1 pKa of 2,4-Dinitrophenol Please Note: Read an MSDS for 2,4-dinitrophenol and understand the hazards and safety precautions necessary to safely work with the compound for doing any lab work. I. Introduction Thermodynamic equilibrium constants (Kth) for the weak acids and bases are very important in most areas of chemistry and are especially important in thermodynamics. In this experiment the thermodynamic equilibrium constant for the weak, monoprotic acid, 2,4 dinitrophenol (2,4 DNP) will be determined. The reason the term, thermodynamic equilibrium constant, is used is due to the fact that activities will be used rather than concentrations in the calculations. Weak acid equilibrium constants are dependent on the solvent, the temperature and the ionic strength of the solution. In this experiment the solvent will be water, the temperature will be 25.00°C and the ionic strength will be 0.05. II. Theory Consider the weak, monoprotic acid HB. The ionization equilibrium for this acid in aqueous solution would be: 23HA H O A H O−+++U (1) The ordinary equilibrium constant (Kc) for this reaction would be: ()()()3ccA cHOKcHA−+= (2) where the concentrations are given as molarities. Equation 2 assumes that the solutions are ideal. If the non-ideal behavior of the ions is taken into account, ion activities (a) must be used in place of concentrations. When the equilibrium constant (Kc) is written in terms of activities, it is called a thermodynamic equilibrium constant (Ka). For eq. 1, Ka is defined by equation 3. ()()()3aaA aHOKaHA−+= (3) where the activities also have units of molarity.2 Equation 4 defines the relationship between concentration and activity. Their ratio is called the activity coefficient (γ). iiiac=γ or iiiacγ= (4) For ideal solutions, γ = 1; therefore, c = a. Solutions containing ions are not ideal; therefore, γ ≠ 1. For equation 3, the following relationships apply. ()()()333aHO HO cHO+++=γ (5) ()()()aA A cA−−−=γ (6) ()()()aHA HAcHA=γ (7) For ease of notation, let γ+ = γ(H3O+) and γ– = γ(A– ). Since solutions of just positive or just negative ions cannot be made, γ+ and γ- cannot be measured separately. For this reason, an average activity coefficient (γ±) is usually used. For 1:1 electrolytes, such as monoprotic acids: 2±+−γ=γγ (8) For dilute aqueous solutions at 25°C, γ± can be calculated from the Debye-Huckel limiting equation. log 0.5091 Z Z I±+−γ=− (9) where: Z+ = charge on cation, Z– = charge on anion and I = ionic strength of the solution 2iii1IcZ2=∑ (10) where i is the index used to sum of all of the ionic species in the solution. For this experiment pKa will be determined, where aapK log K=− (11) Combining equations 3 and 11 yields: ()()()a3aApK log a H O logaHA−+⎡⎤⎢⎥=− −⎢⎥⎣⎦ (12)3 Since pH = -log a(H3O+), equation 12 can be written to give: ()()aaApK pH logaHA−⎡⎤⎢⎥=−⎢⎥⎣⎦ (13) Combining equation 13 with equations 6 and 7 produces: ()()()()aHAAcApK pH logHA c HA−−−⎡⎤γ⎢⎥=−γ⎢⎥⎣⎦ (14) Very little error is introduced by making the approximations that γHA = l and log γ± = log γ–. Combining these approximations with equations 9 and 14 gives equation 15 which will be our working equation. ()()acApK pH 0.5091 Z Z I logcHA−+−⎡⎤⎢⎥=+ −⎢⎥⎣⎦ (15) Equation 15 can be used to determine the pKth for any weak, monoprotic acid. All that is needed is a good pH meter and some way to determine the c(A– )/c(HA) ratio. The method used to determine the c(A– )/c(HA) ratio will depend on the chemical and physical properties of HA and A– . In this experiment we will use the significantly different UV-visible absorption spectra of the A– (2,4 dinitrophenolate ion) and HA (2,4 dinitrophenol) species to determine their equilibrium concentration ratio in aqueous solution. When the absorption peaks of A– and HA are sufficiently separated, as in the example below, then Beer's law can be used to determine the c(A– )/c(HA) ratio. AbsorbanceWavele ngthAcidBase4 III. Beer's law One of the fundamental laws concerning the absorption of light by matter in solution is known as Beer's law. It can be written: A = kc (16) where A = absorption, k = Beer's law constant and c = concentration of the light absorbing species. The Beer’s law constant can be determined from the slope of a linear fit for absorbance/concentration data. The value of k depends on the thickness of the sample, the particular absorbing species and on the wavelength of light being absorbed. For a solution containing a single absorbing species, for example, either only A– or only HA, the Beer's Law equation would be: A(A– ,λ) = k(A– ,λ) × c(A– ) (17) or A(HA,λ) = k(HA,λ) × c(HA) (18) If the concentrations of A– and HA are moderately low, the absorption (At) of a mixture of A– and HA at wavelength (λ1) will be the sum of their individual absorptions. At (λ1) = A(A– ,λ1) + A(HA,λ1) (19) Combining Equations 17, 18, and 19 gives: At (λ1) = k(A– ,λ1) × c(B-) + k(HA,λ1) × c(HA) (20) Equation 20 contains the unknowns c(A-) and c(HA). Assuming that At, , k(A-,λ1) and k(HA,λ1) is known; the equation still has two unknowns. The necessary second equation can be generated by measuring At, on the same mixture of HA and A- at a different wavelength (λ2) . This measurement will give the needed second equation. At (λ2) = k(A– ,λ2) × c(A-) + k(HA,λ2) × c(HA) (21) Equations 20 and 21 can then be solved simultaneously to yield c(A– ) and c(HA). This method requires you to pick λ1 and λ2 and then to determine k(A– ,λ1), k(HA,λ1), k(A– ,λ2) and k(HA,λ2) using Beer's law. Once these values are determined, the c(A– )/c(HA) ratio can be determined.5 IV. General Procedure and Questions Please note: Development of a more detailed procedure for this experiment is expected. 1. Make five solutions of different concentrations which contain only the HA form. 2. Make five solutions of different concentrations which contain only the A– form. 3. Scan the most concentrated HA solution (scan from 200 nm to