# Question 780de

Dec 2, 2016

$\text{75.0 mL}$

#### Explanation:

The thing to remember about dilution calculations is that the ratio that exists between the volume of the diluted solution and the volume of the concentrated solution is equal to the ratio that exists between the concentration of the concentrated solution and the concentration of the diluted solution.

$\text{volume of diluted solution"/"volume of concentrated solution" = "molarity of concentrated solution"/"molarity of diluted solution}$

These two ratios give you the dilution factor, $\text{DF}$, which essentially tells you the factor by which the concentration of the concentrated solution decreased after the dilution.

You know that the concentration of the diluted solution must be $\text{0.750 M}$ and that the concentration of the stock solution is $\text{1.00 M}$.

This will give you

"DF" = (1.00 color(red)(cancel(color(black)("M"))))/(0.750color(red)(cancel(color(black)("M")))) = 4/3

This is exactly the ratio that must exist between the volume of the diluted solution, which is equal to $\text{100.0 mL}$, and the volume of the stock solution, let's say ${V}_{\text{stock}}$

$\text{DF" = "100.0 mL"/V_"stock}$

Therefore,

V_"stock" = "100.0 mL"/(4/3) = 300.0/4color(white)(.)"mL" = color(darkgreen)(ul(color(black)("75.0 mL")))#