Question #2b75e

1 Answer
May 25, 2016

Answer:

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.