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Chapter 20: Problem 65

A voltaic cell is constructed that uses the following reaction and operates at \(298 \mathrm{~K}\) : $$ \mathrm{Zn}(s)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Ni}(s) $$ (a) What is the emf of this cell under standard conditions? (b) What is the emf of this cell when $\left[\mathrm{Ni}^{2+}\right]=3.00 \mathrm{M}\( and \)\left[\mathrm{Zn}^{2+}\right]=0.100 \mathrm{M} ?(\mathbf{c})$ What is the emf of the cell when \(\left[\mathrm{Ni}^{2+}\right]=0.200 M\) and \(\left[\mathrm{Zn}^{2+}\right]=0.900 \mathrm{M} ?\)

Short Answer

Expert verified
(a) The emf of the cell under standard conditions is 0.513 V. (b) The emf of the cell when \([\mathrm{Ni}^{2+}]=3.00 \mathrm{M}\) and \([\mathrm{Zn}^{2+}]=0.100 \mathrm{M}\) is 0.557 V. (c) The emf of the cell when \([\mathrm{Ni}^{2+}]=0.200 M\) and \([\mathrm{Zn}^{2+}]=0.900 \mathrm{M}\) is 0.460 V.

Step by step solution

01

Find the standard reduction potentials

To determine the cell potential, first, look up the standard reduction potentials for both half-reactions: Zn^2+(aq) + 2e^− → Zn(s); \(E^⦵_{\text{red}}\) = −0.763 V Ni^2+(aq) + 2e^− → Ni(s); \(E^⦵_{\text{red}}\) = −0.250 V
02

Calculate the cell potential under standard conditions

Now, use the standard reduction potentials to determine the cell potential under standard conditions: \(E_{\text{cell}}^⦵\) = \(E_{\text{cathode}}^⦵\) - \(E_{\text{anode}}^⦵\) The cathode is where the reduction occurs (Ni^2+ is reduced to Ni), and the anode is where oxidation occurs (Zn is oxidized to Zn^2+). \(E_{\text{cell}}^⦵\) = (−0.250 V) - (−0.763 V) = 0.513 V So, the emf of the cell under standard conditions is 0.513 V.
03

Apply the Nernst Equation

To find the emf of the cell under non-standard conditions, we can apply the Nernst Equation: \(E_{\text{cell}}=E_{\text{cell}}^⦵-\frac{RT}{nF} \ln{Q}\) At 298 K, the simplified Nernst Equation is: \(E_{\text{cell}}=E_{\text{cell}}^⦵-\frac{0.0592}{n} \log{Q}\) In this case, n=2 since there are two electrons transferred in the reaction. Now, we can plug in the given concentrations for each of the conditions:
04

Cell potential with [Ni^2+]=3.00 M and [Zn^2+]=0.100 M

\(Q=\frac{[\text{Zn}^{2+}]}{[\text{Ni}^{2+}]}\) = \(\frac{0.100}{3.00}\) \(E_{\text{cell}}=0.513 - \frac{0.0592}{2}\log{\frac{0.100}{3.00}}\) = 0.513 + 0.0444 = 0.557 V The emf of the cell under these conditions is 0.557 V.
05

Cell potential with [Ni^2+]=0.200 M and [Zn^2+]=0.900 M

\(Q=\frac{[\text{Zn}^{2+}]}{[\text{Ni}^{2+}]}\) = \(\frac{0.900}{0.200}\) \(E_{\text{cell}}=0.513 - \frac{0.0592}{2}\log{\frac{0.900}{0.200}}\) = 0.513 - 0.0530 = 0.460 V The emf of the cell under these conditions is 0.460 V.

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Most popular questions from this chapter

Indicate whether each statement is true or false: (a) The anode is the electrode at which oxidation takes place. (b) A voltaic cell always has a positive emf. (c) A salt bridge or permeable barrier is necessary to allow a voltaic cell to operate.

(a) Aluminum metal is used as a sacrificial anode to protect offshore pipelines in salt water from corrosion. Why is the aluminum referred to as a "sacrificial anode"? (b) Looking in Appendix E, suggest what metal the pipelines could be made from in order for aluminum to be successful as a sacrificial anode.

A voltaic cell consists of a strip of cadmium metal in a solution of \(\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}\) in one beaker, and in the other beaker a platinum electrode is immersed in a NaCl solution, with \(\mathrm{Cl}_{2}\) gas bubbled around the electrode. A salt bridge connects the two beakers. (a) Which electrode serves as the anode, and which as the cathode? (b) Does the Cd electrode gain or lose mass as the cell reaction proceeds? (c) Write the equation for the overall cell reaction. (d) What is the emf generated by the cell under standard conditions?

(a) Based on standard reduction potentials, would you expect copper metal to oxidize under standard conditions in the presence of oxygen and hydrogen ions? (b) When the Statue of Liberty was refurbished, Teflon spacers were placed between the iron skeleton and the copper metal on the surface of the statue. What role do these spacers play?

(a) Which electrode of a voltaic cell, the cathode or the anode, corresponds to the higher potential energy for the electrons? (b) What are the units for electrical potential? How does this unit relate to energy expressed in joules?
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