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# Dilution

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Have you ever had a drink and realized, wow, it’s too sugary! As a result, you proceeded to add water to it. If so, you have performed a dilution. Dilutions are used in chemistry to get a certain amount of the desired reagent.

• First, we’ll go over what a dilution is.

• Next, we’ll learn about how to use the dilution formula.

• Lastly, we’ll learn to calculate dilutions in chemistry.

## Dilution Definition

Dilution is the process in which the concentration of a solution is lowered by the addition of solvent.

• A solute is a substance that dissolves into a solvent.

• A solvent is a substance into which the solute dissolves, resulting in a solution.

• Typically, a solute is a solid substance and a solvent is a liquid.

• Solutions are homogeneous mixtures or mixtures with a uniform composition.

• A concentrated solution is one that has a significant amount of solute dissolved into it when compared to a diluted solution.

• A diluent is a substance that we use to dilute a solution.

For more detailed information regarding concentrations and solutions, please reference our article “Concentration.”

Figure 1: Concentrated vs Diluted solutions shown. Daniela Lin, Study Smarter Originals.

In the figure above, from left to right, the solution gets more diluted, meaning that the amount of solute dissolved into the solution is significantly less when compared to a concentrated solution.

Dilutions involve the addition of a solvent, leading to a less concentrated solution. In contrast, increasing the concentration of a solution means adding more solute.

You can also concentrate a solution by removing solvent. This is usually done by boiling or evaporating the solvent. Keep in mind, that this only works if the solute is not affected by the heat used to boil off/evaporate the solvent.

Figure 2: Solution formation shown. Daniela Lin, Study Smarter Originals.

The solute is usually solid. While the solvent is what the solute dissolves in, and together they form a solution.

## The Dilution Formula

The dilution equation is

$$M_1V_1 = M_2V_2$$

Where

$$M_1$$ = concentration in molarity (mol/L or M) of the concentrated solution we start with.

$$V_1$$ = volume (mL or L) of concentration solution we start with.

$$M_2$$ = concentration in molarity (mol/L or M) of the diluted solution we end with.

$$V_2$$ = volume (mL or L) of diluted solution we end with.

We use the dilution equation to figure out the amount of solvent needed to dilute a solution. We usually dilute a solution by mixing more solvent into the solution. For example, adding water to a drink like lemonade or apple juice means we are diluting the drinks down.

Some of the reasons we dilute solutions are:

• In microbiology, we usually use dilutions to weaken the concentration of bacteria to make them easier to count or test.

• In serology, scientists dilute down antibodies to the lowest concentration that still produces a signal.

• In most labs, dilutions can be used to perform experiments with concentrated stock solutions.

Now that we understand what the dilution equation is and some important reasons as to why we dilute solutions, we can go over how is it that we derive the dilution formula.

Figure 3: Mole concentration formula shown above relates to our dilution formula. Daniela Lin, Study Smarter Originals.

Solving for the number of moles of solute for the equation above gets you:

Simple Dilution Formula:

moles of solute (n) = [Mole concentration or Molarity (M)] x [Volume of Solution (V)]

The product of the number of moles of solute times the volume does not change before and after a change in concentration therefore we can write the equation as:

$$M_1V_1 = M_2V_2$$

which means that the product of the number of moles times the volume, of the initial solution before dilution, is equal to the product of the number of moles times the volume of the final solution after dilution.

## Types and methods of dilution

Above, we introduced $$M_1V_1 = M_2V_2$$

We use this equation when we want to make a fixed amount of a dilute solution from a stock solution.

Within chemistry, a stock solution is usually a large volume of a reagent that’s going to be diluted down in concentration for usage.

This type of dilution is usually called a simple dilution which was shown above.

## Dilution Factor

A second type of dilution is called a serial dilution. This second type of dilution occurs when we dilute a stock repeatedly. We can dilute a stock successively by finding the dilution factor as shown below:

Dilution Factor (DF):

We find the dilution factor by:

$$DF = \frac{V_f}{V_i}$$

where, the initial volume (stock solution) is, Vi, and the final volume (stock solution plus diluent volume) is, Vf.

Given the dilution factor, DF, we can find each successive dilution will be given by:

$$V_i = \frac{V_f}{DF}$$

For example, let's say that we pipette 2 mL of a stock solution into 8 mL of buffer (diluent). Notice that the final volume, Vf, would be, 2 mL (stock solution) + 8 mL buffer (diluent) = 10 mL. Then the dilution factor, DF, will be given by:

$$DF = \frac{10 mL}{2 mL} = 5$$

which means that we diluted the stock solution by a factor of 5. Often the dilution factor is used in the denominator of a ratio. In the example that we just used the dilution would be 1:5. Now let's say that we want to create 100 mL of a 1:50 dilution of the stock solution. We calculate this by using the equation:

$$V_i = \frac{V_f}{DF} = \frac{100\,mL}{50} = 2 mL$$

Thus, you would pipette 2 mL of the stock solution into a 100 mL volumetric flask and then you would diluent (buffer) to the mark on the volumetric flask, (that is you will have added 98 mL of buffer to the flask).

## Examples of dilution in chemistry

You are in science class, and you have a stock solution of 30 mL of 1 M NaCl. The teacher tells you to dilute it to 50 mL by adding water. What’s the final concentration after dilution?

The answer is simple, use our simple dilution formula and follow the steps shown below:

Figure 5: Simple Dilution formula. Daniela Lin, Study Smarter Originals.

And we start with a stock solution of 30 mL of 1 M NaCl

So $$M_1 =$$ 1 M of $$NaCl$$ and $$V_1 = 30 mL$$ of $$NaCl$$ solution

We end up with 50 mL solution which means $$V_2= 50 mL$$ and we're trying to find $$M_2$$.

Since we're solving for $$M_2$$ then we can rearrange the simple dilution formula equation to:

Figure 6: Simple dilution formula example. Daniela Lin, Study Smarter Originals.

So our final concentration is 0.6 M for our solution.

Another interesting question to ask might be what's the amount of solvent we added?

In this case, the answer is simple we just subtract 50 mL by 30 mL and we get 20 mL. This means we added 20 mL of solvent to the solution.

Figure 7 : Serial Dilutions explained. Daniela Lin, Study Smarter Originals.

Serial dilutions are usually performed in the lab. From left to right as shown in the illustration, we’re diluting down by a 1:10 ratio each time. We find the dilution factor by adding 1 mL sample over 9 mL of diluent plus 1 mL of sample, giving you a 1:10 ratio.

We can see that every time we dilute down by a factor of 1:10 the number of colonies of bacteria in the lab decrease. This is useful to do to be able to estimate the concentration of the number of bacteria/colonies of an unknown sample.

Serial dilutions are performed, usually to avoid having to pipette very tiny amounts of liquid to make a specifically required dilution.

To perform a serial dilution, we just need to:

1. Take a sample and dilute it through the same volumes of diluent, which, in the case of microbiology, is usually either distilled water or 0.9% saline solution.

2. The greater the concentration of bacteria there is in a sample, the higher your dilution factor should be. For example, if a sample has 500 colonies, then a 1:1000 dilution would be preferred over a 1:10 dilution.

3. As shown above, serial dilutions can be either calculated from one tube or by adding up the total number of tubes. For instance, the first tube has a 1:10 dilution, which we get by adding 1 mL sample over (9 mL of diluent + 1 mL of the sample). In contrast, we get the third tube’s dilution by multiplying the previous tube dilutions by it, or 1:10 x 1:10 x 1:10= 1:1,000.

## Dilution - Key takeaways

• Dilution is the process in which the concentration of a solution is lowered by the addition of more solute.

• A concentrated solution is one that has a significant amount of solute dissolved into it when compared to a diluted solution.

• A diluent is a substance that we use to dilute a solution.

• There are 2 main types of dilutions: simple and serial.

## References

1. Basic Practical Microbiology-Manual. The society of General Microbiology. Retrieved from https://microbiologyonline.org/file/7926d7789d8a2f7b2075109f68c3175e.pdf
2. Libretexts. (2022, June 12). 11.4: Dilutions and concentrations. Chemistry LibreTexts.
3. Sapkota, A., Morg, Nafisa, Daniyal, Ogugbara, I., Manyonge, D., ferahtia_fs, Singh, D., Sawaira, Romano, D. R., Vishwathi, shah, T., Getahun, N., & Nwachukwu. (2022, May 2). Serial dilution-definition, formula, calculator, procedure, use. Microbe Notes. Retrieved June 22, 2022, from https://microbenotes.com/serial-dilution/

A dilution is a process in which the concentration of a solution is lowered by the addition of more solute.

You calculate a dilution depending on if it’s simple or serial. If it’s simple, just use our M1V1=M2V2 formula and if it’s serial, then make sure to calculate the dilution factor and then perform the steps.

Dilutions are often done in the science labs to calculate the number of colonies, viruses, or bacteria. We also perform dilutions to get an X amount of the desired reagent in a solution. The methods usually involve using tubes to control the amount we dilute.

The dilution factor in chemistry is how much we dilute something by, and it’s usually written as a ratio. For example, diluting by 1:10 factor means diluting 1 mL of sample by 9 mL of diluent.

What is the equation and formula for finding dilution?

The equation or formula for finding dilutions are M1V1=M2V2 or one of the concentration formulas derived. We can also use dilution factors to figure out how much we dilute or diluted something by.

The equation or formula for finding dilutions is M1V1=M2V2 or one of the concentration formulas derived. We can also use dilution factors to figure out how much we dilute or diluted something.

## Final Dilution Quiz

Question

______ is the process in which the concentration of a solution is lowered by the addition of more solute.

Dilution

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Question

What's the difference between a concentrated solution and a diluted solution?

A concentrated solution has more solute dissolved into it.

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Question

How do we form a solution?

We combine a solute and a solvent to form a solution.

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Question

What's the difference between a simple and a serial dilution?

A serial dilution involves stepwise or successive dilutions.

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Question

What's our dilution factor?

Our dilution factor is the amount we diluted our specific tube by.

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Question

What's the difference between the total dilution factor and the dilution factor?

• The difference is that the total dilution factor is all the successive tubes we diluted into added together. While the dilution factor is the specific tube, we diluted.
• For instance, 1:10 is the dilution factor of each tube in the attached illustration, but the total dilution factor is the ratio of the last tube to 1:10,000.

Show question

Question

How do we perform serial dilutions?

1. Take a sample and dilute it through the same volumes of diluent, which is usually either distilled water or 0.9% saline solution.

2. The more bacteria or concentration there’s in a sample, the higher your dilution factor should be. For example, if a sample has 500 colonies, then a 1:1000 dilution would be preferred over a 1:10 dilution.

3. As shown above, serial dilutions can be either calculated from one tube or by adding up the total number of tubes. For instance, the first tube has a 1:10 dilution, which we get by adding 1 mL sample over (9 mL of diluent + 1 mL of the sample). In contrast, we get the third tube’s dilution by multiplying the previous tube dilutions by it, or 1:10 x 1:10 x 1:10= 1:1,000.

Show question

Question

Why are serial dilutions performed?

Serial dilutions are performed, usually to avoid having to pipette very tiny amounts of liquid to make a specifically required dilution.

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Question

A 0.5 M solution of HCl with an initial volume is 55 mL has more diluent added until its concentration equals 0.1 M. What is the new volume of the solution?

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Question

Why do we use a dilution equation for?

We use the dilution equation to figure out the amount of solvent needed to dilute a solution.

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Question

What are some reasons we dilute solutions for?

We use dilutions to weaken the concentration of bacteria to make them easier to count.

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Question

What are some examples of possible diluted solutions?

Lemonade = sugar, water, and lemon juice.

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Question

How do we perform non-serial dilutions?

Basically, to find a non-serial dilution, just figure out 1) what the question is asking and 2) what we’re trying to find. Then you can proceed to just plug and chug into the formula to get your desired answer.

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Question

What's a stock solution?

Within chemistry, a stock solution is usually a large volume of a reagent that’s going to be diluted down in concentration for usage.

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