Calibration Curves

1. Making the Standards: Serial Dilutions

1. Make a concentrated stock solution of the standard. Typically, the compound is accurately weighed out and then quantitatively transferred into a volumetric flask. Add some solvent, mix so the sample dissolves, then fill to the line with the proper solvent.
2. Perform serial dilutions. Take another volumetric flask and pipette the amount of standard needed for the dilution, then fill to the line with solvent and mix. A ten-fold dilution is typically made, so for a 10-mL volumetric flask, add 1 mL of the previous dilution.
3. Continue as needed for more dilutions, pipetting from the previous solution to dilute it to make the next sample. For a good calibration curve, at least 5 concentrations are needed.

2. Run the Samples for the Calibration Curve and the Unknown

1. Run the samples with the UV-Vis spectrophotometer to determine the instrumental response needed for the calibration curve.
2. Take the reading with the first sample. It is a good idea to run the samples in random order (i.e. not highest to lowest or lowest to highest) in case there are any systematic errors. In order to get an estimate of noise, repeat the reading on any given sample 3–5x.
3. Run the additional standard samples, repeating the measurements for each sample to get an estimate of noise. Record the data to make a plot later.
4. Run the unknown sample(s). Use as similar conditions to running the standards as possible. Thus, the sample matrix or buffer should be the same, the pH should be the same, and the concentration should be in the range of the standards run.

3. Making the Calibration Curve

1. Record the data in a spreadsheet and use a computer program to plot the data vs concentration. If at least triplicate measurements were taken for each point, error bars can be plotted of the standard deviation of those measurements to estimate of the error of each point. For some curves, the data might need to be plotted with an axis as a log to get a line. The equation that governs the calibration curve is generally known ahead of time, so a log-plot is used when there is a log in the equation.
2. Examine the calibration curve. Does it look linear? Does it have a portion that looks non-linear (i.e. reached the limit of the instrumental response)? To check, fit all the data to a linear regression using the software. If the coefficient of determination (R²) is not high, remove some of the points at the beginning or ending of the curve that do not appear to fit the line and perform the linear regression again. It is not acceptable to remove points in the middle just because they have a large error bar. From this analysis, decide what portion of the curve is linear.
3. The output of the linear should be an equation of the format y=mx+b, where m is the slope and b is the y-intercept. The units for the slope are the y-axis unit/concentration, in this example (Figure 1) absorbance/μM. The units for the y-intercept are the y-axis units. A coefficient of determination (R²) is obtained. The higher the R² the better the fit; a perfect fit gives an R² of 1. The program may also be able to give an estimate of the error on the slope and the intercept.

4. Results: Calibration Curve of Absorbance of Blue Dye #1

1. The calibration curve for absorbance of blue dye #1 (at 631 nm) is shown below (Figure 1). The response is linear from 0 to 10 µM. Above that concentration the signal begins to level off because the response is out of the linear range of the UV-Vis spectrophotometer.
2. Calculate the LOD. From the slope of the calibration curve, the LOD is 3*S.D. (noise)/m. For this calibration curve, the noise was obtained by taking a standard deviation of repeated measurements and was 0.021. The LOD would be 3*0.021/.109=0.58 µM.
3. Calculate the LOQ. The LOQ is 10*S.D.(noise)/m. For this calibration curve, LOQ is 10*0.021/.109 =1.93 µM.
4. Calculate the concentration of the unknown. Use the line equation to calculate the concentration of the unknown sample. The calibration curve is only valid if the unknown falls into the linear range of the standard samples. If the readings are too high, dilution might be necessary. In this example, the unknown sports drink was diluted 1:1. The absorbance was 0.243 and this corresponded to a concentration of 2.02 µM. Thus the final concentration of blue dye #1 in the in the sports drink was 4.04 µM.

Figure 1. Calibration curves for UV-Vis absorbance of blue dye. Left: The absorbance was measured of different concentrations of blue dye #1. The responses level off after 10 µM, when the absorbance is over 1. The error bars are from repeated measurements of the same sample and are standard deviations. Right: The linear portion of the calibration curve is fit with a line, y=0.109*x + 0.0286. The unknown data is shown in black. Please click here to view a larger version of this figure.