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Chapter 20: Problem 74

During the discharge of an alkaline battery, \(4.50 \mathrm{~g}\) of \(\mathrm{Zn}\) is consumed at the anode of the battery. (a) What mass of \(\mathrm{MnO}_{2}\) is reduced at the cathode during this discharge? (b) How many coulombs of electrical charge are transferred from \(\mathrm{Zn}\) to \(\mathrm{MnO}_{2} ?\)

Short Answer

Expert verified
The mass of MnO₂ reduced at the cathode during dischange is approximately \(7.56 \ g\) and the number of electrical charge transferred from Zn to MnO₂ is approximately \(131,700 \ C\).

Step by step solution

01

1. Balanced Redox Reaction

Determine the balanced redox chemical equation for the overall process occurring in the battery. The balanced redox chemical equation is given as: \[ Zn(s) + 2MnO_{2}(s) + 2H_{2}O(l) \rightarrow Zn(OH)_{2}(s) + 2Mn(OH)(s) \]
02

2. Stoichiometry for Mass of MnO₂

Calculate the stoichiometric relationship between Zn and MnO₂ in the balanced equation. From the balanced equation, we can see that: 1 mole of Zn reacts with 2 moles of MnO₂ Now, we can start calculating the mass of MnO₂.
03

3. Find Mass of MnO₂

Convert the given mass of Zn to moles and use the stoichiometry to find the mass of MnO₂. The molar mass of Zn = 65.38 g/mol First, convert the mass of Zn (4.50 g) to moles: \( moles \ of \ Zn = \frac{4.50 \ g}{65.38 \ g/mol} \) Then, use the stoichiometry from the balanced equation to find moles of MnO₂ reduced: \( moles \ of \ MnO_{2} = 2 \times moles \ of \ Zn \) Finally, convert the moles of MnO₂ to mass using its molar mass (MnO₂ = 86.94 g/mol): \( mass \ of \ MnO_{2} = moles \ of \ MnO_{2} \times 86.94 \ g/mol \)
04

4. Coulombs of Electrical Charge

Determine the number of electrons transferred and use Faraday's constant to find the total coulombs. In the balanced reaction, 1 mole of Zn loses 2 moles of electrons. First, find the moles of electrons transferred: \( moles \ of \ electrons = 2 \times moles \ of \ Zn \) Then, use Faraday's constant (1 mol of electrons = 96,485 C) to calculate the coulombs: \( coulombs = moles \ of \ electrons \times 96,485 \ C/mol \) Now you can plug in the values calculated in the previous steps to find the mass of MnO₂ and the number of coulombs transferred during the battery's discharge.

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Most popular questions from this chapter

The electrodes in a silver oxide battery are silver oxide \(\left(\mathrm{Ag}_{2} \mathrm{O}\right)\) and zinc. (a) Which electrode acts as the anode? (b) Which battery do you think has an energy density most similar to the silver oxide battery: a Li-ion battery, a nickelcadmium battery, or a lead-acid battery?

Consider the half-reaction $\mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)$ (a) Which of the lines in the following diagram indicates how the reduction potential varies with the concentration of \(\mathrm{Ag}^{+}(a q) ?(\mathbf{b})\) What is the value of \(E_{\text {red }}\) when \(\log \left[\mathrm{Ag}^{+}\right]=0 ?\)

(a) Assuming standard conditions, arrange the following in order of increasing strength as oxidizing agents in acidic solution: $\mathrm{MnO}_{4}^{-}(a q), \mathrm{O}_{3}(g), \mathrm{HSO}_{4}^{-}(a q), \mathrm{O}_{2}(g), \mathrm{HClO}(a q)$ (b) Arrange the following in order of increasing strength as reducing agents in basic solution: $\mathrm{Cr}(\mathrm{OH})_{3}(s), \mathrm{Fe}(s), \mathrm{Ca}(s),\( \)\mathrm{H}_{2}(g), \mathrm{Mn}(s)$

A mixture of copper and gold metals that is subjected to electrorefining contains tellurium as an impurity. The standard reduction potential between tellurium and its lowest common oxidation state, \(\mathrm{Te}^{4+}\), is $$ \mathrm{Te}^{4+}(a q)+4 \mathrm{e}^{-} \longrightarrow \mathrm{Te}(s) \quad E_{\mathrm{red}}^{\circ}=0.57 \mathrm{~V} $$ Given this information, describe the probable fate of tellurium impurities during electrorefining. Do the impurities fall to the bottom of the refining bath, unchanged, as copper is oxidized, or do they go into solution as ions? If they go into solution, do they plate out on the cathode?

A voltaic cell is constructed with two silver-silver chloride electrodes, each of which is based on the following half-reaction: $$ \operatorname{AgCl}(s)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)+\mathrm{Cl}^{-}(a q) $$ The two half-cells have \(\left[\mathrm{Cl}^{-}\right]=0.0150 \mathrm{M}\) and \(\left[\mathrm{Cl}^{-}\right]=\) \(2.55 M,\) respectively. (a) Which electrode is the cathode of the cell? (b) What is the standard emf of the cell? (c) What is the cell emf for the concentrations given? (d) For each electrode, predict whether \(\left[\mathrm{Cl}^{-}\right]\) will increase, decrease, or stay the same as the cell operates.
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