Now the
question is: what is the final concentration of compound
A in the diluted sample? The key to dilution problems is
the fact that the total amount of compound A that is
diluted  measured in grams or other units of weight 
does not change. For example in the above example, we
start out with 1 mL of sample that contains 50 mg/mL of
compound A. This means we begin with 50 mg of A
in the 1 mL of initial sample solution. We can generalize
this by proceeding as follows:
concentration
of A = (quantity of A) / (volume of solution)
quantity of A =
(concentration of A) x (volume of solution)
= (50 mg/mL) x (1 mL)
= 50 mg of A
We can also write for cases
of this type:
(initial
quantity) = (final quantity) or
C_{1
}x V_{1}
= C_{2} x V_{2}
Here C_{1} is the
concentration of A in the initial solution and V_{1}
is the volume of that solution (volume of the pipette); C_{2}
is the concentration of A in the final solution (after
dilution) and V_{2} is the volume of final
solution (volume of the flask).
Now we have 50 mg of A
in the initial 1 mL of sample solution that is pipetted,
and the final volume of solution after dilution is 50 mL.
So the concentration of A in the final sample solution is:
(quantity of A)
/ (volume of solution) = (50 mg)/(50 mL)
=1mg/mL
In solving dilution problems we can
proceed in various ways. We can simply calculate a
DILUTION FACTOR (DF) as the ratio of the flask volume (V_{2})
to the pipette volume (V_{1}):
DF = V_{2}
/ V_{1}
Then from we can write:
C_{2}
= C_{1} x V1
/ V_{2} = C_{1}
/ DF
That is, our final sample
concentration C_{2} is equal to the initial
concentration C_{1} divided by the dilution
factor DF. Or we can rearrange into
C2 = C_{1}
x V_{1} / V_{2}
and solve for the new
concentration C_{2} in terms of the initial
concentration (before dilution) C_{1}, the
pipette volume V_{1}, and the flask volume V_{2}.
You should use whichever of these dilution calculations
you feel comfortable with. Most people use the dilution
factor approach.
