Calculating Dilutions: Formula, Examples & Methods (2024)

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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.

In chemistry, a dilution is the process of reducing the concentration of a solute in a solution. 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.

• Then, we’ll read about the types and methods of dilution.

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

Dilution Definition

Let's start by looking at the definition of dilution.

Dilution consists of adding solvent to a solution to lower its concentration.

• 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 hom*ogeneous 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.”

Concentration and dilution, although related, are different concepts. The term "concentration" refers to the amount of solute that is present in a given quantity of solvent or solution. Concentration is often expressed in terms such as molarity (moles of solute per liter of solution), molality (moles of solute per kilogram of solvent), or mass percent (grams of solute per 100 grams of solution).

Dilution, on the other hand, refers to the process of reducing the concentration of a solute in a solution, usually by adding more solvent.

Figure 1: Concentrated vs Diluted solutions shown.

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.

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

Calculating a Dilution: the Dilution Formula

The dilution formula 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.

How is the Dilution Formula Derived?

To derive the dilution formula above (\(M_1 V_1 = M_2 V_2\)), we start with the mole concentration formula, which is used to calculate the concentration of a given solution.

Figure 3: Mole concentration formula shown above relates to our dilution formula.

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

Simple Dilution Formula:

\[\text{moles of solute (n)} = [\text{Mole concentration or Molarity (M)}] \cdot [\text{Volume of Solution (V)}]\]

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 the dilution formula: \(M_1V_1 = M_2V_2\). 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 often called a simple dilution which was shown above. Other types of dilution include:

1. Serial Dilution: A serial dilution is a series of stepwise dilutions where the dilution factor is kept constant at each step. A small amount of the initial concentrated solution (stock solution) is added to a larger volume of solvent, mixed, and then this process is repeated with each subsequent dilution.

2. Gravimetric Dilution: In a gravimetric dilution, a precise amount of a substance is weighed and then added to a solvent to achieve a specific concentration. This method is often used when high accuracy is needed.

3. Volumetric Dilution: In a volumetric dilution, a certain volume of a concentrated solution (the aliquot) is transferred to a new container and more solvent is added until the total volume reaches a predetermined level. This is typically done using precise volumetric glassware like pipettes and volumetric flasks.

4. Dilution of Solutions with Gases: For gases, dilutions are often carried out by introducing a known volume of the gas into a larger container and allowing it to mix with the rest of the gases present.

Serial Dilutions

Serial dilutions are usually performed in the lab. From left to right as shown in the illustration below, 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 typically to avoid having to pipette very tiny amounts of liquid to make a specifically required dilution, as measuring such low volumes comes with a high error rate.

Figure 7: Serial Dilutions explained.

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 × 1:10 × 1:10= 1:1,000.

Uses of Dilutions

Examples of Dilution in Chemistry

Now, let's look at some examples of dilution in chemistry.

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