Question

Question #2b75e

Answer 1

The dilution factor is 5000.

Explanation:

The dilution factor for a single dilution is:

`"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)|)))" "`

`bb(DF_1)`:

In your example,

`DF_1 = V_f/V_i = (500 color(red)(cancel(color(black)("mL"))))/(1 color(red)(cancel(color(black)("mL")))) = 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.

`bb(DF_2)`:

`DF_2 = V_f/V_i = (250 color(red)(cancel(color(black)("mL"))))/(25 color(red)(cancel(color(black)("mL")))) = 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 `"DF"` of 5000 means a 1:5000 dilution.