Physics question.?

Question

How much water would have to evaportate from 64oz.of a 2% salt solution to make a 10% solution?

Answer 1

Assuming weight% and that the 64 oz above is fluid ounces...if not, you can adjust accordingly.

64 fl.oz. * 1.0425 av.oz./fl.oz. = 66.7 av.oz.

There is 0.02 * 66.7 = 1.33 av.oz. salt

A 10% solution would total 13.3 av.oz. of which 12.0 av.oz. is water.

Thus you would need to evaporate 54.7 av.oz. of water to make a 10% solution.

Answer 2

Let x= volume of water needed to evaporate to make a 10% solution.

64-x=remaining volume of solution containing 10% salt.

The amount of salt in the remaining volume of (64-x) is the same amount of salt in the 64 oz volume. Thus

10%*(64-x)=2%*64
10*(64-x)=2*64
640-10x=128
-10x=128-640
10x=512
x=512/10
=51.2oz

Check your answer:

The remaining solution is 12.8 oz, which contains 10% *12.8 of salt or 1.28oz of salt. The original solution before the 51.2oz of water evaporated contained 2%*64=1.28oz of salt also. So the percentage increased only to 10% because of the reduced volume from 64oz to 12.8oz, and not because more salt was added.