Quantitative Analysis by Atomic Absorption

The capability of an atom to absorb very specific wavelengths of light is utilized in atomic absorption spectrometry.

Light of a specific wavelength and of initial intensity I_o is focused on the flame cell containing ground state atoms. The initial light intensity is decreased by an amount determined by the atom concentration in the flame cell. The light is then directed to the detector where the reduced intensity, I_t, is measured. The amount of light absorbed is determined by comparing I_t  to I_o and according to Beer’s law:

A = log I_o / I_t = α * c * d         (1)

Absorbance A is the most convenient term for characterizing light absorption in absorption spectrophotometry, as this quantity follows a linear relationship with concentration c.

Equation (1) can be used for quantitative analysis by atomic absorption spectrometry. A calibration curve is used to determine the unknown concentration of an element – i.e. nickel – in a solution. The instrument is calibrated using several solutions of known concentrations of the element under examination. The calibration curve shows the concentration of the elementin solution against the amount of radiation absorbed (Fig. 1).

Fig. 1: Calibration curve of nickel solutions (absorbance vs. solution concentration) obtained by atomic absorption spectrometry.

 

The sample solution is fed into the instrument and the unknown concentration of the element  – i.e. nickel – is then displayed on the calibration curve (Fig. 1).

For example for the Ni solution above an absorbance of 0.37 was obtained that corresponds to a concentration of 12 mg/l.

Over the region where the Beer’s law relationship is observed, the calibration yields a straight line. As the concentration and absorbance increase, nonideal behavior in the absorption process can cause a deviation from linearity as shown in Fig. 1. There are several reasons for this nonideal behavior  such as nonhomogeneities of temperature and space in the absorbing cell, line broadening, absorption at nearby lines and stray light.

As shown above, after such a calibration is established (Fig. 1) the absorbance of solutions of unknown concentrations may be measured and the corresponding concentrations can be determined from the calibration curve.

The instrument performance for an element can be monitored by the following parameters:

• Characteristic concentration for the element

• Detection limit

The characteristic concentration for an element (called “sensitivity”) is a convention and is defined as the concentration of analyte giving an absorbance of 0.00436 (corresponding to a percent transmittance of 99%). Usually the wavelength providing the best sensitivity is used, although a less sensitive wavelength may be more appropriate for a high concentration of analyte. A less sensitive wavelength also may be appropriate when significant interferences occur at the most sensitive wavelength.

Characteristic Conc. (mg/l) = Conc. of Standard (mg/l) * 0.0044  /  measured absorbance

There are several practical reasons for wanting to know the value of the characteristic concentration for an element. For example, knowing the expected characteristic concentration of an element allows an operator to determine if all instrumental conditions are optimized and if the instrument is performing according to specifications. This is accomplished by simply measuring the absorbance of a known concentration of the element and comparing the results to the expected value.

Even though the magnitude of the absorbance signal can be predicted from the value given for characteristic concentration, no information is given on how small of an absorbance signal can be measured.

The smallest measurable concentration of an element – the detection limit of the element -  will be determined by the magnitude of the absorbance observed for the element and the stability of the absorbance signal.

The detection limit(according to IUPAC) is the smallest concentration or absolute amount of analyte that has a signal significantly larger than the signal arising from a reagent blank.

Mathematically, the analyte’s signal at the detection limit (s_DL) is given by:

s_DL = s_reag + 3 * σ_reag

where s_reag is the signal for a reagent blank, sreag is the known standard deviation for the reagent blank’s signal.

Other approaches for defining the detection limit have also been developed. In atomic absorption spectrometry usually the detection limit is determined for a certain element by analyzing a diluted solution of this element and recording the corresponding absorbances. The experiment is repeated for 10 times. The 3σ of the recorded absorbance signal can be considered as the detection limit for the specific element under the experimental conditions used – wavelength, type of flame, instrument.

For example, let us suppose that the detection limit for Cu has to be determined by AAS under certain experimental conditions. A 0.1 ppm Cu solution is analyzed for 10 times by AAS at a wavelength of 324.8 nm and the corresponding absorbance values are recorded:

Experiment #	Absorbace
1	0.006
2	0.005
3	0.007
4	0.007
5	0.006
6	0.007
7	0.005
8	0.004
9	0.005
10	0.004
Average	0.0056
σ	0.0012
3σ	0.0036

Therefore, the detection limit for Cu (Cu signal at the detection limit) under the above conditions is 0.0036 and this absorbance corresponds to a Cu solution concentration approximately at:

0.1 ppm * (0.0036/0.0056) = 0.064 ppm (assuming we are working on the linear region of the calibration curve)

REFERENCES

1.  (a) R. Ferrus, ; M.R. Egea, Anal. Chim. Acta 1994, 287, 119–145  (b) J.A. Glaser, D.L. Foerst, et al. Environ. Sci.Technol. 1981, 15, 1426–1435; (c) P.W.J. Boumans, Anal. Chem. 1994, 66, 459A–467A

Statistics| Analysis of Data – Confidence intervals

Most of the time the population mean differs from the mean of each individual sample taken from the population.

Consider the following example where absorbance of a solution containing a known concentration of substance A was determined by U.V./Visible spectrometer. The absorbance of the solution was measured three times during each experiment and the average value, standard deviation s and 2s was calculated (see Table 1).

Table 1: Absorbance values measured for a solution A using a U.V./Visible spectrometer. Three consecutive measurements were recorded during each experiment.

The mean values from Table 1 were plotted in the graph shown in Fig. 1 below and 2s (2 * standard deviation s) is shown for each mean. As can you see, the mean value calculated for the absorbance of A in each experiment (sample of the population) differs from the mean of the population (red line). Please also note that the interval - solid line above and below the mean in each experiment (Fig. 1) -  of  each mean (the range of values the mean can take with a certain probability) does not always contain the population mean (experiments 5, 9, 10, 13).

Fig 1: Absorbance values obtained by measuring a solution of substance A with known concentration C using a U.V/Visible spectrometer. Each point shown on the graph is the mean of three consecutive measurements of the solution of substance A with concentration C.

From the above discussion the following question arises:

How can we assess the accuracy of the population mean? Within wich boundaries the true value of the population mean is contained? 

Such boundaries are called confidence intervals or confidence levels. Confidence intervals in a sense give us the range of values that the population mean can take with a certain degree of confidence – usually 90%, 95% or 99%.

Most of the time we look at 95% confidence intervals but all of them have similar interpretation:

they are limits constructed such that a certain percentage of the time 95% in this case the value of the population mean will fall within these limits.

How can we calculate confidence intervals? 

In order to calculate the confidence interval, we need to know the limits within which 95% of means will fall. If we will assume a normal distribution with a mean = 0 and  s = 1 we can use the z-scores with values between -1.96 and  +1.96 (remember that 95% of z-scores fall between these two values). Remember also that we can convert values to z-scores using the formula:

z = (x - x̅ )/ s                      (1)

If we know that the upper limit will be z = +1.96 then from (1) we get:

(x - x̅ )/ s  = 1.96  and  x =   x̅ + 1.96 * s  (this is the upper boundary – limit)

and

(x - x̅ )/ s  = -1.96  and  x =   x̅ - 1.96 * s  (this is the lower boundary – limit)

Therefore, the confidence interval can easily be calculated once the standard deviation s of the mean and the mean are known. The general form of the confidence interval is given below:

                                                           x =   x̅ ± z_critical * s               (2)

where x is the upper or lower value the mean of the population can take with a certain degree of confidence,  x̅ is the mean value of the population of measurements, z_critical is the z critical value from statistical tables (see Table 2) at a certain confidence level (usually 95%) and s is the standard deviation of the measurements.

Confidence Level (%)	z-critical value
99	2.58
95	1.96
90	1.645
50	0.675

Table 2: Critical values of z at different confidence levels