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Chapter 20: Problem 9

Consider the half-reaction $\mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)$ (a) Which of the lines in the following diagram indicates how the reduction potential varies with the concentration of \(\mathrm{Ag}^{+}(a q) ?(\mathbf{b})\) What is the value of \(E_{\text {red }}\) when \(\log \left[\mathrm{Ag}^{+}\right]=0 ?\)

Short Answer

Expert verified
The reduction potential varies linearly with the log of the Ag+ concentration, as shown by the equation \(E = E^0 - \frac{2.303 RT}{F} \log{[\mathrm{Ag}^+]}\). When \(\log{[\mathrm{Ag}^+]} = 0\), the reduction potential is equal to the standard reduction potential (\(E^0\)).

Step by step solution

01

The Nernst equation allows us to determine the reduction potential of half-reactions at various ion concentrations. It is expressed as: \[E = E^0 - \frac{2.303 RT}{nF} \log{Q}\] where E is the potential, \(E^0\) is the standard reduction potential, R is the gas constant, T is the temperature, n is the number of electrons transferred, F is the Faraday constant, and Q is the reaction quotient. #Step 2: Applying the Nernst Equation to the Given Half-Reaction#

The given half-reaction is: \(\mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)\). In this half-reaction, only one electron is transferred (n = 1). The reaction quotient (Q) is equal to the concentration of Ag+ ions. We can rewrite the Nernst equation for this specific reaction as: \[E = E^0 - \frac{2.303 RT}{F} \log{[\mathrm{Ag}^+]}\] #Step 3: Analyzing the Relationship between Reduction Potential and Ag+ Concentration#
02

As seen in the equation from step 2, \(E = E^0 - \frac{2.303 RT}{F} \log{[\mathrm{Ag}^+]}\), the reduction potential (E) is linearly dependent on the log of the Ag+ concentration. #Step 4: Calculating the Reduction Potential When log[Ag+] = 0#

When log[Ag+] = 0, the Nernst equation becomes: \[E = E^0 - \frac{2.303 RT}{F} \times 0\] Since multiplying by zero eliminates the second term, this simplifies to: \[E = E^0\] So when log[Ag+] = 0, the reduction potential is equal to the standard reduction potential (\(E^0\)).

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Most popular questions from this chapter

During a period of discharge of a lead-acid battery, \(300 \mathrm{~g}\) of \(\mathrm{PbO}_{2}(s)\) from the cathode is converted into \(\mathrm{PbSO}_{4}(s)\). (a) What mass of \(\mathrm{Pb}(s)\) is oxidized at the anode during this same period? (b) How many coulombs of electrical charge are transferred from \(\mathrm{Pb}\) to \(\mathrm{PbO}_{2}\) ?

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