Question

A chemist needs to prepare 500 ml of copper-sulfate solution with a 15% concentration. She wishes to use a high concentration solution (60%) and dilute it with a low concentration solution (5%) in order to do this. How much of the 60% solution should she use round to the nearest whole number? Do not use units

Answer 1

Answer:

She should use 91 mL of the 60% solution (rounded to the nearest whole number).

Step-by-step explanation:

The first step to solve this question is to write the correct equations system. The two variables are :

$X_{1}$ : The amount of high concentration solution (60%) (in mL).

$X_{2}$ : The amount of low concentration solution (5%) (in mL).

The first equation for the mixing is :

$(0.60).X_{1}+(0.05).X_{2}=(0.15).(500)$ (I)

Where $(0.60)$ , $(0.05)$ and $(0.15)$ represent the percentages for $X_{1}$ , $X_{2}$ and the final 500 mL of copper-sulfate solution respectively.

The second equation is :

$X_{1}+X_{2}=500$ (II)

The equation (II) represents that the sum from the volumes of high and low concentration solution must be 500 mL.

The final step is to solve this equation system :

From (II) we find that :

$X_{2}=500-X_{1}$ (III)

If we use (III) in (I) :

$(0.60).X_{1}+(0.05).(500-X_{1})=(0.15).(500)$

$0.60X_{1}+25-0.05X_{1}=75$

$0.55X_{1}=50$

$X_{1}=\frac{50}{0.55}=\frac{1000}{11}=90.9090$ ≅ $91$

She should use 91 mL of the 60% solution (rounded to the nearest whole number).