Question

A teapot with a surface area of 750 cm² is to be plated with silver. It is attached to the negative electrode of an electrolytic cell containing silver nitrate (Ag⁺ NO₃⁻). The cell is powered by a 12.0-V battery and has a resistance of 1.40 Ω. If the density of silver is 1.05  10⁴ kg/m³, over what time interval does a 0.133-mm layer of silver build up on the teapot?
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Answer 1

area = 750 cm^2 = 0.075 m^2

thickness(d) = 0.133 mm

resistance (R) = 1.4 ohm

potential difference = 12 volts

density = 10500 kg/m^3

using ohm's law

V = IR

12 = I * 1.4

I = 8.5714 Amperes

now, mass = volume *density

mass = area * thickness * density

m = 0.075 *0.133*10^[-3]*10500

m = 0.10473 kg

number of moles = given wt / molecular wt

= 0.10473/0.1079

= 0.9707

therefore, number of electrons(N) = 6.022 * 10^[23] * 0.9707

= 5.845 * 10^[23] electrons

using , I = Ne/t

t = Ne/I

t = 5.845*10^[23]*1.6 * 10^[-19]/8.57142

t = 10910.7 seconds

t = 3.03 Hours

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