## Electrochemistry question

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Dhamnekar Winod
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### Electrochemistry question

A metal cup of surface area $$200. cm^2$$ needs to be electroplated with silver to a thickness of 0.200 mm. The density of silver is $$1.05 \times 10^4$$kg m⁻³.The mass of a silver ion is $$1 .79 \times$$ 10⁻²⁵ kg and the charge is the same magnitude as that on an electron. How long does the cup need to be in the electrolytic tank if a current of 12.5 A is being used?

Any chemistry help will be accepted. I am working on this question.
Any science consists of the following process. 1) See 2)Hear 3)Smell,if needed 4)Taste, if needed 5)Think 6)Understand 7)Inference 8)Take decision [Believe or disbelieve, useful or useless, true or false, cause or effect, any other criteria]
ChenBeier
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Location: Berlin, Germany

### Re: Electrochemistry question

m = I*t*M(Ag)/(n*F)
m = Rho*V
V = th* A
Rho*th*A = I*t*M(Ag)/(n*F)
t= Rho*th*A* n*F/(I*M(Ag))

m= mass, I = current, t= time, M(Ag) molar mass of silver, n= amount of electrons to Transfer, F Faradyconstant, Rho = specific gravity of silver, th = thickness of plated silver, A = surface of cup
Dhamnekar Winod
Sr. Staff Member
Posts: 192
Joined: Sat Nov 21, 2020 10:14 am
Location: Mumbai[Bombay],Maharashtra State,India

### Re: Electrochemistry question

The volume of silver that gets electroplated is 0.00000400 m³.
The mass of silver that gets electroplated is 0.00000400 m³ × 1.05 × 10⁴ kg m⁻³=0.042 kg.

The molar mass of silver= 107.8682 g/mol , so moles of silver 42 g/107.87 g = 0.38935756 mole of silver.

Hence, moles of electrons required Ag ⁺ (aq) + e ⁺→ Ag(s), so 0.38935756 mole of silver requires 0.38935756 mole of electrons.

If i plugged in these values in your formula answer is $$t= \frac{42 g \times 0.38935756 mol e^- \times 96485 C/mol} {12. 5 C/ s \times 107.87 g} = 1170.165$$ seconds

But the correct answer given is 3005 seconds ~ 50 mins approx.

What is wrong here?
Any science consists of the following process. 1) See 2)Hear 3)Smell,if needed 4)Taste, if needed 5)Think 6)Understand 7)Inference 8)Take decision [Believe or disbelieve, useful or useless, true or false, cause or effect, any other criteria]
ChenBeier
Distinguished Member
Posts: 873
Joined: Wed Sep 27, 2017 7:25 am
Location: Berlin, Germany

### Re: Electrochemistry question

You devided two times by the molar mass.
If you calculated n = m/M then you cannot do the thing twices.
Dhamnekar Winod
Sr. Staff Member
Posts: 192
Joined: Sat Nov 21, 2020 10:14 am
Location: Mumbai[Bombay],Maharashtra State,India

### Re: Electrochemistry question

t= n*F/I , n= number of moles of electrons required, F= Faraday constant, I= current in Ampere or Coulombs/second.

t=(0.38935756 Moles* 96485 C)/12.5 C/s = 3005.37 seconds, or 50 minutes approx.
Any science consists of the following process. 1) See 2)Hear 3)Smell,if needed 4)Taste, if needed 5)Think 6)Understand 7)Inference 8)Take decision [Believe or disbelieve, useful or useless, true or false, cause or effect, any other criteria]
ChenBeier
Distinguished Member
Posts: 873
Joined: Wed Sep 27, 2017 7:25 am
Location: Berlin, Germany

### Re: Electrochemistry question

Yes, now its correct.