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Chapter 20: Problem 92

Metallic magnesium can be made by the electrolysis of molten \(\mathrm{MgCl}_{2}\). (a) What mass of \(\mathrm{Mg}\) is formed by passing a current of 4.55 A through molten \(\mathrm{MgCl}_{2}\), for 4.50 days? (b) How many minutes are needed to plate out \(25.00 \mathrm{~g} \mathrm{Mg}\) from molten \(\mathrm{MgCl}_{2}\) using \(3.50 \mathrm{~A}\) of current?

Short Answer

Expert verified
(a) 222.64 g of magnesium is formed by passing 4.55 A through molten MgCl2 for 4.50 days. (b) It takes 945.5 minutes to plate out 25.00 g of magnesium from molten MgCl2 using 3.50 A of current.

Step by step solution

01

Convert the given time to seconds

We are given a time of 4.50 days. To convert this to seconds, we first convert days to hours, then hours to minutes, and finally, minutes to seconds. 4.50 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute = 388800 seconds
02

Calculate the charge passed through the reaction

We are given a current of 4.55 A. Charge is the product of time and current: Charge = Time × Current = 388800 seconds × 4.55 A = 1769040 Coulombs
03

Find the moles of electrons involved using Faraday's constant

Faraday's constant (F) is 96485 C/mol. To find the moles of electrons passed through the reaction, we divide the charge by Faraday's constant: Moles of electrons = Charge / F = 1769040 C / 96485 C/mol = 18.327 mol
04

Calculate the moles of magnesium formed

According to the reaction, 2 moles of electrons produce 1 mole of magnesium, as shown below: \(Mg^{2+}(l) + 2e^- → Mg(s)\) So, moles of magnesium = moles of electrons / 2 Moles of magnesium = 18.327 mol / 2 = 9.164 mol
05

Determine the mass of magnesium formed

The molar mass of magnesium is 24.31 g/mol. To find the mass of magnesium formed, we multiply the moles of magnesium by its molar mass: Mass of magnesium = Moles of magnesium × Molar mass of Mg = 9.164 mol × 24.31 g/mol = 222.64 g Therefore, 222.64 g of magnesium is formed. ##Part (b)##
06

Convert the given mass of magnesium to moles

We are given the mass of magnesium as 25.00 g. To convert this to moles, we divide the mass by the molar mass of magnesium: Moles of magnesium = 25.00 g / 24.31 g/mol = 1.028 mol
07

Calculate the moles of electrons involved

For 1 mole of magnesium, 2 moles of electrons are needed. So, the moles of electrons needed to plate 25.00 g of magnesium is: Moles of electrons = 1.028 mol × 2 = 2.056 mol
08

Calculate the charge needed to produce the given mass of magnesium

We multiply the moles of electrons needed by Faraday's constant to find the charge: Charge = Moles of electrons × F = 2.056 mol × 96485 C/mol = 198557 C
09

Determine the time needed for plating using the given current

Time = Charge / Current. We are given a current of 3.50 A. So, we divide the charge required by the current to find the time: Time = 198557 C / 3.50 A = 56730 seconds
10

Convert the time to minutes

To convert the time to minutes, simply divide the time in seconds by 60: Time in minutes = 56730 seconds / 60 = 945.5 minutes So, it takes 945.5 minutes to plate out 25.00 g of magnesium using 3.50 A of current.

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Most popular questions from this chapter

(a) Suppose that an alkaline battery was manufactured using cadmium metal rather than zinc. What effect would this have on the cell emf? (b) What environmental advantage is provided by the use of nickel-metal-hydride batteries over nickel-cadmium batteries?

Magnesium is obtained by electrolysis of molten \(\mathrm{MgCl}_{2}\). Why is an aqueous solution of \(\mathrm{MgCl}_{2}\) not used in the electrolysis? (b) Several cells are connected in parallel by very large copper buses that convey current to the cells. Assuming that the cells are \(96 \%\) efficient in producing the desired products in electrolysis, what mass of \(\mathrm{Mg}\) is formed by passing a current of 97,000 A for a period of 24 hr?

A voltaic cell consists of a strip of cadmium metal in a solution of \(\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}\) in one beaker, and in the other beaker a platinum electrode is immersed in a \(\mathrm{NaCl}\) solution, with \(\mathrm{Cl}_{2}\) gas bubbled around the electrode. A salt bridge connects the two beakers. (a) Which electrode serves as the anode and which as the cathode? (b) Does the Cd electrode gain or lose mass as the cell reaction proceeds? (c) Write the equation for the overall cell reaction. (d) What is the emf generated by the cell under standard conditions?

(a) Based on standard reduction potentials, would you expect copper metal to oxidize under standard conditions in the presence of oxygen and hydrogen ions? (b) When the Statue of Liberty was refurbished, Teflon spacers were placed between the iron skeleton and the copper metal on the surface of the statue. What role do these spacers play?

(a) What is meant by the term reduction? (b) On which side of a reduction half-reaction do the electrons appear? (c) What is meant by the term reductant? (d) What is meant by the term reducing agent?
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