How to make dilutions and calculate the dilution factor

The principle of making dilution of any solution:-

The number of molecules of a substance before dilution does not change after dilution. For example, if we have 100 molecules of that substance in 1 ml of distilled water and then we add another 1 ml of distilled water, the 100 molecules are all still there but only the expression is changed where we will say 50 molecules per 1 ml instead of 100 molecules per 2 ml.

Let see this in a mathematical way,

And

So, the molecular weight is constant for the same substance because the molecular weight is constant because it depends on the atoms from which the substance is formed. But, What about the weight? Is it constant? let’s think. If we weigh 10 gm of NaCl and dissolve it in one 1 ml of distilled water and then we add another 1 ml of distilled water, IS THE WEIGHT CHANGED? Of course no, because the 10 gm are still in the 2 ml of distilled water.  This means that:

no. of molesbefore dill = no. of molesafter dill

Therefore,

Analyte concbefore dill × Vbefore dill = Analyte concafter dill × Vafter dill

The (Analyte concafter dill ) is what you get from the test and you should multiply it by

That’s it.

and of course if you need the concentration after dilution, then, the dilution factor will be:

Note that, if you dilute a liquid sample, the Vafter dill is the total volume and equals the volume of the sample and the volume of the solvent.

When do you need to make dilutions?

You need to make dilution and dilution factor in the following cases:-

1. If your sample is not enough to perform all the required tests and you have no chance to get another sample. For example, if your patient is a newborn or an infant or a child and you only get a small sample and you cannot get more, you should dilute the sample.
2. If your sample is icteric or lipemic, you need to dilute the sample 1 to 10 to avoid the errors in your results due to the serum or plasma turbidity (in the case of a lipemic sample) or due to the dark color of the bilirubin (in the case of an icteric sample).
3. In the case of tests performed by kinetic techniques such as ALT test or AST test, f the graph is not linear or the result you get is a negative value such as – 6 not 6, this means the activity of the enzyme is higher than the detection ability of the kits. In this case, you need to dilute the sample 1 to 3 or 1 to 5.
4. In the case of colorimetric tests, each reagent has a detection limit beyond which the reagent will give you false lower readings than the real one. For Example, in the reagent of glucose test from spinreact company, the detection limit is 500 mg/dl. Therefore, if you measure the sample and the result was 500 or more (say 520), you should dilute the sample at least 1 to 2, then multiply the result by a dilution factor. If you do this, you will find that the result may reach 600 mg/dl.
5. In rare cases, you need to calculate a dilution factor such as when you use different volumes of sample and standard. For example, in creatinine test, you can use 100µl of standard and 50µl of the sample on the same volume of your reagent and in this case, you should multiply the result by a dilution factor. see Page 2.

When the sample you get is not enough for performing all the required tests, you have 3 choices

1. Make a new standard using the small volume that you will use to test the sample. For example, in creatinine test, if you have 50µl of the sample. you can prepare a new standard by using 50 µl. In this case, you will consume more standard and also, and after measuring the small-volume sample, you should re-enter the standard using 100µl to adjust it again for the normal procedures.
2. Calculate the dilution factor of the both standard and sample and multiply the concentration of the sample by the dilution factor … Read on page 2.
3. Take 50µl of the sample and dilute it with 100µl saline and then take 50µl from this mix and measure it as a sample. Then multiply the result by 3 where the dilution factor will be 50:150 which means 1:3.

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