Question

You need a 80% alcohol solution. On hand, you have a 240 mL of a 15% alcohol mixture. How much pure alcohol will you need to add to obtain the desired solution?

Answer 1

240 mL of 15% alcohol solution contains 0.15 • 240 = 36 mL of alcohol.

If we add
`x` mL of pure alcohol to it, we increase the total volume to
`240 + x` mL, and it will contain
`36 + x` mL of alcohol.

Solve for
`x` such that the concentration of alcohol (the ratio of the volume of alcohol to total volume of solution) is 80%.

`(36 + x)/(240 + x) = 0.80`

`36 + x = 0.80 (240 + x)`

`36 + x = 192 + 0.80x`

`0.2x = 156`

`x = 780`

You need to add 780 mL of pure alcohol to get the desired concentration.