Calibration Curve


Calibration curve is a procedure for determining the concentration of a compound in an unknown
sample. CalibrationCurve.xls is an Excel workbook to perform a calibration calculation when using
internal standards. This calculation is based on a conventional statistical procedure, described,
for example, in D. A. Skoog, J. J. Leary: Principles of Instrumental Analysis, 4^th edition, and
utilizes the method of least squares for linear regression. In case of any question or problems
with this file, please, contact Dr. Dominik Heger, hegerd@chemi.muni.cz.


The calibration curve production from the HPLC or GC data


 1. Make at least two independently prepared (most concentrated or stock) solutions for each
compound, i.e., an analyt, A (which is the compound you wish to determine in an unknown sample) and
an internal standard, IS. Weigh the solid as well as liquid (non-volatile) compounds. Do not use
volumetric glass for small amounts of liquids or for any amounts of viscous liquids.
 2. Prepare at least 7 different solutions – mixtures of both A and IS. The concentration of the
latter should be similar in all samples (including that of unknown samples). Make sure the A
concentration range is broad enough. Mix diluted A and IS solutions randomly; the points of the
calibration curve should be distributed unevenly. The chromatographic peaks must be well separated
but not too far from each other. Inject each solution at least twice. If the A/IS areas ratio
differs by more than 5%, repeat the measurement. Remove the outliers. All other data should be used
for the calibration calculation. Thus, at least 14 values, obtained from the analysis of 7
solutions, help to avoid errors of rounding the averages and to make the standard deviation
smaller.
 3. Use a new calibr-empty sheet (and rename it as you like) or calibr-empty-Rev (will be discussed
later) in the Excel file CalibrationCurve100310.xls. This workbook also contains some of the
already measured data that you may find useful for practicing: calibr-Krausci, calibr-Krausci-Rev,
A112 (an example a1-12 from D. A. Skoog, J. J. Leary: Principles of Instrmental Analysis, 4^th
edition; this worksheet utilizes the mathematics described there), 119a (an example 19.1a from J.
H. Zar, Biostatistical Analysis, 5^th edition, currently available in the Dominik Heger’s office).
The Calibration curve part, where you create you calibration curve, and the Reading from
calibration curve part, where you can calculate the concentrations of A in your samples, are
located in calibr-empty sheet.

 a. Calibration curve

Fill in the A, B, C, D columns using the concentration values used and the peak areas measured
belonging to both A and IS. Adjust the number of rows you are using. If you do not need them all,
delete those not used in order to avoid seeing #DIV/0! Then you need to check the magenta cells
whether they display the data in all columns. At this point your calibration curve is plotted and
the linear regression is calculated. Check whether all your points are included in the graph and
that the r^2 calculated in W9 is the same as that of the graph, i.e. whether you are using the same
data for both the calculation and the plot itself. Now check the green cells. These values are the
slope m and intercept b with its standard deviations (s[m], s[b]), then the coefficient of
correlation, r, and its standard deviation, s[r], and the coefficient of determination, r^2. You
can also check the range of concentrations of A and IS (P12, 13).

 b. Reading from the calibration curve

To obtain the concentrations of A from the calibration curve, enter the concentration of IS into
the column B and the area of the measured peaks from the chromatogram to the columns C and D. Fill
in the number of measurements you had done into the column E to determine these values of areas
(preset value is 1). Then the Excel calculates the ratio of the areas (column F) and the ratio of
concentrations (column G) and its standard deviation s[x] (column G) from the calibration curve.
The concentration of A is calculated from the concentration of internal standard (column I). The
standard deviation sc of the concentration of A (column J) is calculated by error propagation. The
percent relative standard deviation (sr (%)) is in the next column (K). In case of A, make at least
two injections and then compare the results. The average of these two measurements is calculated on
the right starting from the column M. Make sure that the references in the cells M and N refer to
the correct rows in the column F. The average concentration of the analyt A can be found in the
column Q and its standard deviation sc is in the column R.


The ratio of both the concentrations and areas is calculated in calibr-empty as [A]/[IS]. A reverse
ratio is calculated in calibr-empty-Rev. Although there is only insignificant difference between
both calculations; however, that with a larger coefficient of correlation r gives a smaller
cumulative percent relative standard deviation cprs (as found in L23; make sure you are summing all
the data you want). This approach is thus recommended. The calibration curve using the same
[A]/[IS] gives better distribution of the points as well as a larger r; see calibr-Krausci.