# Question #47a1f

##### 1 Answer

#### 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

The thing to keep in mind here is that the **original sample** is ultimately diluted to

So, you start with

#"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

#"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

#"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#