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Chapter 18: Problem 27

Consider the electrolysis of a molten salt of some metal. What information must you know to calculate the mass of metal plated out in the electrolytic cell?

Short Answer

Expert verified
To calculate the mass of metal plated out during the electrolysis of a molten salt, you need to know the chemical formula of the salt, the amount of electric charge passed through the cell, Faraday's constant, and the atomic mass of the metal ion. Determine the metal ion and its charge from the salt's formula, calculate moles of electrons using the charge and Faraday's constant, determine moles of metal deposited by dividing moles of electrons by the stoichiometric coefficient (equal to the charge of metal ion), and finally, calculate the mass of the metal by multiplying moles of metal ions by the molar mass of the metal.

Step by step solution

01

Determine the metal ion and its charge in the molten salt

First, you need to identify the metal ion present in the molten salt, as well as its oxidation state (charge). Look at the chemical formula of the salt and identify the positively charged metal ion.
02

Calculate the moles of metal ions reduced during the electrolysis

Next, use the amount of electric charge (Q) passed through the electrolytic cell in coulombs, and the Faraday's constant (F) to find the moles of electrons exchanged during the electrolysis. The relationship between the charge and the moles of electrons is given by: Moles of electrons = \(\frac{Q}{F}\)
03

Determine the moles of metal deposited

To calculate the moles of metal deposited, divide the moles of electrons obtained in step 2 by the stoichiometric coefficient of the electrons in the balanced half-reaction of the metal ion being reduced. The stoichiometric coefficient is equal to the charge on the metal ion.
04

Calculate the mass of metal plated out

Finally, multiply the moles of metal ions determined in step 3 by the molar mass (atomic mass) of the metal to find the mass of the metal plated out during the electrolysis: Mass of metal = moles of metal × molar mass of metal

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Most popular questions from this chapter

A zinc-copper battery is constructed as follows at \(25^{\circ} \mathrm{C}:\) $$\mathrm{Zn}\left|\mathrm{Zn}^{2+}(0.10 \mathrm{M}) \| \mathrm{Cu}^{2+}(2.50 \mathrm{M})\right| \mathrm{Cu}$$ The mass of each electrode is \(200 . \mathrm{g}\). a. Calculate the cell potential when this battery is first connected. b. Calculate the cell potential after \(10.0 \mathrm{~A}\) of current has flowed for \(10.0 \mathrm{~h}\). (Assume each half-cell contains \(1.00 \mathrm{~L}\) of solution.) c. Calculate the mass of each electrode after \(10.0 \mathrm{~h}\). d. How long can this battery deliver a current of \(10.0 \mathrm{~A}\) before it goes dead?

Zirconium is one of the few metals that retains its structural integrity upon exposure to radiation. For this reason, the fuel rods in most nuclear reactors are made of zirconium. Answer the following questions about the redox properties of zirconium based on the half-reaction \(\mathrm{ZrO}_{2} \cdot \mathrm{H}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}+4 \mathrm{e}^{-} \longrightarrow \mathrm{Zr}+4 \mathrm{OH}^{-} \quad \mathscr{E}^{\circ}=-2.36 \mathrm{~V}\) a. Is zirconium metal capable of reducing water to form hydrogen gas at standard conditions? b. Write a balanced equation for the reduction of water by zirconium metal. c. Calculate \(\mathscr{8}^{\circ}, \Delta G^{\circ}\), and \(K\) for the reduction of water by zirconium metal. d. The reduction of water by zirconium occurred during the accident at Three Mile Island, Pennsylvania, in \(1979 .\) The hydrogen produced was successfully vented and no chemical explosion occurred. If \(1.00 \times 10^{3} \mathrm{~kg} \mathrm{Zr}\) reacts, what mass of \(\mathrm{H}_{2}\) is produced? What volume of \(\mathrm{H}_{2}\) at \(1.0 \mathrm{~atm}\) and \(1000 .{ }^{\circ} \mathrm{C}\) is produced? e. At Chernobyl, USSR, in 1986 , hydrogen was produced by the reaction of superheated steam with the graphite reactor core: $$\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)$$ A chemical explosion involving the hydrogen gas did occur at Chernobyl. In light of this fact, do you think it was a correct decision to vent the hydrogen and other radioactive gases into the atmosphere at Three Mile Island? Explain.

What reaction will take place at the cathode and the anode when each of the following is electrolyzed? (Assume standard conditions.) a. \(1.0 \mathrm{M}\) KF solution b. \(1.0 \mathrm{M} \mathrm{CuCl}_{2}\) solution c. \(1.0 \mathrm{M} \mathrm{MgI}_{2}\) solution

Consider a cell based on the following half-reactions: $$\begin{aligned}\mathrm{Au}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Au} & \mathscr{C}^{\circ}=1.50 \mathrm{~V} \\ \mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+} & \mathscr{C}^{\circ}=0.77 \mathrm{~V} \end{aligned}$$ a. Draw this cell under standard conditions, labeling the anode, the cathode, the direction of electron flow, and the concentrations, as appropriate. b. When enough \(\mathrm{NaCl}(s)\) is added to the compartment containing gold to make the \(\left[\mathrm{Cl}^{-}\right]=0.10 M\), the cell potential is observed to be \(0.31 \mathrm{~V}\). Assume that \(\mathrm{Au}^{3+}\) is reduced and assume that the reaction in the compartment containing gold is $$\mathrm{Au}^{3+}(a q)+4 \mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{AuCl}_{4}^{-}(a q)$$ Calculate the value of \(K\) for this reaction at \(25^{\circ} \mathrm{C}\).

In the electrolysis of a sodium chloride solution, what volume of \(\mathrm{H}_{2}(g)\) is produced in the same time it takes to produce \(257 \mathrm{~L}\) \(\mathrm{Cl}_{2}(\mathrm{~g})\), with both volumes measured at \(50 .{ }^{\circ} \mathrm{C}\) and \(2.50 \mathrm{~atm} ?\)
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