Welcome back to Beyond’s Science Blog! This A Level Biology entry explores the Products of a Dilution Series.

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**Making Simple Dilutions**

A concentrated solution, or stock solution, can be diluted with a solvent to produce a solution with a lower concentration.

A simple dilution can be used to make solutions of any concentration. For each sample, a volume of stock solution is mixed with a volume of solvent to produce the desired concentration.

The volume of stock solution and volume of solvent required to make a specific volume of a given concentration can be recorded in a table. In the table below, the total volume of each of the solutions made is 10cm^{3}.

You need to be able to calculate the volume of stock solution and the volume of distilled water (or other solvent) needed to produce a solution of a given concentration from a stock solution of known concentration. You could think about this in two different ways.

**Example 1**

You have an initial stock solution with a concentration of 2.0M and need to make 20cm^{3} of a 0.4M solution.

**Method 1**

- Calculate the dilution factor by dividing the concentration of the stock solution with the concentration of the solution you want to make. This will tell you how much more dilute your new solution will be.

dilution factor = 2.0M ÷ 0.4M = 5 - Because the solution will be 5 times more dilute, you will need to use 5 times less of it. To find out how much stock solution to add, divide the total volume of the solution you will make by the dilution factor.

volume of stock solution transferred = 20cm^{3}÷ 5 = 4cm^{3} - You will add 4cm
^{3}of the stock solution, then dilute it with distilled water to get the total volume that you need. The total volume minus the transferred volume will give you the volume of distilled water you need to add.

distilled water added = 20cm^{3}– 4cm^{3}= 16cm^{3}

**Method 2**

- Use the equation to work out the volume of stock solution to transfer:

2.0M x V_{1}= 0.4M x 20cm^{3}

V_{1}=

V_{1}= 4cm^{3} - Calculate the volume of distilled water to add to make the final volume (V
_{2}):

V_{2}= V_{1}+ distilled water

distilled water = V_{2}– V_{1}

distilled water = 20 – 4

distilled water = 16cm^{3}

**Making Serial Dilutions**

A serial dilution creates a set of solutions that decrease in concentration by the same factor each time. In this technique, each dilution that is produced is used as the starting point for the next dilution. An example using a 1.0M initial solution and a dilution factor of 2 is shown below.

Working from left to right, 5cm^{3} of the solution from the previous test tube is mixed with 5cm^{3} of distilled water. This produces a new solution with a concentration that is half the concentration of the previous one.

A serial dilution can be used to dilute by any factor. The table below summarises the dilution of an initial solution by a factor of 10.

**Practice Questions**

1. A scientist needs to make 15cm^{3} of a 0.5g dm^{-3} solution. The initial stock solution has a concentration of 3g dm^{-3}. Calculate the dilution factor.

2. A scientist needs to make 40cm^{3} of a 0.4M solution. The initial stock solution has a concentration of 2.0M. Calculate the volumes of stock solution and distilled water the scientist needs to mix together to produce a 0.4M solution.

3. A stock solution has a concentration of 4.0M. A serial dilution is used to make four solutions that are diluted by a factor of 2 each time. Calculate the concentration of the final solution.

4. In each step of a serial dilution, 4cm^{3} of solution is mixed with 16cm^{3} of distilled water. Calculate the dilution factor.

5. A student created a dilution series of a glucose solution. Describe how they made a 1 in 10 dilution and then used this to make a 1 in 100 dilution and a 1 in 1000 dilution of the original solution.

**Answers**

1. A scientist needs to make 15cm^{3} of a 0.5g dm^{-3} solution. The initial stock solution has a concentration of 3g dm^{-3}. Calculate the dilution factor.

**3 ÷ 0.5 = 6dilution factor = 6**

2. A scientist needs to make 40cm^{3} of a 0.4M solution. The initial stock solution has a concentration of 2.0M. Calculate the volumes of stock solution and distilled water the scientist needs to mix together to produce a 0.4M solution.

**dilution factor = 2.0 ÷ 0.4 = 5volume of stock solution transferred = 40 ÷ 5 = 8cm ^{3}volume of distilled water = 40 – 8 = 32cm^{3}**

**or**

**2.0 x V ^{1} = 0.4 x 40V^{1} = V^{1} = 8cm^{3}volume of distilled water = 40 – 8 = 32cm^{3}**

**volume of stock solution = 8cm ^{3}volume of distilled water = 32cm^{3}**

3. A stock solution has a concentration of 4.0M. A serial dilution is used to make four solutions that are diluted by a factor of 2 each time. Calculate the concentration of the final solution.

**4.0 ÷ 2 ^{4} = 0.25or4.0 ÷ 2 ÷ 2 ÷ 2 ÷ 2 = 0.25**

**concentration = 0.25M**

4. In each step of a serial dilution, 4cm^{3} of solution is mixed with 16cm^{3} of distilled water. Calculate the dilution factor.

**total volume of diluted solution = 4 + 16 = 20cm ^{3}**

**dilution factor = **

**dilution factor = **

**dilution factor = 5**

5. A student created a dilution series of a glucose solution. Describe how they made a 1 in 10 dilution and then used this to make a 1 in 100 dilution and a 1 in 1000 dilution of the original solution.

**Add 1cm**^{3}of the initial glucose solution with 9cm^{3}of distilled water and mix well to produce a 10-1 dilution.**Add 1cm**^{3 }of the 10-1 glucose solution with 9cm^{3}of distilled water and mix well to produce a 10-2 dilution.**Add 1cm**^{3}of the 10-2 glucose solution with 9cm^{3}of distilled water and mix well to produce a 10-3 dilution.

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