Question

Henry has two acid solutions. How much of his first solution, which is 5% acid, should he mix with 150 mL of his second solution, which is 11% acid, in order to make an 8.75% acid solution?

60 mL
120 mL
90 mL
100 mL
80 mL

Answer 1

Henry should mix 90 mL of the first solution, which is 5% acid, with 150 mL of the second solution, which is 11% acid, to make an 8.75% acid solution.

Step-by-step explanation:

To find out how much of the first solution (5% acid) Henry should mix with 150 mL of his second solution (11% acid) to make an 8.75% acid solution, we can set up an equation based on the principle of conservation of mass for the acid.

Let x be the volume of the first solution that Henry needs to add. Then the total amount of acid in the two solutions, before mixing, should equal the total amount of acid in the final mixture. The equation representing this situation will be:

0.05x (amount of acid in the first solution) + 0.11(150) (amount of acid in the second solution) = 0.0875(x + 150) (amount of acid in the final solution)

The equation simplifies to:

0.05x + 16.5 = 0.0875x + 13.125

Subtract 0.05x from both sides:

16.5 = 0.0375x + 13.125

Subtract 13.125 from both sides:

3.375 = 0.0375x

Divide both sides by 0.0375 to find x:

x = 3.375 / 0.0375

x = 90 mL

Henry should mix 90 mL of the first solution (5% acid) with 150 mL of the second solution (11% acid) to obtain a solution with an 8.75% acid concentration.