Question

On passing one faraday of electric charge through a dilute solution of an acid, the volume of hydrogen obtained at S.T.P is:
a) $\text{22400 mL}$
b) $\text{1120 mL}$
c) $\text{2240 mL}$
d) $\text{11200 mL}$

Answer 1

Hint:Faraday is the unit of electricity. It is defined as the amount of electric charge that liberates one gram equivalent of any ion from an electrolytic solution. It is the charge of coulomb of 1 mole of electrons. One faraday of electricity is approximately equal to 96800 C.

Complete answer:
 the equation when the electric charge is passed through dilute solution of acid,
\[2{{H}^{+}}+2{{e}^{-}}\to {{H}_{2}}\]
Now we can see that 2 moles of acid form 1 mole of hydrogen
We know that 1 faraday dissociates 1 mole of acid,
So 1 faraday of electric charge through dilute acid 1 mole of dilute solution of acid,
So, 1 mole of acids will form \[\dfrac{1}{2}\times 22400\] $\text{mL}$ or \[\dfrac{1}{2}\] mole of hydrogen
As we know 1 mole of a substance occupies $\text{22400 mL}$ of volume at S.T.P
So, $\text{22400 mL}$ of acid will form \[\dfrac{1}{2}\times 22400\] $\text{mL}$ of hydrogen
= $\text{11200 mL}$ of hydrogen at S.T.P
So on passing one faraday of electric charge through a dilute solution of an acid, the hydrogen obtained at S.T.P is $\text{11200 mL}$.

Therefore, the correct answer is option (b).

Note:
There are two laws of Faraday, the first law states that the mass of the substance deposited or liberated at any electrode is directly proportional to the quantity of electricity passed through the electrolyte. The second law of electricity states that when the same quantity of electricity is passed through two electrolytic solutions which are connected in series then the mass of the substance produced at the electrode is directly proportional to their equivalent weight.