How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10​% to get the desired concentration?

Question

A laboratory technician needs to make a 42​-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 10​% to get the desired concentration?

Answer 1

The 42 L batch is 40% acid, so 42 x 0.4 = 16.8 L of pure acid in the batch.

Let P = the number of liters of pure acid required, D = the number of liters of the 10 % solution.

Then P + 0.10 x D = 16.8.

Also, P + D = 42

Solve these equations simultaneously by substitution.

P = 42 - D

42 - D + 0.10 x D = 16.8

-D (1 - 0.10) = 16.8 -42

-D = -25.2 / 0.9

D = 28 L

P = 42 - 28 = 14 L

Answer 2

Let x be liters of acid and y be liters of 10% acid. Do a total volume balance and a volume of acid balance:

x + y = 42 Total volume

x + .1y = .4(42) Acid volume

use substitution to eliminate y y = 42 - x

x + .1(42 - x) = .4(42)

solve for x to obtain liters of acid, then solve for y. using the total volume equation.