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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
For part (a), the mass of magnesium produced is 222.92 g. For part (b), it will take 947.77 minutes to plate out 25 g of magnesium using a current of 3.50 A.

Step by step solution

01

Identify relevant information

Given data for (a): - Current (I): 4.55 A - Time (t): 4.50 days - Molar mass of Mg: 24.31 g/mol - Faraday's constant (F): 96485 C/mol Given data for (b): - Mass of Mg: 25.00 g - Current (I): 3.50 A
02

Calculate the charge passed through the electrolyte for part (a)

First, convert time from days to seconds: Time (t) = 4.50 days * (24 hours/1 day) * (60 minutes/1 hour) * (60 seconds/1 minute) = 388800 seconds Next, calculate the charge (Q) using Q = It: Q = (4.55 A) * (388800 seconds) = 1769040 C
03

Calculate the moles of Mg produced for part (a)

Use Faraday's Law to find the moles of Mg produced (n): n = Q / (2 * F) n = 1769040 C / (2 * 96485 C/mol) = 9.17 mol
04

Calculate the mass of Mg produced for part (a)

Use the molar mass of Mg to find the mass of Mg produced: Mass of Mg = n * Molar Mass of Mg Mass of Mg = 9.17 mol * 24.31 g/mol = 222.92 g So, the mass of magnesium produced is 222.92 g.
05

Calculate the charge passed through the electrolyte for part (b)

We know the mass of Mg to be produced is 25 g. First, we'll find the moles of Mg: n = Mass of Mg / Molar Mass of Mg n = 25 g / 24.31 g/mol = 1.03 mol Now we'll use Faraday's Law to find the charge required: Q = n * (2 * F) Q = 1.03 mol * (2 * 96485 C/mol) = 199032.7 C
06

Calculate time needed to plate out Mg for part (b)

Use the relationship Q = It to find the time (t): t = Q / I t = 199032.7 C / 3.50 A = 56866.47 seconds Now convert the time to minutes: t = 56866.47 seconds * (1 minute / 60 seconds) = 947.77 minutes So, it will take 947.77 minutes to plate out 25 g of Mg using a current of 3.50 A.

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Most popular questions from this chapter

Cytochrome, a complicated molecule that we will represent as \(\mathrm{CyFe}^{2+}\), reacts with the air we breathe to supply energy required to synthesize adenosine triphosphate (ATP). The body uses ATP as an energy source to drive other reactions (Section 19.7). At \(\mathrm{pH} 7.0\) the following reduction potentials pertain to this oxidation of \(\mathrm{CyFe}^{2+}\) $$ \begin{aligned} \mathrm{O}_{2}(g)+4 \mathrm{H}^{+}(a q)+4 \mathrm{e}^{-} & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & & E_{\mathrm{red}}^{\circ}=+0.82 \mathrm{~V} \\\ \mathrm{CyFe}^{3+}(a q)+\mathrm{e}^{-} & \longrightarrow \mathrm{CyFe}^{2+}(a q) & E_{\mathrm{red}}^{\circ} &=+0.22 \mathrm{~V} \end{aligned} $$ (a) What is \(\Delta G\) for the oxidation of \(\mathrm{CyFe}^{2+}\) by air? \((\mathbf{b})\) If the synthesis of \(1.00 \mathrm{~mol}\) of ATP from adenosine diphosphate (ADP) requires a \(\Delta G\) of \(37.7 \mathrm{~kJ},\) how many moles of ATP are synthesized per mole of \(\mathrm{O}_{2} ?\)

Indicate whether each statement is true or false: (a) The cathode is the electrode at which oxidation takes place. (b) A galvanic cell is another name for a voltaic cell. (c) Electrons flow spontaneously from anode to cathode in a voltaic cell.

Magnesium is obtained by electrolysis of molten \(\mathrm{MgCl}_{2}\). (a) 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 bars 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 h?

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 voltaic cell is based on \(\mathrm{Cu}^{2+}(a q) / \mathrm{Cu}(s)\) and \(\mathrm{Br}_{2}(l) /\) \(\mathrm{Br}^{-}(a q)\) half-cells. (a) What is the standard emf of the cell? (b) Which reaction occurs at the cathode and which at the anode of the cell? (c) Use \(S^{\circ}\) values in Appendix \(\mathrm{C}\) and the relationship between cell potential and free-energy change to predict whether the standard cell potential increases or decreases when the temperature is raised above \(25^{\circ} \mathrm{C}\). (Thestandard entropy of \(\mathrm{Cu}^{2+}(a q)\) is $\left.S^{\circ}=-99.6 \mathrm{~J} / \mathrm{K}\right)$
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