CHEM 2400/2480
Calibration Curves
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show the response of an analytical method to known quantities of
analyte
Standard solutions - contain known concentrations of analyte
Blank solutions - contain all reagents and solvents in the standard
solutions but no analyte is added
- used to measure any response due to impurities or interferences
Construction of a calibration curve
•
prepare standard solutions in the range of concentration expected
for the unknown sample solution
•
measure the response of the analytical method for each of the
standard solutions and a suitable blank
•
subtract the average reading for the blank solution from each
response for the standard solutions
•
plot the corrected response against concentration for all the
standard solutions
•
perform a linear least squares analysis
•
always examine your calibration curve before performing the
least squares analysis and discard any obvious outliers
•
it is common for a linear curve to drop off at higher
concentrations - the method or instrument is becoming
saturated and the response cannot increase further with
increasing concentration
•
do not extrapolate beyond the concentrations of the standards
Linear range - range over which the response is proportional to
concentration
Dynamic range - range over which the response is measurable, but
not necessarily linear
2-20
CHEM 2400/2480
Linear least squares
•
method for finding the best fit line for data
y = mx + b
•
•
•
minimizes deviations between experimental data and the best fit
line
assumes there is more uncertainty in the y values than in the x
the deviation for point x i, yi is
d = yi - y = yi - (mx i + b)
•
•
deviations can be positive or negative, so they are squared to make
all of them positive
the least squares method finds m and b such that the sum of the
deviations is minimized
Using a calibration curve
•
measure the response of the analytical method for each of the
unknown solution(s) and a suitable blank
•
subtract the average reading for the blank solution from each
response for the unknown solution(s)
•
use the equation from the calibration curve to determine the
concentration of analyte in the unknown(s)
2-21