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Chapter 20: Problem 73

(a) What happens to the emf of a battery as it is used? Why does this happen? (b) The AA-size and D-size alkaline batteries are both \(1.5-\mathrm{V}\) batteries that are based on the same electrode reactions. What is the major difference between the two batteries? What performance feature is most affected by this difference?

Short Answer

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(a) As a battery is used, its emf (electromotive force) gradually decreases. This occurs due to the decrease in the concentration of ions in the electrolyte and buildup of product ions, which create an internal resistance that opposes the flow of electrons. (b) The major difference between AA-size and D-size alkaline batteries, both providing 1.5 V, is their size and capacity. D-size batteries have a larger size, which allows them to store more energy in the form of chemical reactants. The performance feature most affected by this difference is the battery life. D-size batteries have a longer battery life and higher energy capacity compared to AA-size batteries due to their increased size and storage capacity.

Step by step solution

01

Understanding emf changes in a battery as it is used

Emf, or electromotive force, is the energy provided by a cell or battery per unit charge that flows through it. As a battery is used, its emf gradually decreases. This mainly happens because of the decrease in the concentration of ions in the electrolyte and buildup of the product ions that create an internal resistance within the battery. This internal resistance opposes the flow of electrons, causing a decrease in the emf.
02

Identifying the major difference between AA-size and D-size batteries

Both AA-size and D-size alkaline batteries provide the same voltage (1.5 V) and are based on the same electrode reactions. The major difference between them lies in their size and capacity. D-size batteries are larger than AA-size batteries, allowing them to store more energy in the form of chemical reactants.
03

Describing the performance feature most affected by the difference

The performance feature most affected by the size difference between AA-size and D-size batteries is the battery life. As the capacity of a D-size battery is higher compared to that of an AA-size battery, it can deliver the same amount of power at a constant voltage for a longer time before being fully discharged. In other words, D-size batteries have a longer battery life and higher energy capacity compared to AA-size batteries due to their increased size and storage capacity.

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Most popular questions from this chapter

Mercuric oxide dry-cell batteries are often used where a highenergy density is required, such as in watches and cameras. The two half-cell reactions that occur in the battery are $$ \begin{aligned} \mathrm{HgO}(s)+\mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} & \longrightarrow \mathrm{Hg}(l)+2 \mathrm{OH}^{-}(a q) \\ \mathrm{Zn}(s)+2 \mathrm{OH}^{-}(a q) & \longrightarrow \mathrm{ZnO}(s)+\mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} \end{aligned} $$ (a) Write the overall cell reaction. (b) The value of \(E_{\text {red }}^{\circ}\) for the cathode reaction is \(+0.098 \mathrm{~V} .\) The overall cell potential is \(+1.35 \mathrm{~V}\). Assuming that both half-cells operate under standard conditions, what is the standard reduction potential for the anode reaction? (c) Why is the potential of the anode reaction different than would be expected if the reaction occurred in an acidic medium?

Consider a redox reaction for which \(E^{\circ}\) is a negative number. (a) What is the sign of \(\Delta G^{\circ}\) for the reaction? (b) Will the equilibrium constant for the reaction be larger or smaller than \(1 ?\) (c) Can an electrochemical cell based on this reaction accomplish work on its surroundings? [Section 20.5\(]\)

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