Question

A copper voltmeter, a silver voltmeter and a water voltmeter are connected in series and current is allowed to pass for sometime. The ratio of the number of moles of copper, silver and hydrogen formed at the cathode is:
A. 2:1:1
B. 1:1:1
C. 1:2:1
D. 1:2:2

Answer 1

Hint: Recall Faraday's second law of electrolysis, the moles of the substance deposited at the cathode is proportional to the charge transferred. Or, the mass of substances which are liberated or dissolved by the same amount of electricity is said to be directly proportional to their equivalent masses or equivalent weights (E). In a series configuration circuit, the current passed in each voltmeter is the same.

Complete Answer:
The mass of the chemical, deposited because of electrolysis, is not only proportional to the number of electricity passes through the electrolyte, but it also depends upon another factor. Every substance will have its own mass. So for the identical number of atoms, different substances will have different masses.
Again, what number atoms deposited on the electrodes also depends upon their number of valencies. If valency is more, then for the identical amount of electricity, the amount of deposited atoms are less whereas if valency is a smaller amount, then for the identical quantity of electricity, more number of atoms to be deposited.
So, for the identical quantity of electricity or charge passes through different electrolytes, the mass of deposited chemical is directly proportional to its mass and inversely proportional to its valency.
Faraday’s second law of electrolysis states that, when the identical quantity of electricity is capable of several electrolytes, the mass of the substances deposited are proportional to their respective chemical equivalent or combining weight.
Now, we know that copper exists in its +2 oxidation state. So 2 mole charges are transferred in one Faraday of charge.
$\begin{align}
  & 1\,mole\,=2F \\
 & 1F=\frac{1}{2}mole \\
\end{align}$, for copper
Silver exists in +1 oxidation state
$1\,mole=1F$ , for silver
Hydrogen exists in +2 oxidation state
$\begin{align}
  & 1\,mole\,=2F \\
 & 1F=\frac{1}{2}mole \\
\end{align}$, for hydrogen
So, the ratio of moles are:
$\begin{align}
  & \frac{1}{2}:1:\frac{1}{2} \\
 & =1:2:1 \\
\end{align}$

So, we obtain option C as our answer.

Note:
Make sure you have a clear understanding of the definition of Faraday. 1F is the amount of electric charge that is contained, or is carried by one mole of the electrons. Faraday relates charge with the number of moles and not with the current or time.