COLORIMETRIC ANALYSIS
COLORIMETRIC ANALYSIS
(Beer's law or Spectrophotometric Analysis)
Along with operating the
instruments, Beer's law also involves calculations to actually figure out the
concentration of a solution from the absorbance measurements made by using the
colorimeter (or spectrophotometer). There are three methods that can be used
depending on what information is available. They involve using proportionality, graphing
and Beer's Law.
1.
Proportionality; Example
The proportionality approach to
these kinds of problems focuses on the idea that the absorbance of a solution
is directly proportional to its concentration. When using this approach it is
necessary to be sure that the values given are for different concentrations of
the same chemical measured under the SAME conditions (BOTH wavelength
and the path length).
Question: A solution with a concentration of 0.14 M is measured
to have an absorbance of 0.43. Another solution of the same chemical is
measured under the same conditions and has an absorbance of 0.37. What is its
concentration?
The
solution to this problem can be set up using the equation shown below, which
simply says that the ratio of the concentrations is proportional to the ratio
of absorbances. We can use c1 to represent the unknown concentration. You can
derive this equation from Beer's law (Absorbance = e L c)
C1 / C2 = A1 / A2
(ONLY for absorbances that are measured/predicted at the SAME
Wavelength)
Therefore,
C1 = (A1 / A2) * C2
Substitute
all the values as follow:
A1 = 0.37; A2= 0.43 & C2=0.14M
Thus,
C1 = 0.12M
The
graphing method is called for when several sets of data involving STANDARD
SOLUTIONS are available for concentration and absorbance. This is probably
the most common way of Beer's law analysis based on experimental data collected
in the laboratory.
Graphing
the data allows you to check the assumption that Beer's Law is valid by looking
for a straight-line relationship for the data.
Question: What is the concentration of a 1.00 cm (path length)
sample that has an absorbance of 0.60?
Concentration (M) |
Absorbances |
0.20 |
0.27 |
0.30 |
0.41 |
0.40 |
0.55 |
0.50 |
0.69 |
The
solution to the problem here is to graph the data
and draw a straight line through the points. If the data points are
on or close to the line, that will confirm that the absorbance and
concentration are proportional and Beer's Law is valid for this situation.
Recall
that Beer's law is expressed as Absorbance = e L c. To find the concentration for
a solution that has an absorbance of 0.60, you will first need to find the slope of the BEST-FIT line. From the slope of the
best-fit line together with the absorbance, you can now calculate the
concentration for that solution (i.e. Concentration
= Absorbance / Slope)
Notice that the SLOPE of the best-fit line in this case is actually
the PRODUCT of the molar absorptivity constant and the path length
(1.00cm).
Here
is an example of directly using the Beer's Law Equation (Absorbance = e L c) when you
were given the molar absorptivity constant (or molar extinction coefficient).
In this equation, e is the molar extinction coefficient. L is the path length
of the cell holder. c is the concentration of the solution.
Note: In reality, molar absorptivity constant is normally not
given. The common method of working with Beer's law is in fact the graphing
method (see above).
Question: The molar absorptivity constant of a particular
chemical is 1.5/M·cm. What is the concentration of a solution made from this
chemical that has an absorbance of 0.72 with a cell path length of 1.1cm?
To
find the concentration, simply plug in the values into the Beer's law equation.
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