A laboratory technician has 40 liters of a saline solution that is 15\% salt by volume. Ho… — GMAT

A laboratory technician has $40$ liters of a saline solution that is $15\%$ salt by volume. How many liters of pure water must be evaporated from the solution so that the remaining solution is $25\%$ salt by volume?

Cevap: 16 liters

Cevap

The correct answer is

16

liters.

Because evaporation removes only pure water, the quantity of salt remains constant at

6

liters (

40 \times 0.15

). For

6

liters of salt to constitute

25\%

of the final mixture volume

V

, we set up

0.25V = 6

, which yields

V = 24

liters. Subtracting the final volume of

24

liters from the initial volume of

40

liters gives

16

liters of evaporated water.

Adım Adım Çözüm

Calculate the volume of pure salt in the initial solution.

The initial salt volume is

40 \times 0.15 = 6

liters.

The solute amount is determined by multiplying total volume by concentration.

Determine the required total solution volume after evaporation to achieve a 25% concentration.

The required total final volume is

\frac{6}{0.25} = 24

liters.

Since evaporation removes only water, the volume of salt remains 6 liters, which must equal 25% of the new total volume.

Calculate the amount of water evaporated by taking the difference between the initial and final total volumes.

The volume of water evaporated is

40 - 24 = 16

liters.

The decrease in total solution volume equals the volume of pure water removed by evaporation.

Anahtar Kavram

Concentration change via evaporation (solute mass conservation)

Soru

Cevap

Adım Adım Çözüm

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