How many liters of water should be evaporated from 110 liters of a 12% saline solution so that the solution that remains is a 20% saline solution
To determine the amount of water that needs to be evaporated, we can set up a proportion using the initial and final concentrations of the saline solution.
Let x represent the volume of water that needs to be evaporated in liters.
First, let's calculate the amount of salt in the initial solution:
Initial salt = 12% of 110 liters = 0.12 * 110 = 13.2 liters
The amount of water in the initial solution can be calculated as:
Initial water = Total volume of solution - Initial salt = 110 liters - 13.2 liters = 96.8 liters
Now, let's set up the proportion using the amount of salt in the initial solution and the final concentration:
(Initial salt) / (Initial water) = (Final salt) / (Final water)
Plugging in the known values, we get:
13.2 / 96.8 = 20% / (Final water)
To solve for the Final water, let's cross-multiply:
13.2 * (Final water) = 96.8 * 20%
13.2 * (Final water) = 19.36
(Final water) = 19.36 / 13.2
Therefore, the amount of water that needs to be evaporated from 110 liters of a 12% saline solution is approximately 1.47 liters.
if x liters evaporate, the salt content remains the same, so
.12(110) = .20(110-x)
Now just solve for x.