Question

For a science experiment you need to electroplate zinc onto both sides of a very thin, 1.00 cm × 1.00 cm copper sheet. You want the zinc thickness to be 140 nm , and you know that the charge carriers in the ionic solution are divalent (charge 2e) zinc ions. The density of zinc is 7140 kg/m3 If the electroplating apparatus operates at 1.40 mA , how long will it take the zinc to reach the desired thickness?

Answer 1

FIrst we have to find the mass of zinc to be formed

thickness = 140 nm

$140 nm \times \frac{10^{-9}m}{1 nm}$

=1.40x10^-7 m

Surface area of the electrode = 1 x 1 = 1 cm² =

$1cm^{2} \times \frac{(10^{-2}m)^{2}}{(1 cm)^{2}}$

=10^-4 m²

Volume of zinc = area x thickness = 10^-4 m²x1.40x10^-7 m = 1.40x 10^-11 m³

From density we can calculate mass

mass = density x volume = 7140 kg/m³ x 1.40x 10^-11 m³ =1.0x10^-6 kg = 1.0x10^-3 g

For 1 mole Zn requires 2F of current

moles of Zn =

$1.0\times 10^{-3} g Zn\times \frac{1 mol Zn}{65.48 g}$

=1.53x10^-6 mol Zn

Current required to deposit 1.53x10^-6 mol Zn =

$1.53\times 10^{-6} mol Zn\times \frac{2 \times 96485 C}{1 mol Zn}$

Q = 0.295 C

Formula is Q= it

i = 1.40 mA

time = Q/i = 0.295/1.40x10^-3 s

time =210 s