Q21.132CP - Chemistry: Molecular Nature Of Matter And Change

Question

Calcium is obtained industrially by electrolysis of molten ${\mathbf{CaCl}}_{\mathbf{2}}$ and is used in aluminium alloys. How many coulombs are needed to produce 10.0 g of Ca metal? If a cell runs at 15 A, how many minutes will it take to produce 10.0 g of Ca(s)?

Step-by-Step Solution

Answer

The amount of charge needed to produce 10 g of Ca metal is $48,238\mathrm{C}$.

The time it will take to produce 10 g of Ca(s) is $53.60 \min$.

Step 1: Concept Introduction

The process of dissolving ionic compounds into their constituent components by delivering a direct electric current through the complex in a fluid form is known as electrolysis. At the cathode, cations are reduced, whereas anions are oxidized.

Step 2: Calculation for Charge

To get the charge, convert the mass required to moles of electrons. There are two electrons involved in reducing ${\mathrm{Ca}}^{2+}\to \mathrm{Ca}$.

$10.0\mathrm{gCa}\times \frac{1 \mathrm{molCa}}{10.01\mathrm{gCa}}\times \frac{2 {\mathrm{mole}}^{-}}{1 \mathrm{molCa}}=0.50 {\mathrm{mole}}^{-}$

Multiply by Faraday's constant to get the charge.

$0.50 {\mathrm{mole}}^{-}\times \frac{96500\mathrm{C}}{ {\mathrm{mole}}^{-}}=48,238\mathrm{C}$

 

Therefore, the value for the charge is obtained as $48,238\mathrm{C}$.

Step 3: Calculation for Time

Given the current, divide the charge needed by the current to get the time.

$48,238\mathrm{C}\times \frac{1\mathrm{s}}{15\mathrm{C}}=3215.9\mathrm{s}$

Convert to minutes.

$321.59 \mathrm{s}\times \frac{1 \min }{60 \mathrm{s}}=53.60 \min$

Therefore, the value for time is obtained as $53.60 \min$.