Question

How long does it take to electroplate 0.5 mm of gold on an object with a surface area of 31 cm^^ from an Au3+(aq) solution with a 8 A current? Recall the density of gold is 19.3 g/cm^3.

Answer 1

It will take 5492 seconds to electroplate 0.5 mm of gold on an object .

Step-by-step explanation:

Mass of gold = m

Volume of gold = v

Surface area on which gold is plated =
`a=31 cm^2`

Thickness of the gold plating = h = 0.5 mm = 0.05 cm

1 mm = 0.1 cm

`V=a* h=31 cm^2* 0.05 cm=1.55 cm^3`

Density of the gold =
`d=19.3 g/cm^3`

`m=d* v=19.3 g/cm^3* 1.55 cm^3=29.915g`

Moles of gold =
`(29.915 g)/(197 g/mol)=0.152 mol`

`Au^(3+)+3e^-\rightarrow Au`

According to reaction, 1 mole of gold required 3 moles of electrons,then 0.152 moles of gold will require :

`(3)/(1)* 0.152 mol=0.456 mol` of electrons

Number of electrons = N =
`0.456* * 6.022* 10^(23)`

Charge on single electron =
`q=1.6* 10^(-19) C`

Total charge required = Q

`Q=N* q`

Amount of current passes = I = 8 Ampere

Duration of time = T

`I=(Q)/(T)`

`T=(N* q)/(I)`

`=(0.456* * 6.022* 10^(23)* 1.6* 10^(-19) C)/(8 A)=5492 s`

It will take 5492 seconds to electroplate 0.5 mm of gold on an object .