Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

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

Faraday's Law
One of the foundational principles behind electrolysis is Faraday's Law. This law connects the amount of substance being oxidized or reduced at an electrode in an electrolytic cell to the amount of electric charge passed through the system. Faraday's Law can be summarized with the equation \( Q = n imes F \), where:
  • \( Q \) is the total electric charge.
  • \( n \) is the number of moles of electrons.
  • \( F \) is Faraday’s constant, approximately 96485 Coulombs per mole of electrons.
When performing electrolysis, it's crucial to know the relationship between the electron moles and the chemicals involved. This allows us to calculate exactly how much of a specific substance will be produced for a given amount of charge.
Through the understanding of Faraday's Law, we can predict the outcome of chemical reactions in electrolysis and efficiently calculate quantities, such as what is needed in the magnesium production process.
Current and Charge
In the context of electrolysis, a direct current (DC) electricity is used to drive a non-spontaneous chemical reaction. The current, measured in amperes (A), represents the flow of electric charge. To determine the total charge that flows through the system during electrolysis, we use the formula: \( Q = I \times t \).
Here:
  • \( Q \) is the charge in Coulombs (C).
  • \( I \) is the current in amperes.
  • \( t \) is the time in seconds.
The greater the current or the longer the duration, the more charge is transferred, and thus, more substance can be produced. For instance, if you pass a current of 4.55 A for 388800 seconds through magnesium chloride (MgCld{2}), you'd calculate the charge as 1769040 C. Understanding the relationship among current, charge, and time is essential to determine the efficiency and the scale of production.
Stoichiometry
Stoichiometry in electrolysis involves using balanced chemical equations to relate the moles of reactants to the moles of products in a reaction. Understanding the stoichiometric ratios helps us determine how much reactant is needed or how much of a product will be generated.
In the case of producing magnesium by electrolysis, the relevant reaction is \( Mg^{2+} + 2e^- \rightarrow Mg \). This tells us that 2 moles of electrons are required to produce 1 mole of magnesium.
  • This relationship helps in converting between the charge passed in the reaction to the moles of product formed.
  • In the exercise, for the 1769040 C calculated, 18.327 moles of electrons are involved which equates to 9.164 moles of magnesium.
Employing stoichiometry ensures we use resources efficiently and correctly predict amounts in chemical processes.
Magnesium Production
Magnesium is a valuable metal known for its lightweight and strength, widely used in industries like automotive and aerospace. Industrially, it can be produced by the electrolysis of molten magnesium chloride (MgCl d{2}).
This process involves passing an electric current through the molten salt, causing magnesium ions to gain electrons and form magnesium metal. At the same time, chloride ions lose electrons to form chlorine gas.
  • The process requires understanding Faraday's Law to calculate how much current is needed to produce a certain mass of magnesium.
  • In the provided problem, it was calculated that 222.64 g of magnesium could be made using a 4.55 A current over 4.50 days.
  • For producing 25.00 g of magnesium using a 3.50 A current, 945.5 minutes was needed.
Mastering this process of electrolysis, calculations and accurately applying stoichiometry are crucial for efficient and economic magnesium production.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A voltaic cell similar to that shown in Figure 20.5 is constructed. One electrode half-cell consists of a silver strip placed in a solution of \(\mathrm{AgNO}_{3}\), and the other has an iron strip placed in a solution of \(\mathrm{FeCl}_{2}\). The overall cell reaction is $$\mathrm{Fe}(s)+2 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+2 \mathrm{Ag}(s)$$ (a) What is being oxidized, and what is being reduced? (b) Write the half-reactions that occur in the two half-cells. (c) Which electrode is the anode, and which is the cathode? (d) Indicate the signs of the electrodes. (e) Do electrons flow from the silver electrode to the iron electrode or from the iron to the silver? (f) In which directions do the cations and anions migrate through the solution?

(a) Under what circumstances is the Nernst equation applicable? (b) What is the numerical value of the reaction quotient, Q, under standard conditions? (c) What happens to the emf of a cell if the concentrations of the reactants are increased?

Some years ago a unique proposal was made to raise the Titanic. The plan involved placing pontoons within the ship using a surface-controlled submarine-type vessel. The pontoons would contain cathodes and would be filled with hydrogen gas formed by the electrolysis of water. It has been estimated that it would require about \(7 \times 10^{8} \mathrm{~mol}\) of \(\mathrm{H}_{2}\) to provide the buoyancy to lift the ship (J. Chem. Educ, \(1973,\) Vol. 50,61 ). (a) How many coulombs of electrical charge would be required? (b) What is the minimum voltage required to generate \(\mathrm{H}_{2}\) and \(\mathrm{O}_{2}\) if the pressure on the gases at the depth of the wreckage ( \(2 \mathrm{mi}\) ) is \(300 \mathrm{~atm} ?\) (c) What is the minimum electrical energy required to raise the Titanic by electrolysis? (d) What is the minimum cost of the electrical energy required to generate the necessary \(\mathrm{H}_{2}\) if the electricity costs 85 cents per kilowatt-hour to generate at the site?

How does a zinc coating on iron protect the iron from unwanted oxidation? [Section 20.8\(]\)

(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?

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free