Chapter 11, Problem 16CCSR

To determine

Find the amount in liters of 45% acid solution that the Chemistry student needs.

Answer to Problem 16CCSR

The amount of 45% acid solution is 8 liters.

Explanation of Solution

Given:

A chemistry student needs to make 20 liters of a solution that is 60% acid. She plans to make the solution by mixing a solution that is 70% acid with another solution that is 45% acid. How many liters of 45% acid solution will she need?

Concept Used:

Total amount of solution is 20 liters with 60 % acid.

Let the student needs x liters of 45 % acid solution.

Now the student need (20 − x) liters of 70 % acid solution.

The equation: $45\%·x+70\%·(20-x)=60\%·20$

Calculation:

Total amount of solution is 20 liters with 60 % acid.

Let the student needs x liters of 45 % acid solution.

Now the student need (20 − x) liters of 70 % acid solution.

The equation: $45\%·x+70\%·(20-x)=60\%·20$

Now solve for x:

  $\begin{array}{l}45\%·x+70\%·(20-x)=60\%·20\\ 0.45x+0.70(20-x)=0.60·20\\ 0.45x+14-0.70x=12\\ -0.25x+14=12\\ -0.25x+14-14=12-14\\ -0.25x=-2\\ \frac{-0.25x}{-0.25}=\frac{-2}{-0.25}\\ x=8\end{array}$

Thus, the amount of 45% acid solution is 8 liters.