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.
Answers
DrBob222
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%.
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%.
Kimberly
68% or 67.8%