Question

A 10.07 gram silver obtained during the circulation of electricity of 5 ampere up to 30 minutes in a silver nitrate pot (cell). Find out the electrochemical equivalent of silver. If the chemical equivalent of hydrogen is 0.00001036 then what will be the equivalent weight of silver?

Answer 1

Hint: We know that the process of electrolysis is mainly governed by only two laws. Faraday’s first and second law of electrolysis. We can directly apply both of them to them to find out the solution.

Complete Step by step answer:
We know that the Faraday’s first law of electrolysis states that the amount of any substance deposited or liberated at any electrode is directly proportional to the quantity of electricity passed through the electrolyte.
 $ W = ZQ $
Where, $ W $ is the amount of substance deposited or liberated in grams
 $ Q $ is the quantity of electricity in coulombs
 $ Z $ is the electrochemical equivalent of the substance.
We know that,
 $ Q = It $
Where $ I $ is current in ampere and $ t $ is time in seconds
Thus, $ W = ZIt $
Here given that 10.07 gram of silver is obtained, which means
 $ W = 10.07g $
Current is given as 5 ampere and for a time 30 minutes
 $ I = 5A $ and $ t = 30min = 30 \times 60 = 1800s $
Now to find out the electrochemical equivalent of silver, we just have to directly substitute this into the first law of electrolysis.
 $ 10.07 = Z \times 5 \times 1800 $
 $ \Rightarrow Z = \dfrac{{10.07}}{{5 \times 1800}} $
 $ \Rightarrow {\text{Z}} = 0.00111888 $
So we got the electrochemical equivalent of silver.
Now to find out the equivalent weight of silver, we can make use of Faraday’s second law which states when the same quantity of electricity is passed through solutions of different electrolytes connected in series, the amount of different substances deposited at the electrodes is directly proportional to their equivalent weights.
Also we know that equivalent weight is directly proportional to electrochemical equivalent.
Thus, $ \dfrac{{{W_1}}}{{{W_2}}} = \dfrac{{{E_1}}}{{{E_2}}} = \dfrac{{{Z_1}}}{{{Z_2}}} $
We know the electrochemical equivalent of silver and hydrogen. By substituting in the equation we can find the equivalent weight of silver.
 $ Electrochemical\;equivalent\;of\;silver,\;{Z_1} = 0.00111888 $
 $ \Rightarrow Electrochemical\;equivalent\;of\;Hydrogen,\;{Z_2} = 0.00001036 $ [Given]

Now, we know the equivalent weight of hydrogen is 1, hence
 $ \dfrac{{{E_1}}}{{{E_2}}} = \dfrac{{{Z_1}}}{{{Z_2}}} $
Where $ {E_1} $ is equivalent weight of silver and $ {E_2} $ is equivalent weight of hydrogen
 $ \dfrac{{{E_1}}}{1} = \dfrac{{0.00111888}}{{0.00001036}} $
 $ \Rightarrow {E_1} = 108g $

Thus we get the equivalent of silver as 108g.

Note: Faraday’s first law of electrolysis can also state as when one faraday (96500 coulombs) of electricity when passed through the solution, deposits or liberates 1 gram equivalent weight of substance. Hence, Eq. wt of substance = $ Z \times 96500 $.