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When calculating how to perform a simple dilution,
it is important to use the same units for volume and concentration for the
starting and final solutions. For
example if you are starting with a 5 Molar stock solution, it is easy to
calculate how much stock solution is required to produce a given volume of a 2M
solution. It is also simple to calculate
how to dilute percent solutions.
Vol(initial)
X Concentration(initial) = Vol(final) X
Concentration(final)
Example:
How much 100%
ethanol is needed to make 500 ml of 70% ethanol?
Vol(init) X 100% = 500 ml X 70%
Vol(init) = (500 ml X
70%)/100%
Vol(init) = 35000/100 = 350
ml
350 ml of 100% ethanol would be added to a graduated
cylinder. Sufficient water would then be
added to yield a final volume of 500 ml.
SIMPLE DILUTIONS
The calculations shown below are used to determine
the resulting concentration when a given volume of solute is added to a
specified volume of diluent. This is expressed as a ratio called the
dilution factor:
Dilution
factor = (volume of solute)/(vol
of solute + vol of diluent)
Example:
One ml of serum is added to 9 ml of saline. What is the resulting dilution?
D.F. = 1ml serum/(1ml serum + 9 ml saline)
D.F. = 1/10
NOTE! Since
serum is a complex mixture of substances no units of concentration are given
(i.e. M,N,%).
Undiluted serum has a concentration of 1. Therefore in the example above
the resultant dilution is simply expressed as 1/10.
When diluting solutions with a known concentration
of substance, it is necessary to multiply the initial concentration by the
dilution factor in order to determine the final concentration.
Example:
One ml of a 5N NaCl stock
is added to 99ml of water. What is the
concentration of NaCl in the final solution?
D.F. = 1ml 5N NaCl/(1ml
5N NaCl + 99ml water) = 1/100
Final Concentration = 5N X 1/100 = (5N/100) = 0.05N
It is possible to rearrange the formula in order to
determine how much stock is required to make a specified volume of a diluted
solution.
Example:
How much 2M HCl is needed
to make 250ml of a 1/10 dilution?
1/10 = Xml/(250 ml)
Xml = 250ml/10 = 25ml
Therefore, 25ml of 2M HCl
is diluted to 250ml with water to give a 1/10 dilution.
When performing serial dilutions, it is important to
remember two concepts:
1) Tube
dilution-the dilution factor for the specific tube
2)
Sample dilution-the dilution of the initial sample at a given tube
The TUBE DILUTION is calculated as a simple
dilution:
Tube
dilution = vol of sample/(vol of sample + vol of diluent)
NOTE: The tube dilution does not have units of
concentration or volume. It is the
equivalent of the dilution factor in simple dilutions.
The SAMPLE DILUTION is determined by multiplying the
concentration of the sample added to that tube times the tube dilution.
Example:
A ten fold serial dilution is set up using 3
tubes. Each tube contains 9ml of water.
One ml of 5N NaCl is added to the first tube. The tube is mixed and 1ml of this solution is
added to the second tube. The process is
repeated for the third tube. What is the
tube dilution and sample dilution in the three tubes?
Tube Number
0 1 2 3
Tube dilution
1/1 1/(1+9) 1/(1+9) 1/(1+9)
1/1 1/10 1/10
1/10
Sample dil. 5N X 1/1 5N X 1/10
0.5N X 1/10 0.05N X 1/10
5N 0.5N 0.05N 0.005N
Tube #0 is the undiluted sample.
If serum is used in the above example in place of 5N
NaCl, the sample dilution would be determined as
follows (Remember-undiluted serum has a arbitrary
concentration of 1):
Tube Number
0 2 3 4
Tube dilution
1/1 1/(1+9) 1/(1+9) 1/(1+9)
1/1 1/10 1/10 1/10
Sample dil. 1/1 X 1/1 1/1 X 1/10
1/10 X 1/10 1/100 X 1/10
1/1 1/10 1/100 1/1000