Learning Objective

Series Dilution Table
Serial Dilution Table
Serial Dilution Experiment

Divide dilution into cost per gallon. Example: (1:128 dilution selling at $13.40 per gallon) $13.40 ÷ 129 =.1038 -or- 10.4¢ per diluted gallon. Table of Contents. How to Do a Viable Plate Count; 1: Why we need to dilute; 2: Setting the stage: Diluting Cold Press Coffee; 3: The dilution factor; 4: Overall dilution; 5: Design a dilution! 6: How to scale back up; 7: Count a plate! 8: Why plate more than one dilution? 9: Picking the plate count; Section 2. Practice Problems; 10.

Calculate the concentration of a diluted solution.

Key Points

Most commonly, a solution’s concentration is expressed in terms of mass percent, mole fraction, molarity, molality, and normality. When calculating dilution factors, it is important that the units of volume and concentration remain consistent.
Dilution calculations can be performed using the formula M₁V₁ = M₂V₂.
A serial dilution is a series of stepwise dilutions, where the dilution factor is held constant at each step.

Terms

dilutiona solution that has had additional solvent, such as water, added to make it less concentrated
serial dilutionstepwise dilution of a substance in solution

Dilution refers to the process of adding additional solvent to a solution to decrease its concentration. This process keeps the amount of solute constant, but increases the total amount of solution, thereby decreasing its final concentration. Dilution can also be achieved by mixing a solution of higher concentration with an identical solution of lesser concentration. Diluting solutions is a necessary process in the laboratory, as stock solutions are often purchased and stored in very concentrated forms. For the solutions to be usable in the lab (for a titration, for instance), they must be accurately diluted to a known, lesser concentration.

The volume of solvent needed to prepare the desired concentration of a new, diluted solution can be calculated mathematically. The relationship is as follows:

[latex]M_1V_1=M_2V_2[/latex]

M₁ denotes the concentration of the original solution, and V1 denotes the volume of the original solution; M₂ Itsycal mac os 10 11. represents the concentration of the diluted solution, and V2 represents the final volume of the diluted solution. When calculating dilution factors, it is important that the units for both volume and concentration are the same for both sides of the equation.

Example

175 mL of a 1.6 M aqueous solution of LiCl is diluted with water to a final volume of 1.0 L. What is the final concentration of the diluted solution?
[latex]M_1V_1=M_2V_2[/latex]
(1.6 M)(175 mL) = M₂(1000 mL)
M₂ = 0.28 M

Serial Dilutions

Serial dilutions involve diluting a stock or standard solution multiple times in a row. Typically, the dilution factor remains constant for each dilution, resulting in an exponential decrease in concentration. For example, a ten-fold serial dilution could result in the following concentrations: 1 M, 0.1 M, 0.01 M, 0.001 M, and so on. As is evidenced in this example, the concentration is reduced by a factor of ten in each step. Serial dilutions are used to accurately create extremely diluted solutions, as well as solutions for experiments that require a concentration curve with an exponential or logarithmic scale. Serial dilutions are widely used in experimental sciences, including biochemistry, pharmacology, microbiology, and physics.

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This section is not a recipe for your experiment. It explains someprinciples for designing dilutions that give optimal results. Onceyou understand these principles, you will be better able to designthe dilutions you need for each specific case.

Often in experimental work, you need to cover a range ofconcentrations, so you need to make a bunch of differentdilutions. For example, you need to do such dilutions of thestandard IgG to make the standard curve in ELISA, and then againfor the unknown samples in ELISA.

You might think it would be good to dilute 1/2, 1/3, 1/10, 1/100.These seem like nice numbers. There are two problems with this series ofdilutions.

The dilutions are unnecessarily complicated to make. You need to do a differentcalculation, and measure different volumes, for each one. It takes a longtime, and it is too easy to make a mistake.
The dilutions cover the range from 1/2 to 1/100 unevenly.In fact, the 1/2 vs. 1/3 dilutions differ by only 1.5-fold in concentration,while the 1/10 vs. 1/100 dilutions differ by ten-fold. If you are going tomeasure results for four dilutions, it is a waste of time and materialsto make two of them almost the same. And what if the half-maximal signaloccurs between 1/10 and 1/100? You won't be able to tell exactly where itis because of the big space between those two.

Serial dilutions are much easier to make and they cover the range evenly.

Serial dilutions are made by making the same dilution step over and over,using the previous dilution as the input to the next dilution in each step.Since the dilution-fold is the same in each step, the dilutionsare a geometric series (constant ratio between any adjacent dilutions).For example:

1/3, 1/9, 1/27, 1/81Notice that each dilution is three-fold relative to the previous one.In four dilutions, we have covered a range of 181/3 = 60-fold.If that isn't enough range, consider a series of five-fold dilutions:

1/5, 1/25, 1/125, 1/625Here we've covered a (625/5) = 125-fold range.No matter where the half-max falls in a series of 5-fold dilutions,it is no more than2.2-fold ('middle' [square root] of a 5-fold step) awayfrom a data point -- so the coverage of the range is thorough and even.

When you need to cover several factors of ten (several 'orders of magnitude') witha series of dilutions, it usually makes the most sense to plot the dilutions(relative concentrations) on a logarithmic scale. This avoids bunching mostof the points up at one end and having just the last point way fardown the scale.

Before making serial dilutions, you need to make rough estimatesof the concentrationsin your unknowns, and your uncertainty in those estimates. For example,if A₂₈₀ says you have 7.0 mg total protein/ml, and you thinkthe protein could be anywhere between 10% and 100% pure, then yourassay needs to be able to see anything between 0.7 and 7 mg/ml.That means you need to cover a ten-fold range of dilutions, or maybe a bitmore to be sure.

If the half-max of your assay occurs atabout 0.5mg/ml,then your minimum dilution fold is(700mg/ml)/(0.5mg/ml) = 1,400.Your maximum is(7000mg/ml)/(0.5mg/ml) = 14,000.So to be safe, you might want to cover 1,000 through 20,000.

Series Dilution Table

In general, before designing a dilution series, you need to decide:

What are the lowe

Serial Dilution Table