(b) What amperage is required to plate out 0.250 mol Cr from a Cr 3+ solution in a period of 8.00 h?

Hello everyone today. We are being asked the following question. Magnesium can be acquired by the electoral isis or electrolysis of molten, magnesium chloride, calculate the required current to acquire 650 g of magnesium in a span of two hours. So first you want to write down what this equation where this reaction will look like. So we are going to have our liquid mercury and we're going to add two electrons to it. And in doing so we're going to produce our mercury are magnesium solid. Next we are going to write out the equation or solve for our current. So we're going to take that we have g of magnesium Over two hours and work backwards. So what we want to multiply this by first is the molar mass of magnesium and according to the periodic table, one mole of magnesium is equal to 24.305g. Next we want to multiply by the ratio of moles of magnesium to electrons. So we can say that in one mole Of Magnesium We have two moles of electrons. Next because we were dealing with current, we're gonna have to use Faraday's constant And that's to say that in one mole or one mole of an electron is equal to current. We then need to get rid of our hours and turn that into Minutes so that we can get our units. So we're gonna say that in one hour we have 60 minutes And then we're gonna finally multiply that by a conversion that in one minute we have 60 seconds. And so all of our units are going to cancel out our grams of magnesium, our moles of magnesium, our moles of electrons, Our minutes and our hours. And so we are going to be left with the current of 717 amps or amperes as our unit. And this is going to be our final answer. Overall, I hope that this helped, and until next time.

Ch.20 - Electrochemistry

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Brown 14th Edition

Ch.20 - Electrochemistry

Problem 91b

Chapter 20, Problem 91b

(b) What amperage is required to plate out 0.250 mol Cr from a Cr³⁺ solution in a period of 8.00 h?

Verified step by step guidance

Identify the relevant electrochemical reaction: The reduction of Cr³⁺ to Cr metal is represented by the half-reaction: Cr³⁺ + 3e⁻ → Cr.

Determine the total charge needed: Since 1 mole of Cr requires 3 moles of electrons, calculate the total moles of electrons needed for 0.250 mol of Cr using the stoichiometry of the reaction.

Convert moles of electrons to charge: Use Faraday's constant (approximately 96485 C/mol) to convert the moles of electrons to total charge in coulombs.

Calculate the current (amperage): Use the formula I = Q/t, where I is the current in amperes, Q is the total charge in coulombs, and t is the time in seconds. Convert the given time from hours to seconds.

Solve for the current: Substitute the values for Q and t into the formula to find the required current in amperes.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Faraday's Laws of Electrolysis

Faraday's Laws of Electrolysis state that the amount of substance deposited during electrolysis is directly proportional to the quantity of electric charge passed through the electrolyte. The first law quantifies this relationship, while the second law relates the mass of the substance to its molar mass and the number of electrons involved in the reaction.

Amperage and Charge

Amperage, or current (I), is the flow of electric charge measured in amperes (A). The total charge (Q) can be calculated using the formula Q = I × t, where t is the time in seconds. Understanding this relationship is crucial for determining the current needed to achieve a specific electrochemical reaction over a given time.

Electrochemical Equivalent

The electrochemical equivalent (ECE) is the mass of a substance that can be deposited or dissolved by the passage of one coulomb of electric charge. For chromium ions (Cr³⁺), the ECE can be calculated using the molar mass and the number of electrons transferred in the reduction process, which is essential for determining the required amperage for plating.