Calculate E^∘, E, and ΔG for the following cell reactions....

Key Concepts

Standard Electrode Potential

Standard electrode potentials are the potentials associated with individual half-cell reactions measured under standard conditions (1 M concentration for solutions, 1 atm pressure for gases, and usually at 25°C). These values are used as reference points to calculate the overall cell potential for an electrochemical reaction and to assess the feasibility of redox processes.

Cell Potential

The cell potential, or electromotive force (EMF), is the voltage difference between the two electrodes in an electrochemical cell. It indicates the ability of the cell to produce an electric current upon connecting an external circuit. The cell potential under standard conditions (E°) can be adjusted for non-standard concentrations using the Nernst equation to yield the actual cell potential (E).

Nernst Equation

The Nernst equation provides a quantitative relationship between the cell potential, the standard cell potential, temperature, the number of electrons transferred in the redox process, and the reaction quotient (Q). It allows for the calculation of the cell potential under non-standard conditions by accounting for the concentration (or activity) of the reactants and products.

Reaction Quotient (Q)

The reaction quotient is the ratio of the concentrations (or activities) of the products to the reactants, each raised to the power of their stoichiometric coefficients in the balanced chemical equation. This value is crucial in the Nernst equation as it helps to determine how far a reaction has proceeded from equilibrium and how the actual cell potential deviates from the standard cell potential.

Gibbs Free Energy

Gibbs free energy (?G) is a thermodynamic quantity that indicates the maximum reversible work a system can perform at constant temperature and pressure. In the context of electrochemistry, it is directly related to the cell potential (through the equation ?G = -nFE, where n is the number of electrons and F is Faraday's constant), making it a key indicator of the spontaneity and energy efficiency of the cell reaction.

Transcript

00:01 For each one of the overall cell reactions that we are given in each part of this problem, we need to calculate the value of the standard cell potential, the non -standard cell potential, and the non -standard change in gibbs -free energy delta g.

00:16 Starting with the overall reaction that we are given in part a, we know that in order to find the standard cell potential, we need to first determine the two half reactions that are taking place and look up the values for their respective standard reduction potential.

00:32 We can see that solid magnesium is being oxidized into mg2 plus.

00:39 So when we look on the table for the reduction half reaction of mg2 plus plus two electrons going to mg, we should see that it has a standard reduction potential of negative 2 .37 volts.

00:52 We reverse it for the oxidation, so it is now positive 2 .37 volts.

00:57 And we also see that 10 is reduced from its 2 plus state to its solid state.

01:04 So if we add these two together, then we will get the overall cell potential at standard conditions.

01:13 We see that we cancel off two moles of electrons on each side, and we are left with the overall reaction that we are given in the problem.

01:28 And when we combine those two standard potentials together, we get the overall cell potentials.

01:34 Which is the first value that we need to calculate, and 2 .37 minus 0 .14 comes out to 2 .23 volts.

01:43 And now we use the nernsd equation to solve for the non -standard cell potential.

01:49 So we know that that non -standard cell potential is equal to a standard cell potential 2 .23 volts minus 0 .091 over n.

02:02 We saw that we canceled out two moles of electrons on each side of the reaction, so n is equal to two.

02:09 We multiply this by the log of q.

02:13 Based on the overall reaction and the aqueous species present in that reaction, we can see that q is equal to the concentration of mg2 plus divided by the concentration of ends.

02:31 And we are given the values for each one of those concentrations.

02:36 So we plug them into that q expression in the logarithm.

02:42 And so that is equal to 0 .045 molar for the concentration of mg2 plus divided by 0 .035 molar for the concentration of sn2 plus.

02:58 We plug that all in, and we should find that the nonstandard cell.

03:03 Potential still comes out to 2 .23 volts.

03:08 And now to solve for the nonstandard change in gibbs free energy, we use this nonstandard cell potential within the equation delta g equals negative nfe.

03:21 So delta g is equal to negative n, we said, again, was two moles of electrons.

03:29 F is faraday's constant, which is 96 ,485...

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