Question

A certain quantity of electricity deposits $0.54g$ of $Ag$ from silver nitrate solution. What volume of hydrogen will be liberated by the same quantity of electricity at ${27^0}C$ and $750mm$ of $Hg$ pressure?

Answer 1

Hint- In order to deal with this question first we have to apply Faraday's law to get the equivalent mass of hydrogen, further by using the obtained mass of hydrogen we will apply the ideal gas equation to get the required volume.
Formula used- $\dfrac{{{\text{Mass of }}{H_2}}}{{{\text{Mass of }}Ag}} = \dfrac{{{\text{Eq}}{\text{.mass of }}{H_2}}}{{{\text{Eq}}{\text{.mass of }}Ag}},PV = nRT,n = \dfrac{w}{M}$

Complete step-by-step answer:
Given that :
Mass of $Ag$ = $0.54g$
As we know that
Equivalent mass of hydrogen = 1 g
Equivalent mass of $Ag$ = 108 g
Now according to Faraday's law
$
  \dfrac{{{\text{Mass of }}{H_2}}}{{{\text{Mass of }}Ag}} = \dfrac{{{\text{Eq}}{\text{.mass of }}{H_2}}}{{{\text{Eq}}{\text{.mass of }}Ag}} \\
   \Rightarrow {\text{Mass of }}{H_2} = \dfrac{{{\text{Eq}}{\text{.mass of }}{H_2}}}{{{\text{Eq}}{\text{.mass of }}Ag}} \times {\text{Mass of }}Ag \\
   \Rightarrow {\text{Mass of }}{H_2} = \dfrac{{1 \times 0.54}}{{108}} = 0.005g \\
 $
So the mass of ${H_2}$ = 0.005g
We know the ideal gas equation which is given as
$PV = nRT$------ (1)
Where
$n = \dfrac{w}{M}$------ (2)
Let us now substitute the value from equation (2) into equation (1)
$
   \Rightarrow PV = \dfrac{w}{M}RT \\
   \Rightarrow V = \dfrac{w}{M}.\dfrac{{RT}}{P} \\
 $
Substitute the values in above formula we have
$
  \because V = \dfrac{w}{M}.\dfrac{{RT}}{P} \\
   \Rightarrow V = \dfrac{{0.005 \times 0.0821 \times 300 \times 760}}{{2 \times 750}} \\
   \Rightarrow V = 0.06234{\text{ litre}} \\
 $
Hence the volume of hydrogen = $0.06234{\text{ litre}}$

Additional information-
Hydrogen is the only element with no neutrons in it. This is composed of one proton and one electron. Because of this, the periodic table is not a member of any group or family. Hydrogen has special properties not associated by other materials.
Hydrogen may be used to produce electricity, or power and heat, in fuel cells. Hydrogen is most widely used today in the manufacture of petroleum refining and fertilizers, whereas transport and services are emerging markets.

Note- Ideal gas law is a well-defined interpretation of the behavior of other gasses under different conditions. Ideal Gas Equation is a synthesis of scientific principles such as the law of Charles, Boyle's law, the law of Gay-Lussac and the law of Avogadro.
Ideal Gas Equation is the equation that describes the states of the ideal gasses represented mathematically by the combinations of physical and analytical constants. It is sometimes called the general equation of gas. The universal law of gas is the equation of state of an universal imaginary gas. This is a good approximation of other gases' behavior under several circumstances, but it has many drawbacks.