# Question 2a04f

##### 1 Answer
Jul 28, 2016

$\text{DF} = 41$

#### Explanation:

The dilution factor is simply the ratio between the final volume of the solution, i.e. the volume of the diluted solution, and the initial volume of the solution, i.e. the volume of the concentrated sample.

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

In your case, the volume of the concentrated solution is said to be equal to $\text{25 mL}$. This sample is being diluted by the addition of $\text{1000 mL}$ of diluent.

This means that the volume of the diluted solution will be

${V}_{\text{diluted" = V_"stock" + V_"diluent}}$

${V}_{\text{diluted" = "25 mL" + "1000 mL" = "1025 mL}}$

The dilution factor will thus be

"DF" = (1025 color(red)(cancel(color(black)("mL"))) )/(25color(red)(cancel(color(black)("mL")))) = color(green)(|bar(ul(color(white)(a/a)color(black)(41)color(white)(a/a)|)))#

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one sig fig for the volume of diluent.

So, a dilution factor of $41$ means that the stock solution was $41$ times more concentrated than the diluted solution.