HELP A problem on quantitative aspects of electrolysis

[Kudo Shinichi]

HELP!A problem on quantitative aspects of electrolysis

Homework Statement

A quantity of electric charge brings about the deposition of 3.34 g Cu at a cathode during the electrolysis of a solution containing Cu²⁺(aq).
What volume of H₂(g) measured at 27.8^oC and 767 mmHg, would be produced by this same quantity of electric charge in the reduction of H⁺(aq) at a cathode?

The Attempt at a Solution

I don't really know the formula for solving the volume in the electrolysis.
The way I approached this problem is by using the ideal gas law(but I don't think it is the right way):
PV=nRT
2H⁺+2e^--->H₂(g)
we are trying to solve for V, so
V=?
P=767mmHg
R=62.36367L·mmHg·K⁻¹·mol⁻¹
n=2
T=300.95K
plug the numbers into the equation and I got V=48.94L

Can someone please help me with it? Is it the right way for solving the problem? thank you very much.

 

[alxm]

Well, you got the part about using the ideal gas law to get the volume.
But how much gas did you create? n is the number of moles of gas.

First, how many moles of copper did you produce?
How many moles of electrons does that correspond to?
How many moles of hydrogen gas do you get per mol of electrons?

 

[Kudo Shinichi]

Well, you got the part about using the ideal gas law to get the volume.
But how much gas did you create? n is the number of moles of gas.

First, how many moles of copper did you produce?
How many moles of electrons does that correspond to?
How many moles of hydrogen gas do you get per mol of electrons?

there are 0.052 moles of copper
0.103 moles of electrons (2 electrons transferred in copper)

I am not really sure about the moles of hydrogen gas but since there are 2 moles of electrons and 1 moles of hydrogen gas, I think that the moles of hydrogen gas is 1/2 of the moles of electrons which is 0.0515
is it right? and do i just plug the moles of hydrogen gas into the ideal gas equation?

 

[alxm]

there are 0.052 moles of copper
0.103 moles of electrons (2 electrons transferred in copper)

I am not really sure about the moles of hydrogen gas but since there are 2 moles of electrons and 1 moles of hydrogen gas, I think that the moles of hydrogen gas is 1/2 of the moles of electrons which is 0.0515
is it right? and do i just plug the moles of hydrogen gas into the ideal gas equation?

Right, two electrons are used in both reactions so n_Cu = n_H2.
And you put that into the ideal gas equation to get the volume.

 

[Borek]

Kudo, read about Faraday's law of electrolysis. It won't give different result, as it is basically identical to what you did, it is just a systematic way of doing this type of questions.