Making a saturated solution by mixing unsaturated and supersaturated solutions

[rngz]

Homework Statement

at 20 degree celsius, the solubility of a solid substance x in water is 42g/L. There are 3 solutions containing x kept at this temperature: S1 contains 5.1g/L,S2 contains 39g/L, and S3 contains 57g/L.so, how to make a saturated solution containing 45g x per litre overall for every 1L of S1. how much of S2 or S3 should I add??what is the critical assumption that must be taken??

Homework Equations

[n1L1=n2L2]

The Attempt at a Solution

by using the lever rules..

 

[Chrisas]

Do you think that taking any mixture of S1 (5.1 g/L) and S2 (39 g/L), both with lower than 45 g/L, will ever add up to 45 g/L without doing something like boiling off or removing some of the liquid?

If not, then that means it must be some mixture of S1 and S3. How much S3? We don't know, so call it "x". The problem says you have 1 Liter of S1. What if I told you there were x = 5 Liters of S3 (by the way, that's not the correct answer), how would you go about calculating the final concentration? Try that problem first. Use dimensions to help guide you through it.

Now, do the same calculation except set the final concentration to 45 and replace 5 Liters with "x" and do the algebra to find "x".