Question

Question #47a1f

Answer 1

`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`