# Question 59b26

Dec 20, 2017

$\text{0.05 M}$

#### Explanation:

The trick here is to realize that diluting a solution will cause its concentration to decrease by the factor as its volume increases.

$\text{DF" = V_"diluted"/V_"stock" = c_"stock"/c_"diluted}$

Here $\text{DF}$ is the dilution factor.

In your case, the volume of the stock solution increases by $\text{875 mL}$ to a total value of

${V}_{\text{diluted" = "125 mL" + "875 mL}}$

${V}_{\text{diluted" = "1,000 mL}}$

This means that the dilution factor is equal to--remember, we're using the volume of the diluted solution and the volume of the stock solution here!

"DF" = ("1,000" color(red)(cancel(color(black)("mL"))))/(125color(red)(cancel(color(black)("mL")))) = color(blue)(8)

So if the volume increased by factor of $\textcolor{b l u e}{8}$, it follows that the concentration must have decreased by a factor of $\textcolor{b l u e}{8}$.

$\textcolor{b l u e}{8} = {c}_{\text{stock"/c_"diluted}}$

You will thus have

${c}_{\text{diluted" = c_"stock}} / \textcolor{b l u e}{8}$

c_"diluted" = "0.400 M"/color(blue)(8) = color(darkgreen)(ul(color(black)("0.05 M")))#

The answer is rounded to one significat figure because when you're adding the two volumes, the answer, i.e. $\text{1,000 mL}$, has one significant figure and no decimal places.