# Question 47a1f

Oct 12, 2015

$\frac{1}{30}$

#### Explanation:

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

$\text{D.F." = V_"initial"/V_"final}$

In your case, the initial sample has a volume of $\text{25 mL}$.

The thing to keep in mind here is that the original sample is ultimately diluted to $\text{750 mL}$, 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 $\text{25 mL}$ and end up with $\text{750 mL}$, 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 $\text{75 mL}$, 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 $\text{750 mL}$, 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

$\text{D.F"_"total} = \frac{1}{3} \times \frac{1}{10} = \frac{1}{30}$