Question

A laboratory technician needs to make a 56​-liter batch of a 40​% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 20​% to get the desired​ concentration?

Answer 1

for a 40% acid solution by volume
(volume of acid) / (total volume) = 0.40

let's suppose x = the volume of pure acid
since the total volume must be 56, the volume of 20% acid = (56 - x)

now, to figure out how much acid each acid adds to the solution...
the pure acid contributes x L of acid
the 20% acid contributes 0.20(56-x)

so the volume of acid = x + 0.20(56-x)

now, plug this volume of acid into the original formula, along with the total volume 56, and solve for x. as a reminder, x = the amount of pure acid, so you must also evaluate (56-x) to figure out how much of the 20% solution to add as well