Question

dawn schmidt is a chemist. she needs to prepare 24 ounces of a 9% hydrochloric acid solution. find the amount of 12% solution and the amount of 6% solution she should mix to get this solution. how many ounces of the 12% acid solution should be in the mixture?

	first solution	second solution	mixture needed
ounces of solution	x	y	24
ounces of pure acid	0.06x	0.12y	0.09(24)

Explanation:

Step1: Set up equations based on volume and acid - content

We know that the total volume of the mixture is 24 ounces. So, \(x + y=24\), which can be rewritten as \(x = 24 - y\). Also, considering the amount of pure acid in each solution, \(0.06x+0.12y=0.09\times24\).

Step2: Substitute \(x = 24 - y\) into the acid - content equation

Substitute \(x\) into \(0.06x + 0.12y=0.09\times24\):
\[

$$\begin{align*} 0.06(24 - y)+0.12y&=0.09\times24\\ 1.44-0.06y + 0.12y&=2.16\\ -0.06y+0.12y&=2.16 - 1.44\\ 0.06y&=0.72 \end{align*}$$

\]

Step3: Solve for \(y\)

Divide both sides of \(0.06y = 0.72\) by 0.06: \(y=\frac{0.72}{0.06}=12\) ounces.

Answer:

12 ounces