# Dilutions

## DILUTIONS AND DILUTION FACTORS

For questions pertaining to dilutions, we use the equation:

Dilution = sample volume: total volume

For questions pertaining to dilution factors, we use the equation:

$$\text{Dilution factor = \frac{\text{sample volume}}{\text{total volume}}}$$

Sample volume is the volume of the solution being diluted; total volume is the sample volume in addition to the volume of the diluent.

Example: What is the dilution factor when 2 ml of a sample is mixed in 8mL of water?

Solution: This question asks us to find the dilution factor of a solution, so we use the equation for finding the dilution factor:

$$\text{Dilution factor = \frac{\text{sample volume}}{\text{total volume}}}$$

Our sample volume in the question is 2 mL. We can get the total volume by adding our sample volume (2mL) to the volume of water (8mL). The total volume is found to be 10mL (2mL + 8mL).

$$\text{Dilution factor =\frac{2\text{ml}}{10\text{ml}}}$$

$$\text{Dilution factor = 0.2ml}$$

We have found out dilution factor to be 0.2 X.

Now let's find the dilution of the sample.

Dilution = Sample volume: total volume

Dilution = 2:10 or 1:5

Therefore, we have found the dilution of the sample to be 1:5.

## SERIAL DILUTIONS

For questions pertaining to serial dilutions we use the equation:

DFT= (DF1)*(DF2)*(DF3)...(DF11)

DFT is the total dilution factor of a serial dilution; DFn is the dilution factor of a specific dilution in the series.

Example: What is the dilution factor of a substance to which three 1:5 dilutions have been performed?

Solution: To solve a problem with serial dilutions, we first must find the dilution factor of each dilution using the equation:

$$\text{Dilution factor = \frac{\text{sample volume}}{\text{total volume}}}$$

$$\text{DF}_1 = \frac{1}{5} = 0.2$$

$$\text{DF}_2 = \frac{1}{5} = 0.2$$

$$\text{DF}_3 = \frac{1}{5} = 0.2$$

Now we multiply these to get our total dilution factor for our serial dilution.

$$\text{DF}_T = 0.2 \cdot 0.2\cdot 0.2 = 0.008$$

Therefore, the dilution factor for our serial dilutions is 0.008 X.

Now we multiply these to get our total dilution factor for our serial dilution.

DF= 0.2 * 0.2 * 0.2= 0.008

Therefore, the dilution factor for our serial dilutions is 0.008 X.