# Do the units used to express the volume of the solution affect the dilution factor?

Dec 29, 2016

Not necessarily.

#### Explanation:

The dilution factor is simply the ratio that exists between the volume of the diluted solution and the volume of the concentrated solution

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{DF" = V_"diluted"/V_"concentrated}}}}$

The dilution factor must be a unitless quantity since it is calculated by taking the ratio of two volumes. In this regard, you only need the two volumes to be expressed using the same unit of measurement.

As long as both volumes are expressed using the same unit of measurement, their ratio will give you the dilution factor.

For example, if you diluted $\text{5 mL}$ of stock solution to a final volume of $\text{100 mL}$, the dilution factor will be

"DF" = (100 color(red)(cancel(color(black)("mL"))))/(5 color(red)(cancel(color(black)("mL")))) color(white)(color(black)(-> " the volume of the diluted solution")/color(black)(-> " the volume of the concentrated solution"))

$\text{DF} = 20$

Notice what happens when you use liters instead of milliliters. Since

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 L" = 10^3"mL}}}}$

you can say that

"DF" = (100 * color(blue)(cancel(color(black)(10^(-3)))) color(red)(cancel(color(black)("L"))))/(5 * color(blue)(cancel(color(black)(10^(-3)))) color(red)(cancel(color(black)("L")))) = 20

As you can see, the value of the dilution factor does not change.

So remember, the dilution factor must be calculated by dividing volumes expressed in the same unit of measurement.