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Chapter 20: Problem 58

(a) A voltaic cell is constructed with all reactants and products in their standard states. Will this condition hold as the cell operates? Explain. (b) Can the Nernst equation be used at temperatures other than room temperature? Explain. (c) What happens to the emf of a cell if the concentrations of the products are increased?

Short Answer

Expert verified
(a) No, the standard state condition will not hold as the cell operates. As reactants are consumed and products are generated, concentrations change, and the cell potential will decrease as the reaction progresses toward equilibrium. (b) Yes, the Nernst equation can be used at temperatures other than room temperature. Since the temperature appears explicitly in the equation, it can be used to calculate the cell potential at any given temperature by substituting the appropriate value for T. (c) As the product concentrations increase, the emf of a cell will decrease. This is because an increase in product concentrations leads to an increase in the reaction quotient Q, causing a decrease in cell potential (E) according to the Nernst equation.

Step by step solution

01

(a) Explanation of standard state condition in a voltaic cell

A standard state is defined as a situation where the concentration of each reactant and product is at 1 M, the pressure of gases is at 1 atm, and the temperature is 25掳C (298 K). However, as the voltaic cell operates, the concentrations of reactants and products will change. Specifically, reactants will be consumed and products will be generated. Hence, the standard state condition will not hold as the cell operates. The cell potential will ultimately decrease as the reaction progresses toward equilibrium.
02

(b) Nernst equation and its applicability at different temperatures

The Nernst equation is a mathematical relationship that can be used to determine the cell potential at non-standard conditions. It is given by: \(E = E掳 - \frac{RT}{nF} \ln Q\) Where E is the cell potential, E掳 is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of electrons transferred in the redox reaction, F is the Faraday's constant, and Q is the reaction quotient. The Nernst equation can be used at temperatures other than room temperature (298 K). Since the temperature appears explicitly in the equation, it can be used to calculate the cell potential at any given temperature by substituting the appropriate value for T.
03

(c) Effect of product concentration on the emf of a cell

As the product concentrations increase, the reaction quotient (Q) in the Nernst equation will also increase. According to the Nernst equation: \(E = E掳 - \frac{RT}{nF} \ln Q\) An increase in Q will lead to an increase in the natural logarithm term (\(\ln Q\)), which in turn will increase the entire term\(\frac{RT}{nF} \ln Q\). Since this term is subtracted from the standard cell potential (E掳), an increase in the product concentrations will result in a decrease in the cell potential (E). Therefore, the emf of a cell will decrease when the concentrations of the products are increased.

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Most popular questions from this chapter

The hydrogen-oxygen fuel cell has a standard emf of \(1.23 \mathrm{~V}\). What advantages and disadvantages are there to using this device as a source of power, compared to a 1.55-V alkaline battery?

During a period of discharge of a lead-acid battery, \(402 \mathrm{~g}\) of \(\mathrm{Pb}\) from the anode is converted into \(\mathrm{PbSO}_{4}(s) .\) What mass of \(\mathrm{PbO}_{2}(s)\) is reduced at the cathode during this same period?

A voltaic cell similar to that shown in Figure \(20.5\) is constructed. One electrode compartment consists of an aluminum strip placed in a solution of \(\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\), and the other has a nickel strip placed in a solution of \(\mathrm{NiSO}_{4}\). The overall cell reaction is $$ 2 \mathrm{Al}(s)+3 \mathrm{Ni}^{2+}(a q) \longrightarrow 2 \mathrm{Al}^{3+}(a q)+3 \mathrm{Ni}(s) $$ (a) What is being oxidized, and what is being reduced? (b) Write the half-reactions that occur in the two electrode compartments. (c) Which electrode is the anode, and which is the cathode? (d) Indicate the signs of the electrodes. (e) Do electrons flow from the aluminum electrode to the nickel electrode, or from the nickel to the aluminum? (f) In which directions do the cations and anions migrate through the solution? Assume the \(\mathrm{Al}\) is not coated with its oxide.

Gold exists in two common positive oxidation states, \(+1\) and \(+3\). The standard reduction potentials for these oxidation states are $$ \begin{aligned} \mathrm{Au}^{+}(a q)+\mathrm{e}^{-}-\longrightarrow \mathrm{Au}(s) & E_{\mathrm{red}}^{\circ}=+1.69 \mathrm{~V} \\ \mathrm{Au}^{3+}(a q)+3 \mathrm{e}^{-}-\ldots \mathrm{Au}(s) & E_{\mathrm{red}}^{\circ}=+1.50 \mathrm{~V} \end{aligned} $$ (a) Can you use these data to explain why gold does not tarnish in the air? (b) Suggest several substances that should be strong enough oxidizing agents to oxidize gold metal. (c) Miners obtain gold by soaking goldcontaining ores in an aqueous solution of sodium cyanide. A very soluble complex ion of gold forms in the aqueous solution because of the redox reaction $$ \begin{array}{r} 4 \mathrm{Au}(s)+8 \mathrm{NaCN}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)-\longrightarrow \\ 4 \mathrm{Na}\left[\mathrm{Au}(\mathrm{CN})_{2}\right](a q)+4 \mathrm{NaOH}(a q) \end{array} $$ What is being oxidized, and what is being reduced, in this reaction? (d) Gold miners then react the basic aqueous product solution from part (c) with Zn dust to get gold metal. Write a balanced redox reaction for this process. What is being oxidized, and what is being reduced?

(a) Under what circumstances is the Nernst equation applicable? (b) What is the numerical value of the reaction quotient, \(Q\), under standard conditions? (c) What happens to the emf of a cell if the concentrations of the reactants are increased?
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