How much water must be evaporated from 100 gallons of a 10% brine (saltwater) solution to get a 40% brine (saltwater)?

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Answer 1 · 2015-10-18T15:12:15

75 gallons of water

Let

$V_1$ be volume of 10 % brine solution

$V_2$ be volume of 40 % of brine solution after evaporation of water

Mass of brine in volume of $V_1$ = $V_1$ *(10/100) = 0.1 $V_1$

Mass of brine in 100 gallons of 10 % brine solution = $0.1X100$ =10 =

Mass of brine in volume of $V_2$ = $V_2$ *(40/100) = 0.4 $V_2$

Total mass of the salt is constant due to evaporation

0.4 $V_2$ = 10
$V_2$ = 10/0.4 =25 gallons

Volume of water evaporated = $V_1 - V_2$

Volume of water evaporated = 100-25 = 75 gallons