# Question dfd4e

Aug 20, 2015

Here's my take on this one.

#### Explanation:

I'm not really sure about what exactly you want to know, so I'll try and cover as many options as possible.

So, let's assume that you want to

• dilute a 0.1 mL sample by adding 0.9 mL of water

This one is pretty straightforward. When you dilute a 0.1-mL sample by adding 0.9 mL of water, you're essentially performing a $1 : 10$ dilution.

The volume of the final solution will be

${V}_{\text{final" = 0.1 + 0.9 = "1 mL}}$

The dilution factor, which is simply the ratio between the final volume of the solution and the initial volume of the sample, will be

$\text{DF" = V_"final"/V_"initial}$

"DF" = (1color(red)(cancel(color(black)("mL"))))/(0.1color(red)(cancel(color(black)("mL")))) = 10

• dilute a 0.1-mL sample by a specific dilution factor

If you want to dilute a 0.1-mL sample by a specific dilution factor, you can determine how much water you need to add by using the formula for the dilution factor to calculate the final volume of the solution.

Let's say that you want to dilute this sample by a dilution factor of $50$. You would have

$\text{DF" = V_"final"/V_"initial" implies V_"final" = "DF" * V_"initial}$

${V}_{\text{final" = 50 * "0.1 mL" = "5 mL}}$

This means that you need to add

${V}_{\text{water" = V_"final" - V_"initial" = 5 - 0.1 = "4.9 mL water}}$

to dilute a 0.1-mL sample by a dilution factor of 50.

• dilute a 0.1-mL sample to a specific final volume

This one is easier to calculate, because you know what the volume of the final solution must be. The difference between this volume and the initial volume of the sample will represent the volume of water you need to add.

${V}_{\text{final" = V_"water" + V_"initial}}$

Let's say that you want to dilute the sample to a final volume of 0.9 mL. This would mean that you must add

${V}_{\text{water" = 0.9 - 0.1 = "0.8 mL water}}$

In this case, the dilution factor would be

"DF" = (0.9color(red)(cancel(color(black)("mL"))))/(0.1color(red)(cancel(color(black)("mL")))) = 9#

The formulas are true regardless of what the volume of the initial sample is, so you can use these as a guideline to help you with your dilution calculations.