Question

The densities of three solutions with known concentrations ( 20% , 50%, and 70%), and one unknown solution were determined. If the densities of 20%, 50% and 70% solutions are 0.69 and 0.58 and 0.49 g/mL, respectively, and the denisty of the unknown solution is 0.50 g/mL, what is the approximate concentration of the unknown solution? Hint: try to think of a range of two values between which the concentration of the unknown falls.

Answer 1

It would be easier to explain if we could draw diagrams on this forum but alas, we can't.
The density of the unknown falls between 70% and 50% with the answer VERY close to the 70% known (0.49 vs 0.50).
Therefore, the difference in density of 0.50-0.49 = 0.01 while the difference between 0.58 and 0.49 (= 0.09) represents 20%. You want to know what part of 20% is that 0.01.Therefore,
20 x (0.01/0.09) = ? and
70%-? = xx.

Note: You could think of it the other way; i.e., how far is it from 50%? That would be 20% x (0.08/0.09) and add that to 50%.

Answer 2

68% or 67.8%