# Question 4ab7b

Aug 27, 2016

Not quite!

#### Explanation:

The important thing to always keep in mind when dealing with dilution factors is that the dilution factor depends on two things

• the volume of the initial solution, i.e. the concentrated solution
• the total volume of the final solution, i.e. the diluted solution

More specifically, the dilution factor is calculated like this

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{DF" = V_"final"/V_"initial} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Here

${V}_{\text{final}}$ - the final volume of the solution
${V}_{\text{initial}}$ - the initial volume of the solution

In your case, you make a solution by dissolving $\text{0.4772 g}$ of solute in $\text{100 mL}$ of water. You then take $\text{1 mL}$ of this solution and add it to another $\text{100 mL}$ of water.

This means that in your case you have

${V}_{\text{initial" = "1 mL}}$

${V}_{\text{final" = "1 mL" + "100 mL" = "101 mL}}$

you add the concentrated sample to another $\text{100 mL}$ of water

The dilution factor will thus be

"DF" = (101 color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("mL")))) = 101

In order to have a dilution factor of $100$, you must take the $\text{1 mL}$ sample and add enough water to get the total volume to $\text{100 mL}$. This would then get you

"DF" = (100color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("mL")))) = 100#

As a final note, a dilution factor equal to $101$ means that your initial solution was $101$ times more concentrated than the diluted solution.