Question

Passage of the current for $ 548 $ seconds through a silver coulometer results in the deposition of $ 0.746g $ of silver. What is the current in $ A $ ?
(A) $ 1.22 $
(B) $ 1.16 $
(C) $ 1.07 $
(D) $ 1.00 $

Answer 1

Hint : Here, the current is set to pass through a silver coulometer and this results in the deposition of silver there. So, at first we have to find the comparison between the farads and grams so that we can calculate the required current. As we know that the charge flowing in the electrochemical cell is equivalent to n times farad.
Use: $ 1F = 96500C{\left( {mole} \right)^{ - 1}} $
 $ Q = nF $ ; $ n $ no. of electrons, $ Q $ is the charge and $ F $ is the faraday constant and it is the charge carried by $ 1mole $ of electrons.
 $ Q = It $ ; $ I $ is current, $ t $ is the time for which the current is flowing.
Molecular weight of the silver: $ 108g $ .

Complete Step By Step Answer:
Let us consider the reaction when the current is passed through the silver coulometer as:
 $ A{g^ + } + {e^ - } \to Ag $
Now, let us consider the comparison between the molecular weight of silver $ Ag $ and the charge as below:
 $ 1F \to {\text{molecular weight of }}Ag $
Therefore, charge carried by the total weight of the silver is
 $ 1F \to 108g $
But $ 1F = 96500C{\left( {mole} \right)^{ - 1}} $
Thus, we have
 $ 96500C \to 108g $
Charge carried by one gram of silver is:
 $ 1g \to \dfrac{{96500}}{{108}}C $
Now, according to the given condition the deposition of silver is $ 0.746g $ and we are asked to find the current through this weight of silver. So, we will multiply both the sides by $ 0.746g $ and we get:
 $ 0.746g \to 0.746 \times \dfrac{{96500}}{{108}}C $
This is called the charge flowing through the deposition.
On calculation we get
 $ Q = 0.746 \times \dfrac{{96500}}{{108}}C $ …. (by $ Q = nF $ )
 $ t = 548\sec $
We know the current flowing through the deposition of silver is given by:
 $ Q = It $
 $ \Rightarrow I = \dfrac{Q}{t} $
 $ \Rightarrow I = \dfrac{{0.746 \times \dfrac{{96500}}{{108}}C}}{{548\sec }} $
On calculating the above equation for current we have
 $ I = 1.22A $
Thus, the current flowing in the deposition of silver is $ 1.22A $
The correct answer is option A.

Note :
Remember the concept of the electrochemistry that the charge flowing in the given material is equal to the product of no. of electrons flowing in that material and the charge per mole of electron i.e. faraday constant. We must remember what one farad equivalent is to. Be careful in the calculation part.