# Question 2b75e

May 25, 2016

The dilution factor is 5000.

#### Explanation:

The dilution factor for a single dilution is:

$\text{Dilution Factor" = "final volume"/"initial volume}$

or

color(blue)(|bar(ul(color(white)(a/a) "DF" = V_f/V_i color(white)(a/a)|)))" "

If you are doing successive dilutions, the overall dilution factor is the product of each successive dilution factor.

color(blue)(|bar(ul(color(white)(a/a) "DF" = "DF"_1 × "DF"_2 × "DF"_3 × …color(white)(a/a)|)))" "

$\boldsymbol{D {F}_{1}}$:

$D {F}_{1} = {V}_{f} / {V}_{i} = \left(500 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{mL"))))/(1 color(red)(cancel(color(black)("mL}}}}\right) = 500$

Your sample is not a liquid, but it is generally agreed that 1 g of sample has a volume of 1 mL, even if that is not actually the case. You still get convenience and reproducibility.

$\boldsymbol{D {F}_{2}}$:

$D {F}_{2} = {V}_{f} / {V}_{i} = \left(250 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{mL"))))/(25 color(red)(cancel(color(black)("mL}}}}\right) = 10$

Overall Dilution:

bb(DF) = "DF"_1 × "DF"_2 = 500 × 10 = 5000#

The overall dilution factor is 5000.

The dilution factor is often used as the denominator of a fraction.

For example, a $\text{DF}$ of 5000 means a 1:5000 dilution.