# How long will it take the zinc to reach the desired thickness?

## Homework Statement

For a science experiment you need to electroplate a 130 nm thick zinc coating onto both sides of a very thin, 3.0 cm*3.0 cm copper sheet. You know that the charge carriers in the ionic solution are divalent (charge 2e) zinc ions. The density of zinc is 7140 kg/m^3
If the electroplating apparatus operates at 1.3 mA, how long will it take the zinc to reach the desired thickness?

## The Attempt at a Solution

we know area and thickness of the plate and the density of the zinc, and the current.
so we can get the volume of the plate and using density we can figure out the mass.
volume = 3*10^-2* 3*10^-2* 130*10^-9 m = 1.17*10^-10 m^3
and the mass = 1.17*10^-12 m^3 * 7140 kg/m^3 = 8.35*10^-7 kg
in 1 mole the weight of zinc is 65.38 g
so in 8.35*10^-7 kg 1.3*10^-8 mole
1 mole we have 6.022*10^23 atoms
so in 1.3*10^-8 mole we have 1.3*10^-8 * 6.022*10^23 = 7.83*10^15 atoms
so number of electrons = 7.83*10^15 *2 = 1.57*10^16
1 Coulomb is equal to 6.241*10^18 electrons.
so 1.57*10^16 electron = 2.5*10^-3 C
I = Q/t
so t = Q/I
= 2.5*10^-3/1.3*10^-3
= 1.92 s
so for both side the total time would be 1.92*2 = 3.84 s

i tried plugging that number but apparently it was wrong.
Any ideas what i am doing wrong in here?
Any help would be appreciated.

Redbelly98
Staff Emeritus
Homework Helper

in 1 mole the weight of zinc is 65.38 g
so in 8.35*10^-7 kg 1.3*10^-8 mole

Check the units, both kg and g appear here. Use one or the other.

yes you are right.
i redo the part.
does it look good?

in 1 mole the weight of zinc is 65.38 g
so in 8.35*10^-7 kg 1.3*10^-5 mole
1 mole we have 6.022*10^23 atoms
so in 1.3*10^-5 mole we have 1.3*10^-5 * 6.022*10^23 = 7.83*10^18 atoms
so number of electrons = 7.83*10^18 *2 = 1.57*10^19
1 Coulomb is equal to 6.241*10^18 electrons.
so 1.57*10^19 electron = 2.5 C
I = Q/t
so t = Q/I
= 2.5/1.3*10^-3
= 1923 s
so for both side the total time would be 1923*2 = 3846 s

Redbelly98
Staff Emeritus