EXPERIMENT 5 MOLAR CONDUCTIVITIES OF AQUEOUS ELECTROLYTES

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Kelley Stevenson
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1 EXPERIMENT 5 MOLR CONDUCTIVITIES OF QUEOUS ELECTROLYTES Objective: To determine the conductivity of various acid and the dissociation constant, K for acetic acid a Theory. Eectrica conductivity in soutions n eectric current in soution is the resut of the net movement of free ions in a specific direction. The current may be determined by measuring the resistance R between two simiar inert eectrodes immersed in the soution, as in the figure beow where the ova region represents the soution; represents the eectrode area and is the norma distance between the eectrode panes. In actua practice an.c. current with a ow frequency of the order of approximatey 000 Hertz is used (to prevent eectroysis) in the measurement, and the components representing the resistance R in the compex impedance Z for the circuit is determined. We wi aways refer to this component (the rea portion of the compex impedance) for what foows. The resistance is aso dependent on the frequency (Debye-Fakenhagen effect). The theory and measurement here concentrates on ow frequency measurements where the Onsager equation is meaningfu. The fuy automated measuring apparatus has been configured for ow frequency measurement in accordance with the theory of eectroytes. Eectrod e =Distance between eectrode = rea of eectrode Figure of conductivity circuit ccording to Ohm s aw, the resistance R (unit Ohm, symbo Ω ) for the above circuit is given by R = ρ () where ρ is the resistivity of the soution. The ce constant refers to but there is no need to refer to this quantity here. The eectrica conductivity of the soution κ is defined as κ = where the current density, j, is given by j = κ Ε. The conductance ρ 6

2 of the soution, L, is defined as L = and has units Siemen, where = S ( R Ω Siemen). On the other hand, from (), has the units (S.I) [S][M - ]. This is the quantity that the conductivity apparatus measures. Normay, (such as the ones currenty used in the aboratory), the units of κ = is ms cm S cm ρ S m -. Because the conductivity is dependent on the concentration of the eectroytes, Kohrausch defined the moar conductivity, Λ m, so that comparisons can be made at any concentration as foows κ Λ Λ m = = ; κ = (2) c c R where c is the concentration of the eectroyte concerned. Ceary, Λm has S.I. units S m 2 mo -. Normay Λ m drops in vaue as the concentration of the eectroyte increases. This observation can be expained by the Debye-Hucke theory where an ionic atmosphere of opposite charge to the ion is formed which retards the motion of the ion by inducing a force in the opposite direction to the motion of the ion. This dynamic asymmetry effect (aso a reaxation effect) reduces the vaue of the moar conductivity compared to that when c 0( 0 ) by a factor of form B Λο c ; there is another effect caed the eectrophoretic effect which refers to the retardation due to the movement of sovent moecues dragged by the ion and the ionic atmosphere and this effect has the form c separate effects has the form for univaent ions. Thus the tota effect due to the two 2 Λ = Λο + BΛο c + c = Λο _ βc (3) for any one sovent at any one temperature for a univaent system. If the conductivity of the soution is Λ (c.g.s) = x ms cm - as given in most readouts, and the concentration is c mo dm -3 (as is the case is most machine readouts), then the moar conductivity in S.I. units wi be Λ = c x x0-4 S m 2 mo -. We recommend that you pot the vaues using c.g.s units. Potting Λ vs c inearizes the curve and determines Λ ο as the intercept and -β as the gradient for strong eectroytes that are essentiay fuy dissociated at a concentrations. This pot does not work we for weak eectroytes because the steep gradient in the vicinity of ow concentrations does not yied accurate vaues of the intercept. This is what wi be discovered in the course of the experimentation according to the procedure beow. The steep sopes are due to the constant dissociation of the eectroyte. For such cases, the foowing aw is required..2 Kohrausch s Law This aw states that the moar conductivity at infinite diution Λ ο for an ionic sat is the sum of the moar conductivities at infinite diution of its separate ions + _ λο, λο signs referring to charge, i.e.,, the + ο _ Λο = λ + λο. (4) 7

3 Note that at infinite diution, even weak eectroytes are fuy dissociated and cannot be distinguished from strong eectroytes..3 Diution Effects of Weak Eectroytes For any one temperature and concentration, the degree of dissociation α impies the foowing for a weak eectroyte such as acetic acid Hc, where the weak acid has the foowing equiibrium reative to its tota concentration, c. Reaction: Hc(aq) + H 2 O H + + c - (aq) (aq) Cons.: (-α)c αc αc (5) From the above equiibrium (5), ignoring activity coefficients, the acid dissociation constant K is given by a K a + [H ][c = [Hc] _ 2 ] α c = a (6) where, according to rrhenius, α is given as α = Λ m Λ ο (7) for a concentrations (and α, when Λm Λ ο ). The norma procedure is to measure Λ m and do the above extrapoation to determine Λ ο for some reated strong sat of the above acid and then to use the Kohrausch aw to determine Λ ο for this acid, rather than to do a direct extrapoation, which is used ony for strong eectroytes. In this experiment, you wi determine Λ for the reated sats CH 3 COONa, HC and NaC and then use some inear subtractions to yied CH 3 COOH. 2 Experimenta procedure 2. Variation of moar conductivities with different eectroytes ο Λ ο for n aready caibrated machine is avaiabe, which consists of a rod-ike eectrode connected by an eectrica ead to a box housing the read-out dispay and the eectronics. Pease ensure that you NEVER use the eectrode as a stirrer. Instead, pease agitate or shake the beaker in which the test soution is paced; the eectrode must remain vertica and stationary at a times, camped to its stand. Eectrodes are very expensive and damage to them must be minimized. The reading for the conductivity is the one for the test soutions K s ess the conductivity of distied H 2 O used for the preparation of the soutions. (sk the technician for sampes of HO 2 distied water used for the preparation), so that ( M s H ) / c. Normay, 2O M HO 2 is not significant and may be negected, but check to be sure and decide for yoursef. You wi be briefed on the usage of the device. The range of measurement is approximatey ms. 8

4 (i) Prepare the foowing soutions with the indicated concentrations by using the 00m voumetric fasks and the 5, 0, 25 and 50 m pipettes (either bub or graduated pipettes). In each case ()-(4) beow, the first vaue in the series is the stock soution, and the rest are prepared from it by successive diution. Normay 00 m is sufficient for each soution voume, but your situation may differ. () 0., 0.05, 0.025, 0.0 mo L - for NaC, (2) 0., 0.05, 0.025, 0.0, mo L - for CH 3 COONa, (3) 0.02, 0.0, 0.005, , 0.00 mo L - for HC, and (4) 0., 0.05, 0.025, 0.0, 0.005, mo L - for CH 3 COOH. (ii) Measure the conductivity of each of the soutions at east three (3) times, and take the average vaue and determine the mean temperature of your soutions for which the conductivities appy. Tabuate the soution concentration c, c /2, the conductivity and the moar conductivity for each of the preparations using the tabe (a) -(d) on the handout sheets provided. (iii) Draw a graph Λ m vs. c /2 for each of the eectroytes using your experimenta data and determine Λ ο (using (3)) by extrapoating to c = 0 for each of the eectroytes and compare the vaues of Λ ο derived from experiment to the ones from iterature (tabe 2). The method fais for one of the eectroytes. Identify the eectrode and why? 2.2 Determination of the degree of dissociation index α of acetic acid (iv) (v) From the determinations in (iii) above, use Kohrausch s aw to determine the degree of dissociation index, α for acetic acid. For each of the concentrations given in (i) (4), cacuate the required constant; α may be determined from (7) with the experimenta vaues of Λ m and Λ ο for each eectroyte. K a is determined from α which was derived previousy and (6), where the concentration of the acid is known (sk technician on duty). Since these measurements are at constant temperature, the K a vaues shoud not vary much and the average gives an indication of the absoute vaue. Compare the iterature vaue of K a =.8 x 0-5 (mo dm -3 ) at 298.5K with your own. Record your cacuation into tabe 3. K a 3 Discussion. Reative to your error bounds, are the vaues for Λ ο and these experiments cose to the iterature vaues? K a derived from 2. The degree of dissociation is given by α = Λm /Λο. Why is this expression not very accurate? How can it be corrected so that it becomes exact? [Hint: refer to the Onsager equation] 4 References 9

5 . Barrow, G. M. (996). Physica Chemistry, 6 th edn. McGraw-Hi. 2. Moore, W. J. (972). Physica Chemistry, 5 th edn. Longmans. 3. Levine, I.N. (2002). Physica Chemistry, 5 th edn. McGraw-Hi. Pagiarism Warning! Some of these experiments are carried out in groups of usuay a pair of students. Therefore expectedy, each member of a group foowed an identica procedure in the aboratory and has the same set of raw data. Members of a group are aowed to discuss the anaysis of data with one another. However, preparation of the report incuding data anaysis, interpretation and discussion must be prepared by the individua student submitting the report. The Department does not toerate pagiarized report! nb: Pease quote experimenta error estimates for a your data presented. 20

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