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Chapter 13: Problem 18

A nickel-metal hydride rechargeable battery formerly used in laptop computers is based on the following chemistry: Cathode: $$ \mathrm{NiOOH}(s)+\mathrm{H}_{2} \mathrm{O}+\mathrm{e}^{-\frac{\text { discharge }}{\rightleftharpoons}} \mathrm{Ni}(\mathrm{OH})_{2}(s)+\mathrm{OH}^{-} $$ Anode: $$ \mathrm{MH}(s)+\mathrm{OH}^{-} \stackrel{\text { discharge }}{\rightleftharpoons} \mathrm{M}(s)+\mathrm{H}_{2} \mathrm{O}+\mathrm{e}^{-} $$ The anode material, \(\mathrm{MH}\), is a transition metal hydride or rare earth alloy hydride. Explain why the voltage remains nearly constant during the entire discharge cycle.

Short Answer

Expert verified
Voltage is constant due to solid-state equilibrium reactions at constant concentration.

Step by step solution

01

Understand Electrode Reactions

Begin by examining the electrode reactions provided. At the cathode, the reaction is \( \mathrm{NiOOH}(s)+\mathrm{H}_{2} \mathrm{O}+\mathrm{e}^{-} \rightarrow \mathrm{Ni}(\mathrm{OH})_{2}(s)+\mathrm{OH}^{-} \). At the anode, the reaction is \( \mathrm{MH}(s)+\mathrm{OH}^{-} \rightarrow \mathrm{M}(s)+\mathrm{H}_{2} \mathrm{O}+\mathrm{e}^{-} \). These reactions involve solid-state reactants and products, which are critical in analyzing the voltage behavior.
02

Evaluate Reaction Type and Implications

Notice that both reactions are equilibrium reactions with solids on both sides. Because the reactants and products in each reaction are solids or involve liquid water, these are known as constant-potential reactions. This means the potential (voltage) of the reactions remains constant as concentration of solids and water do not dramatically affect potential changes.
03

Analyze Concentration Changes During Discharge

Because the solids (including water) involved in both reactions do not significantly change concentration during the discharge process, the potential remains stable. The constant concentration of reactants and products ensures the reactions take place at a constant potential.
04

Relate to Battery Voltage Stability

The stable potential of the electrode reactions translates to a nearly constant battery voltage throughout the discharge cycle. This stability is a result of the reactions labeled 'discharge' in both the cathode and anode processes being at equilibrium and not significantly changing concentrations with discharge.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Cathode Reactions
In a battery, the cathode reaction is where reduction occurs, meaning electrons are gained. Using the nickel-metal hydride rechargeable battery as an example, the cathode reaction can be observed as follows: \[\mathrm{NiOOH}(s)+\mathrm{H}_{2} \mathrm{O} + \mathrm{e}^{-} \rightarrow \mathrm{Ni}(\mathrm{OH})_{2}(s) + \mathrm{OH}^{-}\]In this equation, nickel oxyhydroxide (NiOOH) reacts with water and gains an electron, transforming into nickel hydroxide (Ni(OH)鈧�) and hydroxide ions (OH鈦�).
The cathode's main role is to gain electrons, which is essential for the battery's discharge process.
Key aspects of cathode reactions include:
  • Involvement of solid and liquid reactants making the process less susceptible to concentration changes.
  • Contribution to the stable voltage of the battery by maintaining equilibrium.
Understanding the cathode reaction helps us grasp how the battery continues to operate efficiently over time.
Decoding Anode Reactions
The anode reaction is where oxidation happens, meaning electrons are lost. For the nickel-metal hydride battery, the anode equation is seen as:\[\mathrm{MH}(s) + \mathrm{OH}^{-} \rightarrow \mathrm{M}(s) + \mathrm{H}_{2} \mathrm{O} + \mathrm{e}^{-}\]Here, the metal hydride (MH) reacts with hydroxide ions (OH鈦�) to produce a metal (M), water, and releases an electron.
Key points about anode reactions include:
  • The use of solid and stable reactants and products, which ensures minimal changes in concentration.
  • Role in consistent electron flow necessary for maintaining battery function.
By understanding the anode reaction, we appreciate its role in sustaining battery operations by balancing the electron flow initiated at the cathode.
Maintaining Battery Voltage Stability
Battery voltage stability is a desirable trait as it ensures that the device powered by the battery performs consistently. For nickel-metal hydride batteries, this stability is attributed to the equilibrium state of the electrode reactions, which involve solid reactants and products.
Here's why battery voltage remains stable:
  • The electrodic reactions are constant-potential reactions, meaning their voltage doesn't change significantly as discharge occurs.
  • Both cathode and anode processes have equilibrium reactions that naturally resist changes in voltage despite potential external influences.
  • Due to low involvement of changing ion concentrations, the discharge cycle smoothly progresses without significant voltage fluctuations.
Understanding the chemistry behind these reactions provides insight into why this type of battery can serve its electronic applications without sudden declines in power output.

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Most popular questions from this chapter

Lithium-ion battery. (a) Ideal formulas for the electrodes of the \(\mathrm{Li}^{+}\)-ion battery described in the chapter opener are \(\mathrm{C}_{6} \mathrm{Li}\) (FM 79.01) and \(\mathrm{LiCoO}_{2}\) (FM 97.87). When the battery operates, \(\mathrm{C}_{6} \mathrm{Li}\) is consumed and \(\mathrm{LiCoO}_{2}\) is formed. Write a half-reaction for each electrode, assuming that \(x=1\) in the reaction \(\mathrm{C}_{6} \mathrm{Li}+\mathrm{Li}_{1-x} \mathrm{CoO}_{2} \rightleftharpoons \mathrm{C}_{6} \mathrm{Li}_{1-x}+\mathrm{LiCoO}_{2}\). (In fact, \(x \neq 1\) in real cells.) Which is the anode and which is the cathode? (b) Charge capacity of an electrode in a battery is expressed as \(\mathrm{mA} \cdot \mathrm{h} / \mathrm{g}\), which is the number of milliamperes delivered by \(1 \mathrm{~g}\) of material for 1 hour. How many coulombs are in \(1 \mathrm{~mA} \cdot \mathrm{h}\) ? (c) Show that the theoretical capacity of the battery is \(274 \mathrm{~mA} \cdot \mathrm{h} / \mathrm{g}\) \(\mathrm{LiCoO}_{2}\). (d) \(\mathrm{A} \mathrm{Li}^{+}\)-ion battery can deliver \(140 \mathrm{~mA} \cdot \mathrm{h} / \mathrm{g} \mathrm{LiCoO}_{2}\). What fraction of \(\mathrm{Li}\) in the formula \(\mathrm{LiCoO}_{2}\) is available? (e) Energy stored by a battery per unit mass of an electrode material is expressed as \(\mathrm{W} \cdot \mathrm{h} / \mathrm{g} . \mathrm{A} \mathrm{Li}^{+}\)-ion battery delivers \(140 \mathrm{~mA} \cdot \mathrm{h} / \mathrm{g}\) \(\mathrm{LiCoO}_{2}\) at \(3.7 \mathrm{~V}\). Express the energy storage as \(\mathrm{W} \cdot \mathrm{h} / \mathrm{g} \mathrm{LiCoO}_{2}\).

The following cell was constructed to find the difference in \(K_{\text {sp }}\) between two naturally occurring forms of \(\mathrm{CaCO}_{3}(s)\), called calcite and aragonite. \({ }^{21}\) Each compartment of the cell contains a mixture of solid \(\mathrm{PbCO}_{3}\) \(\left(K_{\mathrm{sp}}=7.4 \times 10^{-14}\right)\) and either calcite or aragonite, both of which have \(K_{\mathrm{sp}} \approx 5 \times 10^{-9}\). Each solution was buffered to \(\mathrm{pH} 7.00\) with an inert buffer, and the cell was completely isolated from atmospheric \(\mathrm{CO}_{2}\). The measured cell voltage was \(-1.8 \mathrm{mV}\). Find the ratio of solubility products, \(K_{\mathrm{sp}}\) (for calcite) \(/ K_{\mathrm{sp}}\) (for aragonite).

For the reaction \(\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}, \Delta G^{\circ}=-257 \mathrm{~kJ}\) per mole of \(\mathrm{CO}\) at \(298 \mathrm{~K}\). Find \(E^{\circ}\) and the equilibrium constant for the reaction.

What must be the relation between \(E_{1}\) and \(E_{2}^{0}\) if the species \(\mathrm{X}^{+}\)is to diproportionate spontaneously under standard conditions to \(\mathrm{X}^{3+}\) and \(\mathrm{X}(s)\) ? Write a balanced equation for the disproportionation.

Consider the redox reaction $$ \mathrm{I}_{2}+2 \mathrm{~S}_{2} \mathrm{O}_{3}^{2-} \rightleftharpoons 2 \mathrm{I}^{-}+\mathrm{S}_{4} \mathrm{O}_{6}^{2-} $$ Thiosulfate \(\quad\) Tetrathionate (a) Identify the oxidizing agent on the left side of the reaction and write a balanced oxidation half-reaction. (b) Identify the reducing agent of the left side of the reaction and write a balanced reduction half-reaction. (c) How many coulombs of charge are passed from reductant to oxidant when \(1.00 \mathrm{~g}\) of thiosulfate reacts? (d) If the rate of reaction is \(1.00 \mathrm{~g}\) of thiosulfate consumed per minute, what current (in amperes) flows from reductant to oxidant?
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