's Constant

Faraday's constant (F) is a fundamental constant that represents the electric charge per mole of electrons, approximately equal to 96485 coulombs per mole. It is used in electrochemical calculations to convert between amounts of electrical charge and the amount of substance involved in a redox reaction. This constant is integral in linking the electrical measurements (like cell potentials) to the thermodynamic quantity ?G°.

Standard Gibbs Free Energy Change

Standard Gibbs free energy change (?G°) is a thermodynamic quantity that indicates the maximum amount of work obtainable from a chemical process at constant temperature and pressure. It is directly related to the spontaneity of the reaction, with a negative ?G° indicating a spontaneous process under standard conditions. In the context of electrochemistry, ?G° is crucial for understanding how chemical energy is converted into electrical energy in electrochemical cells.

Voltaic (Galvanic) Cell

A voltaic cell, also known as a galvanic cell, is an electrochemical cell that converts chemical energy into electrical energy through a spontaneous redox reaction. These cells are fundamental in studying the relationship between redox potential and energy conversion, and they provide practical applications, such as batteries, where the cell reaction drives the flow of electrons through an external circuit.

Transcript

00:01 To answer this question, we need to know the relationship between delta g and e -cell standard.

00:07 And it's simply delta g standard will be equal to negative n, where n is the number of moles of electrons that are being transferred in the balanced chemical reaction, multiplied by f, which is faraday's constant, multiplied by e -cell standard.

00:23 The first chemical reaction is this one shown here.

00:26 To calculate e -cell standard, we simply need to look up the two reactions that can, two half reactions in the back of the book that can be combined to create this entire reaction, and then take the cathode potential minus the anode potential, the one that is being reduced, minus the one that is being oxidized.

00:50 And we get 2 .06, so 2 .016 volts.

00:54 So we'll use this with the six moles of electrons that are being transferred.

00:59 You can look at either the copper and see that it has, it needs two electrons to become copper solid.

01:06 Copper 2 plus needs two electrons to become copper solid.

01:09 And there are three of them, so that's the total of six.

01:12 Or we can look at aluminum and we'll get six.

01:17 And our delta g standard becomes negative 1 .17 times 10 to the 6 joules.

01:24 Here's our second half reaction.

01:25 We'll go to the back of the book and find, i'm sorry, our second entire reaction...