What mass of gold is produced when 24.4 a of current are passed through a gold solution for 46.0 min?

To solve this problem, we make use of the Faraday’s law for Electrolysis. The formula is given as:

I t = m F / e

where the variables are,

I = current = 24.4 A

t = time = 46 min = 2760 s

m = mass produced = (unknown)

F = Faraday’s constant = 96500 C/equivalent

e = gram equivalent weight of gold

The gram equivalent weight is calculated by dividing the molar mass with the amount of charge produced per atom. Gold has charge of 3 + therefore the gram equivalent weight is:

e = (196.97 g/mol) (1 mol/3 equivalents) = 65.66 g/equivalents

Solving for the mass m:

m = e I t / F

m = (65.66 g) (24.4 A) (2760 s) / (96500 C)

m = 45.82 g