Question

How many spoons can be electroplated by silver when $7$ ampere current is passed through an electrolyte cell of $AgN{O_3}$ for $1.93$ hours? $0.01$ grams Ag layer is deposited on each spoon. ($Ag = 108\dfrac{g}{{mol}}$).

Answer 1

In the above given question we need to first see how much charge is generated and then the moles of charge would be equal to the moles of the silver deposited and then divide the moles by the moles deposited on one spoon to calculate the number of spoons.

Complete answer:
Now in the above given question we are given the ampere of current which is flown for some $1.93$ hours. -
First let’s observe the reaction that happens for the silver ions to get converted to silver metal.
The reaction is as follows: -
$A{g^ + } + {e^ - } \to Ag$
The reaction is balanced so by observing the reaction we can say that one mole of charge is needed to form one mole of silver metal.
Now first let’s calculate the charge we have, now we know that charge is equal to current multiplied by time by the formula $Q = It$
Now we have current equal to $7$ ampere which is been flown during a time span of $1.93$hours, by using the above given formula we can say that
$Q = It = 7 \times 1.93 \times 3600 = 48636\,C$
We know that one mole of electron charge has about $96500\,C$ charge, therefore if we have $48636\,C$ of charge then the moles of change or electron that we have are
$moles\,of\,electron = \dfrac{{48636}}{{96500}} = 0.504\,moles$
So, we have about $0.504\,moles$ of charge and the equation $A{g^ + } + {e^ - } \to Ag$ says that one mole of charge generates about one mole of silver metal therefore $0.504\,moles$ of charge will generate about $0.504\,moles$ of silver.
Now if we have total of $0.504\,moles$ So, silver then the mass of silver we have in weight would be equal to the moles multiplied by the elementary weight of silver that is $Ag = 108\dfrac{g}{{mol}}$
Now mass of silver we got is equal to: -
$mass\,of\,silver = moles \times M.W. = 0.504 \times 108 = 54.432\,gm$
Now as we can see we have about $54.432\,gm$ of silver and the question says that one silver spoon has about $0.01$ grams of silver,
By stoichiometry we can say that if one silver spoon has $0.01$ grams of silver then $54.432\,gm$ will form spoons which are equal to the division of total weight of silver by the weight of silver on one spoon
$spoons = \dfrac{{total\,weight\,of\,silver}}{{silver\,weight\,on\,one\,spoon}}$
$spoons = \dfrac{{54.432}}{{0.01}} = 5443\,spoons$
And hence $5443\,spoons$ are formed when $7$ ampere current is passed through the electrolyte cell of $AgN{O_3}$ for $1.93$ hours and when a $0.01$ grams Ag layer is deposited on each spoon.

Note:
The thing to note in such questions is that you need to figure out the stoichiometric reaction after which is balanced you can equate the moles according to coefficients. If given the number of spoons and the weight on one spoon we can calculate the charge.