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1. How many CFUs/ml were in the original urine sample?
2. You have received a sample from a sewage treatment plant, and have been asked to determine how many CFUs/ml are in this sample. You want to make a 1/100,000 fold dilution, but the smallest volume you can measure is 1.0 ml, and the tubes available to you only hold 10 ml. Explain/draw how you would do this!
3. You have a bacterial culture that you know has 650,000 bacteria/ml. You do serial dilutions to achieve a 1/10,000 dilution, and then plate 0.1 ml of each of these dilutions. How many colonies will you see at each dilution?
4. You do a series of dilutions as shown below, and you plate 1.0 ml of each dilution. Given the information below, fill in the number of colonies you would expect on each of the plates.
5. You do serial dilutions on a water sample, and plate the dilutions on TSA plates. You count the colonies on each of the plates as follows: (Note: TMTC = too many to count)
|Dilution||Number of CFUs|
Based on these results, what is your estimate for the total number of CFUs/ml in the original sample?
Dilutions: Explanations and Examples of Common Methods
There are many ways of expressing concentrations and dilution. The following is a brief explanation of some ways of calculating dilutions that are common in biological science and often used at Quansys Biosciences.
Using C1V1 = C2V2
To make a fixed amount of a dilute solution from a stock solution, you can use the formula: C1V1 = C2V2 where:
- V1 = Volume of stock solution needed to make the new solution
- C1 = Concentration of stock solution
- V2 = Final volume of new solution
- C2 = Final concentration of new solution
- Example: Make 5 mL of a 0.25 M solution from a 1 M solution
- Formula: C1V1 = C2V2
- Plug values in: (V1)(1 M) = (5 mL)(0.25 M)
- Rearrange: V1 = [(5 mL)(0.25 M)] / (1 M)V1 = 1.25 mL
- Answer: Place 1.25 mL of the 1 M solution into V1-V2 = 5 mL – 1.25 mL = 3.75 mL of diluent
To make a dilute solution without calculating concentrations, you can rely on a derivation of the above formula:
(Final Volume / Solute Volume) = Dilution Factor (can also be used with mass)
This way of expressing a dilution as a ratio of the parts of solute to the total number of parts is common in biology. The dilution factor (DF) can be used alone or as the denominator of the fraction, for example, a DF of 10 means a 1:10 dilution, or 1 part solute + 9 parts diluent, for a total of 10 parts. This is different than a “dilution ratio,” which typically refers to a ratio of the parts of solute to the parts of the solvent, for example, a 1:9 using the previous example. Dilution factors are related to dilution ratios in that the DF equals the parts of the solvent + 1 part.
- Example: Make 300 μL of a 1:250 dilution
- Formula: Final Volume / Solute Volume = DF
- Plug values in: (300 μL) / Solute Volume = 250
- Rearrange: Solute Volume = 300 μL / 250 = 1.2 μL
- Answer: Place 1.2 μL of the stock solution into 300 μL – 1.2 μL = 298.8 μL diluent
If the dilution factor is larger than the final volume needed, or the amount of stock is too small to be pipetted, one or more intermediary dilutions may be required. Use the formula: Final DF = DF1 * DF2 * DF3 etc., to choose your step dilutions such that their product is the final dilution.
- Example: Make only 300 μL of a 1:1000 dilution, assuming the smallest volume you can pipette is 2 μL
- Choose step DFs: Need a total dilution factor of 1000. Let’s do a 1:10 followed by a 1:100 (10 * 100 = 1000)
- Formula: Final Volume / Solute Volume = DF
- Plug values in: (300 μL) / Solute Volume = 10
- Rearrange: Solute Volume = 300 μL / 10 = 30 μL
Answer: Perform a 1:10 dilution that makes at least 30 μL (e.g. 4 μL solute into 36 μL diluent), then move 30 μL of the mixed 1:10 into 300 μL – 3 μL = 297 μL diluent to perform the 1:100 dilution
A dilution series is a succession of step dilutions, each with the same dilution factor, where the diluted material of the previous step is used to make the subsequent dilution. This is how standard curves for ELISA can be made. To make a dilution series, use the following formulas:
15.2: Serial Dilution - Biology
This section is not a recipe for your experiment. It explains some principles for designing dilutions that give optimal results. Once you understand these principles, you will be better able to design the dilutions you need for each specific case.
Often in experimental work, you need to cover a range of concentrations, so you need to make a bunch of different dilutions. For example, you need to do such dilutions of the standard IgG to make the standard curve in ELISA, and then again for the unknown samples in ELISA.
- The dilutions are unnecessarily complicated to make. You need to do a different calculation, and measure different volumes, for each one. It takes a long time, and it is too easy to make a mistake.
Serial dilutions are much easier to make and they cover the range evenly.
When you need to cover several factors of ten (several "orders of magnitude") with a series of dilutions, it usually makes the most sense to plot the dilutions (relative concentrations) on a logarithmic scale. This avoids bunching most of the points up at one end and having just the last point way far down the scale.
Before making serial dilutions, you need to make rough estimates of the concentrations in your unknowns, and your uncertainty in those estimates. For example, if A280 says you have 7.0 mg total protein/ml, and you think the protein could be anywhere between 10% and 100% pure, then your assay 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 bit more to be sure.
If the half-max of your assay occurs at about 0.5 m g/ml, then your minimum dilution fold is (700 m g/ml)/(0.5 m g/ml) = 1,400. Your maximum is (7000 m g/ml)/(0.5 m g/ml) = 14,000. So to be safe, you might want to cover 1,000 through 20,000.
- What are the lowest and highest concentrations (or dilutions) you need to test in order to be certain of finding the half-max? These determine the range of the dilution series.
Now suppose you decide that six tests will be adequate (perhaps each in quadruplicate). Well, starting at 1/1,000, you need five equal dilution steps (giving you six total dilutions counting the starting 1/1,000) that end in a 20-fold higher dilution (giving 1/20,000). You can decide on a good step size easily by trial and error. Would 2-fold work? 1/2, 1/4, 1/8, 1/16, 1/32. Yes, in fact that covers 32-fold, more than the 20-fold range we need. (The exact answer is the 5th root of 20, which your calculator will tell you is 1.82 fold per step. It is much easier to go with 2-fold dilutions and gives about the same result.)
So, you need to make a 1/1,000 dilution to start with. Then you need to serially dilute that 2-fold per step in five steps. You could make 1/1,000 by adding 1 microliter of sample to 0.999 ml diluent. Why is that a poor choice? Because you can't measure 1 microliter (or even 10 microliters) accurately with ordinary pipeters. So, make three serial 1/10 dilutions (0.1 ml [100 microliters] into 0.9 ml): 1/10 x 1/10 x 1/10 = 1/1,000.
Routine means of reducing concentrations without employing extremely large volumes or having to measure extremely small volumes.
Serial refers to events occurring in series, that is, one after another. With serial dilutions, dilutions take place one after another, with each subsequent dilution building upon the previous. This allows one to generate substantial levels of dilution without needing to employ very large volumes of diluent nor very small to-be-diluted volumes.
For example, it is quite simple to generate a ten-billion-fold dilution in only a handful of steps. If only a single step, however, then one would have to dilute 1 &mul (one-thousandth of an ml) to 10 liters of diluent. With serial dilutions, however, this same total dilution requires only five one-hundred-fold dilutions, such as 1 ml to 99 ml or 0.1 ml to 9.9 ml or even 0.01 ml (10 &mul) to 0.99 ml, repeated five times and with the last four steps serving to further dilute the previously diluted volumes. That is,
100×100×100×100×100 = 10,000,000,000 = 10 billion (= 100 5 = 10 10 )
It is important to make sure that volumes are well mixed before drawing volumes to generate the next dilution, and that neither transfer devices nor vessels are reused prior to thorough rinsing or cleaning as well as, if necessary, sterilization.
How to Do Serial Dilutions
This article was co-authored by Bess Ruff, MA. Bess Ruff is a Geography PhD student at Florida State University. She received her MA in Environmental Science and Management from the University of California, Santa Barbara in 2016. She has conducted survey work for marine spatial planning projects in the Caribbean and provided research support as a graduate fellow for the Sustainable Fisheries Group.
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A dilution in chemistry is a process that reduces the concentration of a substance in a solution. A serial dilution is the repeated dilution of a solution to amplify the dilution factor quickly.  X Research source It’s commonly performed in experiments requiring highly diluted solutions, such as those involving concentration curves on a logarithmic scale or when you are determining the density of bacteria. Serial dilutions are used extensively in experimental sciences like biochemistry, microbiology, pharmacology and physics.
One in a Million: Using Serial Dilutions to Understand Concentration
A serial dilution is a simple technique for reducing the concentration of a solution in a systematic way. In this activity, students prepare beverage solutions over a wide range of concentrations and determine the minimum concentration required to taste the sweetness of a solution.
This activity involves taste-testing a prepared solution. Note: Do not use laboratory materials or glassware. All materials should be purchased for consumer use and discarded at the conclusion of the activity. Consider performing the One in a Million activity in the school cafeteria or trading classrooms with a food science teacher for the day. Emphasize that students should not eat, drink, or chew gum during activities performed in their science classroom.
Materials (per student)
- Presweetened Powdered Drink Mix (Kool-Aid® or similar)*, 8 to 9 g
- Plastic Spoon
- Large Cup (10 oz or larger)
- 6 Small Cups (4 oz or larger)
- Permanent Marker
- Tap Water
*Or you can add table sugar to unsweetened drink mix according to instructions printed on the package. Do not add water. Students will add water during the activity.
- Use a permanent marker to label the 6 small cups with letters A through F, respectively.
- Use a permanent marker to label the large cup “water.”
- Fill the large cup with tap water.
- To prepare solution A:
Set up the test tube racks with four test tubes per group. Place the other equipment and supplies at the student work stations or in a central location where they can be located by group members and taken to their work stations.
If your students are not familiar with how to use a pipette and pump, review the proper way to attach the pipette and pump and how to hold the equipment and how to measure accurately with the pipette. Also, review how to mix the solutions in the tube by using the pipette to draw in the contents of the tube and then releasing back down. Repeat that step two times for a full mix.