Question

How many grams of chromium metal are plated out when a constant current of 8.00 a is passed through an aqueous solution containing cr3+ ions for 160. minutes?

Answer 1

We can solve this without a concrete formula through dimensional analysis. This works by manipulating the units such that you end up with the unit of the final answer. Manipulate them by cancelling units that appear both in the numerator and denominator side. As a result, we must be left with the units of g. The current in A or amperes is equivalent to amount of Coulombs per second. Since this involves Coulombs, we will use the Faraday's constant which is 96,500 C/mol electron. The reaction is:

Cr³⁺(aq) + 3e⁻ --> Cr(s)

This means that for every 3 moles of electron transferred, 1 mole of Chromium metal is plated. The molar mass of Cr: 52 g/mol. The solution is as follows:

Mass of Chromium metal = (8 C/s)(60 s/1 min)(160 min)(1 mol e⁻/96,500 C)(1 mol Cr/3 mol e)(52 g/mol)
Mass of Chromium metal = 13.79 g