Question

A chemistry lab needs to make 100 gallons of an 18% acid solution by mixing a 12% acid solution with a 20% solution. find the number of gallons needed of each solution.

Answer 1

Answer:

25 gallons of 12 % acid solution and 75 gallons of 20% solution are required.

Explanation:

Let the volume of the solution 12% acid solution and 20% acid solution be x and y.

x + y  = 100 gallons...[1]

Percentage of acid solution desired to prepare = 18%

$x\times \frac{12}{100}+y\times \frac{20}{100}=100\times \frac{18}{100} gallons$ ...[2]

On solving [1] and [2] we get:

y = 75 gallons , x = 25 gallons

25 gallons of 12 % acid solution and 75 gallons of 20% solution are required.

Answer 2

The question above can be answered by using the volume balance concept. Two equations can be established by total volume balance and the component (acid) volume balance.

If we let x be the volume of the 12% acid solution, the volume of the 20% acid solution will have to be 100 - x.

                 x + (100 - x) = 100

Then, the acid mass balance will give us the equation,

     (x)(0.12) + (100 - x)(0.20) = (100)(0.18)

Simplifying,
     0.12x + 20 - 0.20x = 18
             -0.08x = 20 - 18 
               -0.08x = 2

The value of x from the equation is 25.

Hence, the volume of the 12% acid solution is 20 galloons and that of the 20% acid solution is 75 galloons.