You are working in a plant that produces copper for use in electrical circuits by electrolysis of acidic solutions of CuSO₄(aq). A customer has placed an order for a small quantity of high-purity copper, and you need to tell the customer how long it will take to produce the metal. How many hours are required to plate 25.00 g of copper metal from 1.00 m CuSO₄(aq) by using a current of 3.00 A?

PLAN Use the second procedure in Toolbox 6O.1.

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Toolbox 60.1 HOW TO PREDICT THE RESULT OF ELECTROLYSIS CONCEPTUAL BASIS The number of electrons required to reduce a given amount of a species is related to the stoichiometric coefficients in the reduction half-reaction. The same is true of oxidation. Therefore, a stoichiometric relation can be set up between the reduced or oxidized species and the amount of electrons required to carry out the reaction. The amount of electrons required is cal- culated from the current and the length of time for which the current flows. PROCEDURE To determine the amount of product that can be produced: Step 1 Identify the stoichiometric relation between electrons and the species of interest from the applicable half-reaction. Step 2 Calculate the amount (in moles) of electrons supplied from Eq. 2, n = It/F. Use the stoichiometric relation from step 1 to convert n into the amount of substance. If required, use the molar mass to convert the amount of substance into mass (or molar volume to convert into volume). This procedure is illustrated in Example 60.2. To determine the time required for a given amount of product to be produced: Step 1 Identify the stoichiometric relation between electrons and the species of interest from the applicable half-reaction. Step 2 If required, use the molar mass to convert mass into amount (in moles). Use the stoichiometric relation from step 1 to convert amount of substance into amount of electrons passed, n (in moles). Step 3 Substitute n, the current, and Faraday's constant into Eq. 2 rearranged to t = Fn/I and solve for time. This procedure is illustrated in Example 60.3.