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Chapter 18: Problem 33

Calculate the standard potential of the cell consisting of the \(\mathrm{Zn} / \mathrm{Zn}^{2+}\) half-cell and the \(\mathrm{SHE}\). What will the emf of the cell be if \(\left[\mathrm{Zn}^{2+}\right]=0.45 \mathrm{M}, \mathrm{P}_{\mathrm{H}_{2}}=\) \(2.0 \mathrm{~atm},\) and \(\left[\mathrm{H}^{+}\right]=1.8 \mathrm{M} ?\)

Short Answer

Expert verified
The standard potential of the cell is 0.76 V and the emf of the cell under the given conditions is approximately 0.99 V.

Step by step solution

01

Determine the Standard Reduction Potentials

Firstly, note the standard reduction potentials from a standard reduction potentials table. This table lists the potentials of various half-cells when they gain electrons (undergo reduction). Note that the standard reduction potential of the SHE is defined as \(0~V\) and the standard reduction potential of the Zn/Zn2+ half-cell is \(-0.76~V\).
02

Calculate the Standard Potential of the Cell

Next, calculate the overall standard cell potential, \(E^°_{cell}\), using the equation \(E^°_{cell} = E^°_{cathode} - E^°_{anode}\). The zinc half-cell acts as the anode (the site of oxidation), and the hydrogen half-cell acts as the cathode (the site of reduction). So, we get \(E^°_{cell} = 0~V - (-0.76~V) = 0.76~V\).
03

Use the Nernst Equation to Find the emf

Finally, we need to find the emf under the given conditions. For that, use the Nernst equation: \(E_{cell} = E^°_{cell} - \(\dfrac{0.0592}{n}\) \log \dfrac {[Zn^{2+}]}{[H^+]^2{(PH_2)}^{1/2} }\), where \(n\) is the number of electrons transferred in the half-reaction, which is 2 in this case. So, we can substitute all the given values: \(E_{cell} = 0.76~V - \(\dfrac{0.0592}{2}\)\log \dfrac {0.45~M}{(1.8~M)^2(2.0~atm)^{1/2} }\).
04

Calculate the emf

Perform the calculations inside the logarithm and then evaluate the Nernst equation. The log term can be simplified into the log of a dimensionless constant, thus removing any effects of units. After calculation, it's found to be approximately 0.99 V.

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Most popular questions from this chapter

In recent years there has been much interest in electric cars. List some advantages and disadvantages of electric cars compared to automobiles with internal combustion engines.

From the following information, calculate the solubility product of AgBr: \(\mathrm{Ag}^{+}(a q)+e^{-} \longrightarrow \operatorname{Ag}(s) \quad E^{\circ}=0.80 \mathrm{~V}\) \(\operatorname{AgBr}(s)+e^{-} \longrightarrow \operatorname{Ag}(s)+\operatorname{Br}^{-}(a q) \quad E^{\circ}=0.07 \mathrm{~V}\)

A piece of magnesium ribbon and a copper wire are partially immersed in a \(0.1 M \mathrm{HCl}\) solution in a beaker. The metals are joined externally by another piece of metal wire. Bubbles are seen to evolve at both the \(\mathrm{Mg}\) and \(\mathrm{Cu}\) surfaces. (a) Write equations representing the reactions occurring at the metals. (b) What visual evidence would you seek to show that \(\mathrm{Cu}\) is not oxidized to \(\mathrm{Cu}^{2+} ?\) (c) At some stage, NaOH solution is added to the beaker to neutralize the HCl acid. Upon further addition of \(\mathrm{NaOH}\), a white precipitate forms. What is it?

Gold will not dissolve in either concentrated nitric acid or concentrated hydrochloric acid. However, the metal does dissolve in a mixture of the acids (one part \(\mathrm{HNO}_{3}\) and three parts \(\mathrm{HCl}\) by volume \()\) called aqua regia. (a) Write a balanced equation for this reaction. (Hint: Among the products are \(\mathrm{HAuCl}_{4}\) and \(\mathrm{NO}_{2} .\) ) (b) What is the function of \(\mathrm{HCl} ?\)

A galvanic cell is constructed by immersing a piece of copper wire in \(25.0 \mathrm{~mL}\) of a \(0.20 \mathrm{M} \mathrm{CuSO}_{4}\) solution and a zinc strip in \(25.0 \mathrm{~mL}\) of a \(0.20 \mathrm{M} \mathrm{ZnSO}_{4}\) solution. (a) Calculate the emf of the cell at \(25^{\circ} \mathrm{C}\) and predict what would happen if a small amount of concentrated \(\mathrm{NH}_{3}\) solution were added to (i) the \(\mathrm{CuSO}_{4}\) solution and (ii) the \(\mathrm{ZnSO}_{4}\) solution. Assume that the volume in each compartment remains constant at \(25.0 \mathrm{~mL}\). (b) In a separate experiment, \(25.0 \mathrm{~mL}\) of \(3.00 \mathrm{M} \mathrm{NH}_{3}\) are added to the \(\mathrm{CuSO}_{4}\) so- lution. If the emf of the cell is \(0.68 \mathrm{~V},\) calculate the formation constant \(\left(K_{\mathrm{f}}\right)\) of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\)
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