Justify each answer by appropriate calculations. Assume that...

Justify each answer by appropriate calculations. Assume that each reaction occurs at standard electrochemical conditions. (See directions preceding Exercise 58.) The element ytterbium forms both $2+$ and $3+$ cations in aqueous solution. $E^{0}=-2.797 \mathrm{~V}$ for $\mathrm{Yb}^{2+} / \mathrm{Yb}(\mathrm{s})$, and $-2.267 \mathrm{~V}$ for $\mathrm{Yb}^{3+} / \mathrm{Yb}(\mathrm{s})$. What is the standard-state reduction potential for the $\mathrm{Yb}^{3+} / \mathrm{Yb}^{2+}$ couple?

Justify each answer by appropriate calculations. Assume that each reaction occurs at standard electrochemical conditions.
(See directions preceding Exercise 58.) The element ytterbium forms both $2+$ and $3+$ cations in aqueous solution. $E^{0}=-2.797 \mathrm{~V}$ for $\mathrm{Yb}^{2+} / \mathrm{Yb}(\mathrm{s})$, and $-2.267 \mathrm{~V}$ for
$\mathrm{Yb}^{3+} / \mathrm{Yb}(\mathrm{s})$. What is the standard-state reduction potential for the $\mathrm{Yb}^{3+} / \mathrm{Yb}^{2+}$ couple?

Key Concepts

Standard Electrode Potentials

Standard electrode potentials represent the inherent tendency of a chemical species to be reduced under standard conditions (1 M concentration, 1 atm pressure, and 25°C). These potentials are established relative to a standard hydrogen electrode and are useful for comparing the oxidizing or reducing strengths of various half-reactions. They are a fundamental aspect of electrochemistry, allowing one to predict the direction of redox reactions and calculate cell potentials.

Half-Reactions in Electrochemistry

In redox chemistry, reactions are split into two half-reactions—the oxidation half and the reduction half—which separately show the loss or gain of electrons. This division helps in balancing the charge and mass in redox reactions and is critical when combining different redox couples, especially when the number of electrons exchanged in each half-reaction is not the same.

Relationship between Electrode Potentials and Gibbs Free Energy

The connection between electrode potentials and Gibbs free energy is given by the equation ?G = -nFE°, where ?G is the change in Gibbs free energy, n is the number of electrons transferred, F is the Faraday constant, and E° is the standard electrode potential. This relationship is essential for converting between potential differences and the thermodynamic feasibility of the reaction, enabling calculations of overall reaction spontaneity.

Standard Electrochemical Conditions

Standard electrochemical conditions refer to the set of agreed-upon conditions (1 M concentration for solutions, 1 atm pressure for gases, and 25°C temperature) under which electrode potentials are measured. These conditions provide a common reference point for comparing redox potentials and ensure consistency across different experiments and calculations.

Transcript

00:01 So in this question we've been asked to confirm whether or not certain reactions okay.

00:06 So for an electrolytic cell, electro -letic cell, we have to appreciate that we can check whether a reaction occurs or is spontaneous by looking at the standard cell electrode, the standard cell potential.

00:23 So if this is greater than zero, we can confirm that that reaction is spontaneous and will okay but if we check the cell potential and we find that it is less than zero it means that that reaction is not spontaneous probably the reverse is going to okay so for an electrolytic cell we have to appreciate that there are three main components that is the anode this is where oxidation occurs and we've got the cathode where reduction occurs reduction and we also have an so for us to determine the cell potential, all we have to do is to look at what is happening at the electrodes.

01:13 We write the half equations for the anode and the cathode and we have the electrode potential for the individual electrodes.

01:25 Then we sum them up to determine the overall cell potential.

01:30 Then we compare that against the zero and check with the or not it is greater than the result.

01:34 Than zero.

01:36 So for this reaction, say we've got the reduction, the reduction reaction and oxidation reaction in which for reduction we've got yp 3 plus being reduced to yp.

01:52 For us to balance this, this has to be three electrons and we have an oxidation reaction where yp is being oxidized to form 2 plus and we're going to have two electrons.

02:04 So if if we are looking at this, say we want to balance this out.

02:10 Remember we have to cancel out the electrons in the overall cell reaction...

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