Question

6. Solve: A chemist needs 30 ounces of 50% hydrochloric acid solution. In her lab, she has some 80% hydrochloric acid solution, some 60% hydrochloric acid solution, and some 40% hydrochloric acid solution. She must use 2 ounces of the 80% solution. How many ounces each of the 40% and 60% solutions must be mixed with the 2 ounces of 80% to obtain the 30 ounces of 50% hydrochloric acid solution she needs?

Answer 1

To prepare 30 ounces of a 50% hydrochloric acid solution, the chemist must mix 17 ounces of the 40% solution with 11 ounces of the 60% solution and 2 ounces of the 80% solution.

Step-by-step explanation:

The student needs to mix different concentrations of hydrochloric acid to end up with 30 ounces of a 50% solution. We know that 2 ounces of the 80% solution are used, so the remaining 28 ounces must be a mix of the 40% and 60% solutions.

Let x represent the ounces of the 40% solution and 30 - 2 - x, or 28 - x, represent the ounces of the 60% solution. Setting up the equation based on mass of pure hydrochloric acid:

• 0.80(2) + 0.40(x) + 0.60(28 - x) = 0.50(30)

Solving for x:

1. 1.6 + 0.40x + 16.8 - 0.60x = 15
2. -0.20x + 18.4 = 15
3. -0.20x = -3.4
4. x = 17

The chemist needs to use 17 ounces of the 40% solution and 11 ounces of the 60% solution, combining them with the 2 ounces of the 80% solution to obtain 30 ounces of 50% hydrochloric acid.

Answer 2

I have no idea. I think you have to add up to 30 ounces but when added up and divided together the acid becomes 50%