Question

Chromium plating is applied by electrolysis to objects syspended in a dichromate solution, according to the following (unbalanced) half-reaction: Cr2O7^2- (aq) + e- +H+ (aq) --> Cr(s) + H2O(l)
How long in hours would it take to apply a chromium plating 2.6 x 10^-2 mm thick to a car bumper with a surface area of 0.25m^2 in an electrolytic cell carrying a current of 5.0 A? (The density of chromium is 7.19 g/cm^3)

Answer 1

Step 1. Calculate the weight chromium required to be plated on a surface area of 0.25m^2 with thickness = 2.6 x 10^-2 mm

= surface area in cm^2 x thickness in cms x density of chromium in gm /cm^3

= ( 0.25 x 10000 ) ( 2.6 x 10^-2 / 10 ) (7.19 ) = 2500 x 0.0026 x 7.19 = 46.735 gms

Step 2 . / Calculate the electrochemical equivalent weight of chromium -

Electrochemical equivalent weight = gram equivalent mass* / 96500

-------------------------------------------------- = [ 294.185 / 6 ] / ( 96500 ) = 49.00 / 96500 = 5.0809 x 10^-4

Step 3 , / Apply the relation w = zct ; (according to Faraday's laws of electrolysis) where I is current in amperes(given as 5.0amp , ) , z = electrochemical equivalent weight of chromium , t is time in seconds ( to be calculated ) , w = weight of metal to be deposited in gms.

So , 46.735 = 5.0809 x 10^-4 x 5.0 x t

--------------- t = 46.735 / ( 5.0 x 5. 0809 x 10^-4 ) = 18399.6 06 seconds

--------------or, = 18399.606 /3600 = 5.11 hours

* From the half cell reaction we see that 6e per Cr2O7^2- are translated to an equivalent weight of K2 Cr2 O7

so the equivalents of chromium = Molar mass of K2 Cr2 O7 / 6 = 294 .185 / 6 = 49.03

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