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.

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.