Expert: Bobby Soltani - 12/10/2004

Question
How many kilograms of water must be evaporated from 12 kg of a 5% salt solution to produce a solution that is 30% salt?

When I set up the chart, I do not understand why the x for the evaporated water's percentage is 0. I also do not understand how to setup the equation.

Answer
Hi Trent,

If we assume that percent is based on weight, then in 12 kg, there is 12kg*0.05 = 0.6 kg of salt and 12kg*0.95 = 11.4 kg of water.  When doing math, 5% is the same as 0.05.  We multiply the weight by .95 because if the solution is 5 % salt, then it must be 95% water.  We want the weight of the salt to equal 30 percent of the total weight.  Putting it into math terms:
(weight of salt) = 0.3*(total weight)

We know that the weight of salt is 0.6kg and it will not evaporate, so we can solve for the total weight we want.

0.6 = 0.3*(total weight)
divide both sides by 0.3
(total weight) = 2 kg

That means that (2kg total - 0.6kg salt) = 1.4 kg water.  Since we started off with 11.4kg water, we must evaporate 11.4 - 1.4 = 10 kg of water.

That's it.  Let me know if you have any questions.

Bobby