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Chapter 18: Problem 102

A solution containing \(\mathrm{Pt}^{4+}\) is electrolyzed with a current of 4.00 \(\mathrm{A} .\) How long will it take to plate out 99\(\%\) of the platinum in 0.50 \(\mathrm{L}\) of a \(0.010-M\) solution of \(\mathrm{Pt}^{4+} ?\)

Short Answer

Expert verified
It will take approximately 132.8 hours to plate out 99% of the platinum present in the 0.50 L of a 0.010-M solution of \(Pt^{4+}\) electrolyzed with a current of 4.00 A.

Step by step solution

01

Calculate the number of moles of Pt

First, we need to determine the total number of moles of \(\mathrm{Pt}^{4+}\) ions present in the solution. We are given that the solution is 0.50 L in volume and has a concentration of 0.010 M. Therefore, the number of moles can be calculated using the equation: moles = volume × concentration moles of Pt = (\(0.50\,\mathrm{L}\)) × (\(0.010\,\mathrm{M}\)) moles of Pt = \(0.005\,\mathrm{mol}\)
02

Calculate the moles of Pt to be plated out

Next, we need to calculate the number of moles of Pt that we want to plate out, which is given as 99% of the total moles. moles of Pt to be plated out = (0.99) × (0.005 mol) moles of Pt to be plated out = \(0.00495\,\mathrm{mol}\)
03

Calculate the amount of charge needed

Now, we need to calculate the amount of charge required to plate out the desired amount of Pt. Since we are dealing with a \(\mathrm{Pt}^{4+}\) ion, we know that 4 moles of electrons are needed for each mole of Pt. Thus, the amount of charge required can be calculated using Faraday's constant (F), where F = \(96,485\,\mathrm{\dfrac{C}{mol e^{-}}\): Charge (C) = moles of Pt × 4 × F Charge (C) = (0.00495 mol) × 4 × (96,485 \(\dfrac{\mathrm{C}}{\mathrm{mol\,e^{-}}\)) Charge (C) = \(1,911,538\,\mathrm{C}\)
04

Calculate the time required

Finally, to determine the time required to plate out 99% of the Pt, we will use the current value given in the problem. The current is the amount of charge being transferred per unit of time, which in this case is 4.00 A. Therefore, we can use the following equation to find the time required: time (s) = \(\dfrac{\text{Charge (C)}}{\text{Current (A)}}\) time (s) = \(\dfrac{1,911,538\,\mathrm{C}}{4.00\,\mathrm{A}}\) time (s) = \(477,885\,\mathrm{s}\) Now, we can convert the time in seconds to minutes or hours for a more practical understanding: time (min) = \(\dfrac{477,885\,\mathrm{s}}{60\,\mathrm{s/min}}\) = \(7,965\,\mathrm{min}\) time (hr) = \(\dfrac{7,965\,\mathrm{min}}{60\,\mathrm{min/h}}\) ≈ \(132.8\,\mathrm{h}\) So, it will take approximately 132.8 hours to plate out 99% of the platinum present in the solution.

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Most popular questions from this chapter

Under standard conditions, what reaction occurs, if any, when each of the following operations is performed? a. Crystals of \(\mathrm{I}_{2}\) are added to a solution of \(\mathrm{NaCl}\) . b. \(\mathrm{Cl}_{2}\) gas is bubbled into a solution of \(\mathrm{Nal}\). c. A silver wire is placed in a solution of \(\mathrm{CuCl}_{2}\) d. An acidic solution of \(\mathrm{FeSO}_{4}\) is exposed to air. For the reactions that occur, write a balanced equation and calculate \(\mathscr{E}^{\circ}, \Delta G^{\circ},\) and \(K\) at \(25^{\circ} \mathrm{C}\)

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