Get the Facts About Titer Calculations
Jump to How to calculate dilution factor - If you're still asking yourself 'how to find dilution factor? If you are want to calculate dilution factor by hand.
The 'titer' is the measurement of the amount of a substance in a solution. An antibody titer test is a blood test that doctors may use to help with diagnosis.
Titer often describes concentrations of biological molecules (i.e., bioproducts) such as antibodies and other proteins. The titer indicates the number of times a solution can be diluted and still contain detectable amounts of a particular molecule.
Serial Dilution
To calculate antibody titer, a blood serum sample containing antibody is diluted in serial ratios (1:2, 1:4, 1:8, 1:16...etc.). Using an appropriate detection method (e.g., colorimetric, chromatographic, etc.), each dilution is tested for the presence of detectable levels of antibody. The assigned titer value is indicative of the last dilution in which the antibody was detected.
Examples of Calculations
Say, for instance, that the antibody was detected in each of the tubes listed above but was not detected in a 1:32 ratio dilution. In this case, the titer is 16. However, if it is detected in the 1:2 and 1:4 dilutions, but not in others, the titer is said to be 4.
Why Doctors Test a Patient's Level of Antibody Titers
Doctors test patients' antibody levels to determine whether or not they have been exposed to an antigen or another foreign substance. When this happens, antibody levels rise, because the body enlists the aid of antibodies to attack and destroy the threatening foreign substance.
Physicians often decide to test patients' antibodies to determine if they've been exposed to common childhood infections like chickenpox. These tests will help determine if a patient needs a booster shot or if an already administered immunization has triggered a strong enough response. Titer tests can also indicate if the patient has had a recent infection.
According to the U.S. National Library of Medicine, antibody titer is also used to determine if the body has had an immune response to the body's own tissues, which happens to people afflicted with lupus.
What Are Normal Levels of Antibody Titers?
It's difficult to say what a normal level of antibody titers is, without knowing why they are being tested. However, if the level is negative, that outcome is helpful in excluding a diagnosis of certain medical conditions. And if the antibody titers are tested to determine if the body is attacking its own tissues, the normal level is zero.
Real-life chemists in real-life labs don’t make every solution from scratch. Instead, they make concentrated stock solutions and then make dilutions of those stocks as necessary for a given experiment.
To make a dilution, you simply add a small quantity of a concentrated stock solution to an amount of pure solvent. The resulting solution contains the amount of solute originally taken from the stock solution but disperses that solute throughout a greater volume. Therefore, the final concentration is lower; the final solution is less concentrated and more dilute.
How do you know how much of the stock solution to use and how much of the pure solvent to use? It depends on the concentration of the stock and on the concentration and volume of the final solution you want. You can answer these kinds of pressing questions by using the dilution equation, which relates concentration (C) and volume (V) between initial and final states:
C1V1 = C2V2
You can use the dilution equation with any units of concentration, provided you use the same units throughout the calculation. Because molarity is such a common way to express concentration, the dilution equation is sometimes expressed in the following way, where M1 and M2 refer to the initial and final molarity, respectively:
M1V1 = M2V2
For example, how would you prepare 500. mL of 0.200 M NaOH(aq) from a stock solution of 1.5 M NaOH?
Start by using the dilution equation,
M1V1 = M2V2
The initial molarity, M1, comes from the stock solution and is therefore 1.5 M. The final molarity is the one you want in your final solution, which is 0.200 M. The final volume is the one you want for your final solution, 500. mL, which is equivalent to 0.500 L. Using these known values, you can calculate the initial volume, V1:
The calculated volume is equivalent to 67 mL. The final volume of the aqueous solution is to be 500 mL, and 67 mL of this volume comes from the stock solution. The remainder, 500 mL – 67 mL = 433 mL, comes from pure solvent (water, in this case). So to prepare the solution, add 67 mL of 1.5 M stock solution to 433 mL water. Mix and enjoy!
Try another problem: What is the final concentration in molarity of a solution prepared by diluting 2.50 mL of 3.00 M KCl(aq) up to 0.175 L final volume?
You can use the dilution equation,
M1V1 = M2V2
In this problem, the initial molarity is 3.00 M, the initial volume is 2.50 mL or 2.50 x 10–3 L and the final volume is 0.175 L. Use these known values to calculate the final molarity, M2:
So, the final concentration in molarity of the solution is
4.29 x 10–2M