Chapter 19, Problem 19.56QP

Interpretation Introduction

Interpretation:

Need to determine the time consumed for chrome plating of car bumper.

Concept introduction:

Chrome plating is the electrolytic deposition of chromium over another metal to protect it from rust formation.  The metal to be plated was used as cathode at which the $\text{Cr(VI)}$ gets reduced and deposited.  The cell reaction for electroplating of chromium was given below.

  ${\text{cathode (reduction) Cr}}_{\text{2}}{\text{O}}_{\text{7}}{{}^{\text{2}}}^{\text{-}}{}_{\text{(aq)}}+14{\text{H}}^{+}{}_{\text{(aq)}}+12{\text{e}}^{\text{-}}\stackrel{}{\to }{\text{2Cr}}_{\text{(s)}}{\text{+7H}}_{\text{2}}{\text{O}}_{\text{(l)}}$

Since the thickness and surface area of the metal was given. From which the volume of chromium coated can be attained by the following equation.

    $\text{Volume of chromium plated =}\text{Thickness}\times \text{surface area }$

By knowing the volume, mass of chromium plated can be calculated by using the density equation.

    $\text{Mass of chromium plated (g) =}{\text{Volume (m}}^{\text{3}}\text{)}\text{×}{\text{Density(g/m}}^{\text{3}}\text{) }$

From the mass of chromium plated, the number of moles can be calculated as shown below

    $\text{Number of moles of chromium = }\frac{\text{mass of chromium plated}}{\text{molar}\text{mass}\text{of}\text{chromium}}$

From half-cell reaction it was known that two mole of chromium need twelve mole of electrons, Therefore the number of mole of electrons involved was attained using the below equation

$\text{Number of moles of electrons = Number of moles of chromium deposited }\times \frac{\text{12}\text{mole}{\text{e}}^{\text{-}}}{\text{2}\text{mole}\text{Cr}}$

Coulombs of charges involved in the reaction was calculated by multiplying the number of moles of electron with faraday constant.

    $\text{Charges (C) = Number of moles of electrons}\text{}\times 96500\text{C/mole}$

Since current utilized was given,

So,

    $\text{time}\text{(s)}\text{=}\frac{\text{charges}\text{(C)}}{\text{current}\text{(A)}}$