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

Oct 18, 2015

75 gallons of water

#### Explanation:

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 = $0.1 X 100$ =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