Question

How much water must be added to one gallon of $8\% $ saline solution to get a $2\% $saline solution?
A.$1\,gallons$
B.$2\,gallons$
C.$3\,gallons$
D.$4\,gallons$

Answer 1

Hint: 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 question we are given an $8\% $ solution that is saline and to be converted to $2\% $ solution.
First, we need to understand what exactly the $8\% $ solution exactly means. It means that in $1$ gallons of water about $0.08$ gm of salt is present. Now we need to convert it into a $2\% $ solution which means on adding some quantity of water we get a solution whose one gallons would have $0.02$ gm of salt.
Now let’s say that we add some quantity $x$ in the solution $8\% $ saline
Now the final volume of the solution is $1 + x$ and this solution already has about $0.08$ gm of salt
And we are already given in the question that the final solution is a $2\% $saline that means $0.08$ gram in $1 + x$ volume of water
Now we can say that $\dfrac{{0.08}}{{1 + x}} = 0.02$
$\dfrac{{0.08}}{{0.02}} = 1 + x$
$x = 3\,gallons$
On adding $3\,gallons$ of water in one gallons of $8\% $ saline solution, we get a $2\% $ saline solution.

Note:
If we would have been given that some volume of water is added to some percentage of saline solution, then directly add the imaginary volume of water to the existing amount of water and divide it by the amount of salt and we will get the percentage saline of the final solution.