Question #47a1f

1 Answer
Oct 12, 2015

Answer:

#1/30#

Explanation:

The dilution factor is defined as the ratio between the initial volume of the sample and the final volume of the solution.

#"D.F." = V_"initial"/V_"final"#

In your case, the initial sample has a volume of #"25 mL"#.

The thing to keep in mind here is that the original sample is ultimately diluted to #"750 mL"#, so all you really need to consider are the initial voume of the sample and the final volume of the solution.

So, you start with #"25 mL"# and end up with #"750 mL"#, so the dilution factor is

#"D.F." = (25color(red)(cancel(color(black)("mL"))))/(750color(red)(cancel(color(black)("mL")))) = color(green)(1/30)#

Alternatively, you can think of it like this. You fist dilute the original sample to #"75 mL"#, which will give you a dilution factor equal to

#"D.F"_1 = (25color(red)(cancel(color(black)("mL"))))/(75color(red)(cancel(color(black)("mL")))) = 1/3#

Now you dilute this solution to a final volume of #"750 mL"#, so you have

#"D.F"_2 = (75color(red)(cancel(color(black)("mL"))))/(750color(red)(cancel(color(black)("mL")))) = 1/10#

The overall dilution factor will be the product of the two dilutions

#"D.F"_"total" = 1/3 xx 1/10 = 1/30#