CHEM 254 EXPERIMENT 9. Chemical Equilibrium-Colorimetric determination of equilibrium constant of a weak acid

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1 CHEM 254 EXPERIMENT 9 Chemical Equilibrium-Colorimetric determination of equilibrium constant of a weak acid For a weak acid that can only partly dissociate the equilibrium constant is related to activities of the products and reactants HA + H2O A - + H3O + K a (HA) = a A.a H3O + a HA The activities can be approximated to concentrations in very dilute solutions. Then, K a (HA) = [A ][H 3 O + ] [HA] [H 3 O + ] = K a[ha] [A ] ph = pk a log ( [HA] [A ] ) = pk a log ( [acid] [base] ) A commonly used method for determining the concentration of hydrogen ion in solution is through the use of indicators-dyes, which undergo a color change at a particular ph. The indicator dyes are weak organic acids or bases for which the protonated (acidic) and unprotonated (basic) forms have different colors indicating that the two forms of the molecule absorb light at different wavelengths. As the indicator concentrations are about 10-5 M, in the presence of more concentrated acids or buffers, the [H3O + ] concentration established can be determined by the ratio [acidic form]/[basic form]. Since acidic and basic forms have different absorption spectra, the ratio of their concentrations can be determined quantitatively by using a colorimeter or a spectrophotometer. Absorption Spectra In the uv- visible region of the electromagnetic spectrum, molecules undergo electronic transitions from the ground state to the excited state. The energy separation between these states, E is E = hv = hc/λ The absorption in the visible range directly affects the color of the chemicals involved. When white light passes through or is reflected by a colored substance, a characteristic portion corresponding to

2 certain wavelengths is absorbed. The remaining light will then assume the complementary color to the wavelength(s) absorbed. This relationship is demonstrated by the color wheel shown in Figure 2. Figure 2. Color wheel A schematic representation of a spectrometer is given in Figure 3. It basically consists of a source of radiation, a diffraction grating or monochromator to separate different wavelengths of light a sample holder with a path length b, and a detector. b Source of radiation monochromator incident radiation I 0 transmitted radiation I detector sample Figure 3. Schematic representation of a spectrophotometer A spectrophotometer measures the change in intensity of incident radiation passing through the sample. Transmittance is T = I/I 0 and related to Absorbance, A is based on transmittance A = log ( I I 0 ) The relationship between the absorption of radiation and the concentration of absorbing species is given by Beer-Lambert Law, (at low concentration limit),

3 A = log ( I I 0 ) = εbc where ε is molar extinction coefficient that is characteristic of the absorbing specie at the wavelength of absorption, b is cell length and c is concentration. If two substances, A and B, absorb light at the same wavelength then observed absorbance is sum of the absorbances of each species. Absorbance = A = A A + A B = (ε Ac A+ ε Bc B)b The acidic and basic forms of indicator methyl orange, HMO + and MO respectively have different colors. The basic form absorbs predominantly in the region nm, and the acidic form absorbs predominantly in the region nm (Figure 4). λ 3 Absorbance λ λ 2 1 MO HMO λ, nm Figure 4. Absorption spectrum of individual MO and HMO + and total absorbance For a solution containing both MO and HMO + absorbance at a given wavelength λ, then is, A = AMO + AHMO = (εmocmo+ εhmochmo)b

4 Purpose: The aim of this experiment is to determine pka of an unknown acid. Apparatus and Chemicals Apparatus: UV-VIS spectrophotometer, volumetric flasks (100 ml) and a few pipettes (5 ml) Chemicals: Methyl orange (1 g /L) Mwt= g.mol -1, 0.10 M HCl, 0.10 M NaOH, 0.1 M unknown weak acid Procedure I. Determination of pk of the indicator 1. Prepare a M HCl (name it as solution 7) b M HCl (name it as solution 8) c M HC (name it as solution 9) d. 1.0 x10-4 M HCl (name it as solution 10) e. 1.0 x10-5 M HCl (name it as solution 11) f M NaOH (name it as solution 12) 2. Take 5 ml methyl orange (MO) from the stock solution (1 g methyl orange /1 L water) and dilute it to 100 ml by adding distilled water. 3. Take 2.5 ml from the dilute methyl orange solution and dilute it to 50 ml by adding the solutions (which were numerated as 7, 8, 9, 10, 11, and 12 by you) that you have already prepared in step 1 of this part; a M HCl (name it as solution 1) b M HCl (name it as solution 2) c M HCl (name it as solution 3) d. 1.0 x10-4 M HCl (name it as solution 4) e. 1.0 x10-5 M HCl (name it as solution 5) f M NaOH (name it as solution 6) Because of different ph values the solution color will be orange to yellow. Calculate the molarity of [MO]0 in each solution C1 to C6.

5 4. Measure the absorbance of each solution at 450 and 510 nm wavelengths (Consult your assistant). 5. Please bear in mind that it is essential to measure the blank solution firstly when you change the wavelength otherwise your measurements will be wrong. II. Determination of K a of a weak acid 1. Prepare 100 ml of M and M unknown acid solutions. 2. Take 2.5 ml methyl orange (C1) from the diluted solution and dilute it with unknown weak acid solutions (0.10, 0.01, and M) to 100 ml. 3. Measure the absorbance of each solution at 450 and 510 nm wavelengths. (Waste container of experiment: aqueous, acid and base waste containers) Treatment of experimental data I. Determination of pk a of an indicator As methyl orange is a weak acid, at any concentration; [MO]0 = [HMO + ]eq + [MO + ]eq You have taken 5 ml [MO] which was 1 g/ 1 L water and you diluted it to 100 ml. From the M = n relationship, calculate the concentration of the indicator in units of Molar V (moles per litre). You need to find the molecular weight of the indicator from literature firstly. Then calculate the concentrations of the indicator after diluting them with the acid solutions. This will be your [MO]0; in other words the final concentration of methyl orange at each solution before getting into equilibrium. A. Determination of molar extinction coefficients of the acidic and basic forms of the indicator 1. i. Calculate the concentrations of the acidic form of the indicator using solution 1 C1 =[MO]0 = [HMO + ]eq as the solution is acidic the indicator is totally in its acid form. [MO + ]eq ~ 0 ii. Calculate the concentrations of the basic form of the indicator prepared in solution 6 C6 =[MO]0 =[MO + ]eq as the solution is basic, the indicator is totally in its basic form CHMO+~ 0

6 2. Calculate the molar extinction coefficients of acidic and basic forms at 450 and 510 nm A450 = εmo,450 x C1 x b A510 = εmo,510 x C1 x b A450 = εhmo,450 x C6 x b A510 = εhmo,510 x C6 x b,where the constant b has the value of 1 cm, and C6 and C1 are equal to each other, which you calculated at the end of the Determination of pka of an indicator part above. B. Determination of [MO] / [HMO + ] ratios at each ph 1. Calculate the concentrations of basic and acidic forms, [MO] and [HMO + ] respectively, for the solutions 2 to 5 in which both acidic and basic forms of the indicator exist. Thus, Ci = [MO]0,i = [MO]i + [HMO]i where i is a positive integer; i = 2, 3, 4 and 5. Example: For solution 3: [MO]0,3 = CMO3 + CHMO3 A 450,3 = (εmo,450 x CMO3+ εhmo,450 x CHMO3) x b A 510,3 = (εmo,510 x CMO3 + εhmo,510 x CHMO3) x b You measured the absorptions of each solution, and you calculated the molar extinction coefficients of acidic and basic forms of the indicator, then your task is to solve both of the equations above with two unknowns. 2. Calculate the ph of the solutions 1 to 6. (take into account dilution upon addition of 2.5 ml MO), use HCl, the strong acid, to calculate the ph (remember that you have used 47,5 ml of acid to dilute the 2.5 ml of indicator) 3. Calculate [MO] / [HMO + ] ratios at each ph (Note that cell length b cancels in the calculations) C. Determination of pk a of the indicator Plot ph versus log [MO]/[MOH + ] and determine pkindicator from the intercept of the line obtained. II. Determination of pk a of an unknown acid 1. Calculate [MO] / [HMO + ] ratios for each solution as described above. You use the molar extinction coefficients of the indicator here as well because the light absorbing part of the solution is the indicator, not the acid. Then from the equations A 450,3 = (εmo,450 x CMO3+ εhmo,450 x CHMO3) x b A 510,3 = (εmo,510 x CMO3 + εhmo,510 x CHMO3) x b

7 find [MO] / [HMO + ] ratios of each solution.. 2. Calculate the ph of each solution using the following relation. ph = pkmo log([mo] / [HMO + ]) 3. Calculate [HA]eq, by using M1 V1 = M2 M2 formula ( you used 47,5 ml of acid to dilute ethe indicator, which changes the conc. of the acid) 4. Calculate Ka of the acid using the concentrations [H3O + ] and [HA] values. HA+ H2O = H3O + + A - Ka = [H3O + ][A - ]/[HA] = x 2 /([HA]0 -x) where x=[h3o + ]=[A - ] 5. Compare the average value with the theoretical Ka, which you should find from the literature (from the internet or some textbook). Discuss source of possible errors. Questions 1. How does light interact with an object that is red in colour such that we perceive the object as being red? 2. What is the relationship between absorbance and concentration? Justify this relationship. 3. What are the limitations of the Beer-Lambert law? 4. Are your results in good agreement with the literature value of Ka of your unknown weak acid? Explain. 5. How does the color of a methyl orange solution relate to its ph? Use your knowledge of the equilibrium reaction of methyl orange to explain how it works as an acid base indicator.

8 DATA SHEET Group Number: Experiment 9-Colorimetric determination of equilibrium constant of a weak acid Date: Assistant name and signature: I. Determination of pk of methyl orange II. Determination of pk a of an unknown acid Solution A 450 A Solution A 450 A