SPECTROCHEMICAL METHODS QUANTITATIVE CALCULATIONS

Transcription

1 SPECTROCHEMICAL METHODS QUANTITATIVE CALCULATIONS

2 INTRODUCTION Beer's law also involves calculations to actually figure out the concentration of a solution from the absorbance measurements made by using the spectrophotometer. There are three methods that can be used depending on what information is available such as 1. PROPORTIONALITY 2. GRAPHING 3. BEER S LAW

3 1. Beer's Law The Beer Lambert law, also known as Beer's law relates the absorption of light to the properties of the material through which the light is travelling (cell pathlength).

4 Derivation of Beer s Law Schematic of a simple spectrometer. Irradiance In Irradiance Out Pathlength Irradiance, P (Wm -2 ), is the energy per second per unit area of the beam of light.

5 Transmittance, T, is the fraction of original light not absorbed by the sample. Transmittance is T=P o /P P o = power of incident light P= power of transmitted light Putting transmittance in logarithmic form: log T = log P/P o = -kb -log T = - log P/P o = A -log T = log P o /P = A

6 The fractional decrease in power (P) is porpotional to the sample thickness (α) and the analyte s concentration (C) - presented in Equation 1. Change the equation (1) -dp o = αcdx P ln Po = αbc P (1) Converting from ln to log and substituting equation for absorbance gives: A = abc Where a = analyte s absorptivity and replaced by ε; b = pathlength through the material; C= concentration A = εbc

7 Equations The law states that there is a logarithmic dependence between the transmission, T, of light through a substance and the product of the absorption coefficient (extinction coefficient of the absorber, ε) and the distance the light travels through the material (i.e., the path length), l. Beer's Law Equation: Absorbance, A = ε L c ε is the molar extinction coefficient L is the path length of the cell holder c is the concentration of the solution. ε 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

8 Example 1: A sample in a 1.0-cm cell is determine with a spectrometer to transmit 80% light at certain wavelength. If the absorptivity of this substance at this wavelength is 2.0, What is the concentration of the substance? Solution: The percent of the transmittance is 80%, and so T = log 1/T =εbc log 1/0.80 = 2.0 cm -1 g -1 L x 1.0 cm x c log 1.25 = 2.0 g -1 L x c c = 0.10/2.0 = gl -1

9 In analytical applications, we often want to measure the concentration of an analyte independent of the effects of reflection, solvent absorption, or other interferences. The figure to the right shows the two transmittance measurements that are necessary to use absorption to determine the concentration of an analyte in solution. The top diagram is for solvent only and the bottom is for an absorbing sample in the same solvent. In this example, Ps is the source light power that is incident on a sample, P is the measured light power after passing through the analyte, solvent, and sample holder, and Po is the measured light power after passing through only the solvent and sample holder. The measured transmittance in this case is attributed to only the analyte. Depending on the type of instrument, the reference measurement (top diagram) might be made simultaneously with the sample measurement (bottom diagram) or a reference measurement might be saved on computer to generate the full spectrum.

10 ANALYTICAL TECHNIQUES Beer's law, A = k C, not always true making a calibration curve necessary. Standard addition method is used to minimize the effects from the matrix Anion- height of the absorbance peak is influenced by type and concentration of anion. It can reduce the number of atoms made. An unknown matrix is thus hard to correct for. Cation: The presence of a second cation sometimes causes stable compounds to form with the cation being analyzed. e.g. Al + Mg produces low results for Mg due to the formation of an Al/Mg oxide. Chapter 8&9-10

11 Beer s Law Assumption/Limitation The light being shined on the sample must be monochromatic (one color or wavelenght) The analyte must not be participate in a concentration dependent equilibrium This isn t good technique for many weak acid systems, as dilution increases dissociation and HA and A- probably don t have the same absorbance.

12 Beer s Law Assumption/Limitation Problems: Calibration curves are found to be nonlinear because occuring of deviation. Deviation from linearity are divided into three categories: 1)Fundamental : Law is valid for low concentration analyte. At higher concentration, there will be interaction between particle of analyte that may change the value of ε. 2) Chemical: when the absorbing species is involved in an equiblirium reaction. HOAc + H 2 O H 3 O + + Cl - Each of ionized species will contribute to ε and C value and therefore will result in non linearity of the curve. 3) Instrumentation: 2 principal limitation: i) Stricly valid for purely monochromatic instrumentation. ii) The effect of leakage light from imperfections within wavelength selector. This phenomena is called stray radiation.

13 Deviation from beer s law:- From the beer s law plot the absorbance against the conc. A straight line passing through origin is obtained. Deviation is due to the following factors:- A foreign substance having colour particle may affect the absorption & extinction coefficient. Deviation also occur if colored solute ionized or dissociates in the solution. for e.g.- benzyl alcohol in chloroform Due to the presence of impurities that fluoresce or absorb at the absorption wave length. If monochromatic light is not used deviation may occurs. If width of the slit is not proper. If the solution species undergoes polymerization

14 2. PROPORTIONALITY METHOD 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).

15 Question: A solution with a concentration of 0.14M is measured to have an absorbance of Another solution of the same chemical is measured under the same conditions and has an absorbance of What is its concentration? ANSWER: 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 = ε L c). C 1 / C 2 = A 1 / A 2 (ONLY for absorbances that are measured/predicted at the SAME Wavelength) Therefore, C 1 = (A 1 / A 2 ) * C 2 Substitute all the values as follow: A 1 = 0.37; A 2 = 0.43 & C 2 =0.14M Thus, C 1 = 0.12M

16 3. GRAPHING METHOD 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.

17 Question: What is the concentration of a 1.00 cm (path length) sample that has an absorbance of 0.60?

18 ANSWER 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 = εlc. 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).

19 Spectroscopy Nomenclature Recommended Name Unit Absorbance (A) - Absorptivity (a) cm -1 g -1 L Pathlength (b) l or d Transmittance (T) - Wavelength (nm) mμ (milicron) Concentration (c) moles per liter (moles L -1 )

20 Wavelenghts and Color Wavelength of Maximum absorption (nm) Color absorption Color Observed Violet Green-yellow Violet-blue Yellow Blue Orange Blue-green Red Green Purple Yellow-green Violet Yellow Violet-blue Orange Blue Red Blue-green Purple Green

21 Example 2: A solution containing 1.00 mg ion (as thiocyanate complex) in 100 ml was observed to transmit 70.0% of the incident light compared to an appropriate blank. (a)what is the absorbance of the solution at this wavelength? (b) What fraction of light would be transmitted by a solution of iron four times as concentrated. Solution: (a) T = A = log 1/0.700 = log 1.43 = (b) A = 15.5 L/g x (4x g/l) = log 1/T = T = 0.240

22 The absorbance of the new solution could have been calculated more directly:

23 Example : ppm Zn Absorbance unknown ) Plot a graph of absorbance versus the concentration of standard Zn on a graph paper. 2) Recognize a linear regression of the plot. 3) Calculate the concentration of Zn in the unknown.

24 Concentration Vs. Absorbance y = x R² = 1 Regression line and equation absorbance Regression line (absorbance) Series1 Linear (Series1) Calculate the concentration of Zn in the unknown. Solution: y = x x = (0.270) =