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Chapter 1: Problem 21

Which expression below should be used to calculate the mass of copper that can be plated out of a 1.0 \(\mathrm{M} \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\) , solution using a current of 0.75 A for 5.0 minutes? (A) \(\frac{(5.0)(60)(0.75)(63.55)}{(96500)(2)}\) (B) \(\frac{(5.0)(60)(63.55)(2)}{(0.75)(96500)}\) (C) \(\frac{(5.0)(60)(96500)(0.75)}{(63.55)(2)}\) (D) \(\frac{(5.0)(60)(96500)(63.55)}{(0.75)(2)}\)

Short Answer

Expert verified
The correct expression to calculate the mass of copper that can be electroplated is (A) \(\frac{(5.0)(60)(0.75)(63.55)}{(96500)(2)}\)

Step by step solution

01

Identifying the constants

In this case, the constants are: current \(I = 0.75 A\), time \(t = 5.0 \, min = 5.0 \times 60 \, s\), Faraday constant \(F = 96500 \, C/mol\), molecular weight of copper \(M_{Cu} = 63.55 \, g/mol\), valency of copper \(n = 2\).
02

Applying Faraday’s law of electrolysis

According to Faraday's law, the mass of an element deposited during electrolysis is proportional to the product of the current and time and inversely proportional to the Faraday constant and the valency (number of electrons transferred in the chemical reaction). Hence, the relationship that calculates the mass of copper (m) is \(m = \frac{(ItM_{Cu})}{(Fn)}\).
03

Comparing the expression with the choices given

Examining the options provided, the expression that matches the relationship derived in the previous step is \(\frac{(5.0)(60)(0.75)(63.55)}{(96500)(2)}\).

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