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

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

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)=(50)/(0.55)=(1000)/(11)=90.9090` ≅
`91`

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