Dilution Factor Equation

Introduction

Dilution is the act of lowering the concentration of a solute in a solution by mixing it with various solvents, such as water. Adding extra solvent to a solution without adding more solute is diluting it. The final solution is thoroughly mixed to ensure that all components are identical.

The aliquot volume to the final volume ratio is described by the dilution factor, which is an expression. In commercial assays, the dilution factor is a standard notation. In a 1:5 dilution, for example, 1 unit volume of solute (the item to be diluted) is combined with (roughly) 4 unit volumes of the solvent to produce five units of total volume. It’s worth noting that some solutions and combinations have a smaller volume than their constituents.

Table Of Contents

• What is Dilution?
• What is the Dilution Factor?
• Dilution Factor Formula (Equation)
• How to Calculate Dilution Factor
• Examples
• Frequently Asked Questions – FAQs

What is Dilution?

Dilution is the process of lowering the concentration of a solute in a solution by adding more solvents to the solution, such as water and diluting a solution on more solvent without adding more solute. The resulting solution is thoroughly mixed to confirm that all of the solution’s components are the same.

Mixing a higher-concentration solution with a lower-concentration solution can also be used to dilute. Diluting solutions is a necessary laboratory procedure since stock solutions are regularly bought and stored in extremely concentrated proportions. Before being employed in the lab, the solutions must be accurately diluted to a known, lower concentration.

In both dilution and concentration, the amount of solute remains constant. This enables us to determine the new solution volume needed to achieve the target solute concentration. Using the concept of molarity as a starting point:

Molarity = moles of solute / liters of solution

Moles of solute = (molarity)(litres of solution)

moles of solute = MV

Because this quantity does not change before or after a change in concentration, the product MV must be the same before and after the concentration change. Numbers are used to denote the beginning and final circumstances.

Because M₁V₁ = M₂V₂ is a dilution equation, the volumes must be measured in the same units. Here, M₁ is the initial concentration or molarity, V₁ is the initial volume, M₂ is the final concentration or molarity, and V₂ is the final volume.

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Dilution Definition

What is the Dilution Factor?

After dilution, the dilution factor (or dilution ratio) represents how much of the original stock solution remains in the entire solution. It’s usually expressed as a ratio, although it can also be expressed as an exponent.

The part of the stock solution to the part of the dilutant added (S:D) or the part of the stock solution to the part of the total solution (S:T) is described by the dilution factor, which can be expressed as a ratio or an exponent.

Because the differences between these two representations are so minor, an example would be helpful:

Let’s imagine we have a 10 cm³ acyl chloride aqueous solution. However, because this solution is excessively concentrated for our experiment, we add 90 cm³ of water to dilute it further. We get 100 cm³ of acyl chloride in the end. The S:D ratio is 1:9 since we have 10 parts stock solution and 90 parts dilutant (cancelling down from 10:90). The dilution factor is 1:10 in S:T notation. Thus we have 10 cm³ of stock solution that now makes up a 100 cm³ solution.

It’s also worth noting that dilution factors merely represent a reduction in concentration; no molecules are lost, but the number of molecules per mL does. This is beneficial in a variety of experimental circumstances.

Although the dilution factor is merely a convenient method of thinking about dilutions, they are highly widespread in both science and everyday life. They’re also employed in almost all chemical and biological research because the stock solution of our substance is frequently far more concentrated than you want.

Dilution Factor Formula (Equation)

As previously stated, the dilution factor is frequently given as a ratio. For both sorts of dilution factors, the simplest formula is as follows:

S:D = stock volume:dilutant volume

S:T = stock volume:total volume

We can cancel each side down using their largest common factor to get the simplest integer expression of the dilution factor if these volumes are expressed in the same units. Some of us, on the other hand, may prefer to describe this ratio is 1:X, where X is the number of parts of the dilutant/total solution in one part of the stock solution.

This is also how the calculator expresses results due to technological limitations. The dilution factor can alternatively be stated as an exponent, such as 3^-1, 5^-3, or 10^-4. The exponent simply shows the ratio of the dilutant/total parts to the stock parts. We use the following ratio order:

S:D = exponent:1

S:T = exponent:1

How to Calculate Dilution Factor

Below mentioned are the steps to calculate the dilution factor by hand:

• Find any two of the following three values: stock solution volume (stock), dilutant solution volume (dilutant), and total solution volume (total) (total). This can be done either theoretically (before conducting the experiment) or experimentally (after the experiment).
• With this equation, we can find the third volume using the two volumes: stock + dilutant = total. This step may not be necessary if we know which notation we want to use (S:D or S:T), but it is included for completeness.
• Convert the numbers to the same units as each other.
• We decide which notation we require:
  • S:D = Set the stock and dilutant amount values as a ratio – stock:dilutant.
  • S:T = Set the stock and total amount values as a ratio – stock:total
• If necessary, we find the Greatest Common Factor to cancel down the fractions.

Examples

Note: We divide the final volume by the initial volume.

Example 1:

When a 0.1 mL aliquot of a specimen is added to 9.9 mL of diluent, what is the dilution factor?

Solution:

V_f = aliquot volume + diluent volume = (0.1 + 9.9) mL = 10.0 mL

DF = V_f / V_i = 10.0 / 0.1 = 100

Thus, we have diluted the sample by a factor of 100.

The denominator of a fraction is frequently the dilution factor. A DF of 100, for example, indicates a dilution of 1:100.

Example 2:

How would you make a 1:250 dilution in 500 mL?

Solution:

DF = V_f / V_i

V_i = V_f / DF = 500 mL / 250 = 2.00 mL

Fill a 500 mL volumetric flask with 2.00 mL of the stock solution.

To the mark on the flask, we add diluent (will have to add about 498 mL of water).

Thus, the original solution has now been diluted to 1:250.