Question

A chemist wishes to mix a solution that is 12​% acid. She has on hand 14 liters of a 6​% acid solution and wishes to add some 16​% acid solution to obtain the desired 12​% acid solution. How much 16​% acid solution should she​ add?

Answer 1

To obtain the desired 12% acid solution, the chemist needs to add a certain volume of a 16% acid solution to the existing 14 liters of a 6% acid solution. By setting up an equation and solving for the unknown volume, the chemist can determine how much 16% acid solution to add.

Step-by-step explanation:

To solve this problem, we can use the concept of the amount of acid in a solution.

Let the volume of the 16% acid solution that needs to be added be x liters.

Since the initial solution is 14 liters of 6% acid, we can calculate the amount of acid in this solution as follows:

(14 liters) x (0.06) = 0.84 liters of acid

Now, when we add x liters of a 16% acid solution, we can calculate the amount of acid in this solution as:

(x liters) x (0.16) = 0.16x liters of acid

For the desired 12% acid solution, the total volume would be 14 + x liters, and the total amount of acid would be 0.84 + 0.16x liters.

Since the desired solution is 12% acid, we can set up the equation:

(0.84 + 0.16x) / (14 + x) = 0.12

By solving this equation, we can find the value of x, which represents the volume of the 16% acid solution that needs to be added.

Answer 2

25 liters of the 16% solution should be added.

Step by Step Explanation:

pure acid amount + pure acid amount = total pure acid amount

So,

0.02*10 + 0.16*x = 0.12*(10+x)

0.02*10 + 0.16x = 0.12*10 + 0.12*x

0.16*x - 0.12*x = 0.12*10 - 0.02*10

(0.16 - 0.12)*x = 0.12*10 - 0.02*10

x = (0.12*10-0.02*10)/(0.16-0.12)=25

Check: (0.2*10+0.16*25)/(10+25) = 0.12 = 12% of concentration of the final mixture. ! Correct !