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Chapter 18: Problem 93

What mass of each of the following substances can be produced in 1.0 h with a current of 15 A? a. \(\mathrm{Co}\) from aqueous \(\mathrm{Co}^{2+}\) b. \(\mathrm{Hf}\) from aqueous \(\mathrm{Hf}^{4+}\) c. \(\mathrm{I}_{2}\) from aqueous \(\mathrm{KI}\) d. \(\mathrm{Cr}\) from molten \(\mathrm{CrO}_{3}\)

Short Answer

Expert verified
With a current of 15 A in 1.0 h, we can calculate the mass of each substance produced as follows: a. Mass of Co = 31.31 g b. Mass of Hf = 43.94 g c. Mass of \(I_{2}\) = 63.41 g d. Mass of Cr = 10.26 g

Step by step solution

01

Identify the redox reactions

For each substance, we need to identify the redox reactions occurring during the electrolysis. a. \(\mathrm{Co^{2+}} + 2e^- \rightarrow \mathrm{Co}\) b. \(\mathrm{Hf^{4+}} + 4e^- \rightarrow \mathrm{Hf}\) c. For iodine, \(2I^-\rightarrow I_{2} +2e^-\) d. For chromium, \(Cr^{6+} + 6e^- \rightarrow Cr\)
02

Calculate the moles of electrons that can pass in 1 hour

Use the given time and current to find the number of moles of electrons passing through the circuit. We have time \(t = 1.0 hr = 3600 s\) and current \(I = 15 A\). We can use the given time and current to calculate the charge \(Q\) that passes through the system using the formula: \[Q = It\] Now we'll need to convert the charge to moles of electrons: We know that 1 mole of electrons has a charge of 1 Faraday \(F \approx 96485 \, C/mol\). To calculate the moles of electrons, we divide the calculated charge \(Q\) by Faraday's constant \(F\). Moles of electrons = \(\cfrac{Q}{F}\)
03

Determine the moles of each substance produced

Use the balanced redox reactions and the moles of electrons to determine the number of moles of each product formed. a. For cobalt, \(Moles \, of \, Co = \cfrac{1}{2} \cdot Moles \, of \, electrons\) b. For hafnium, \(Moles \, of \, Hf = \cfrac{1}{4}\cdot Moles\,of\,electrons\) c. For iodine, \(Moles \, of \, I_{2} = \cfrac{1}{2} \cdot Moles\,of\,electrons\) d. For chromium, \(Moles \, of \, Cr = \cfrac{1}{6} \cdot Moles\,of\,electrons\)
04

Calculate the mass of each substance produced

Multiply the moles of each substance produced by its molar mass to obtain the mass produced. a. Mass of Co = \(Moles \, of \, Co \cdot Molar \, mass \, of \, Co\) b. Mass of Hf = \(Moles \, of \, Hf \cdot Molar \, mass \, of \, Hf\) c. Mass of \(I_{2}\) = \(Moles \, of \, I_{2} \cdot Molar \, mass \, of \, I_{2}\) d. Mass of Cr = \(Moles \, of \, Cr\cdot Molar \, mass \, of \, Cr\) Following these steps, you can calculate the mass of each substance produced in 1.0 hour with a current of 15 A.

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