Determination of ionic product constant of water (K w ) Handout 2016

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Roland Fisher
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1 Determination of ionic rouct constant of ater (K ) Hanout 016 Determination of ionic rouct constant of ater (K ) by hyrogen electroe 1) Task In this exeriment e use an electrochemical cell consisting of a hyrogen electroe an a saturate calomel electroe to fin the ionic rouct constant of ater (K ) at room temerature. We set u hyrogen electroes using NaOH solutions of ifferent concentrations to measure the electromotive force ith a igital voltmeter ith very high internal resistance. The electromotive force gives the cell reaction otential ith goo aroximation if the liqui junction otential (iffusion otential) is eliminate by the Bjerrum-metho. Once the cell reaction otential an the electroe reaction otential of calomel electroe are knon, the electroe reaction otential of the investigate hyrogen electroes may be foun. In terms of Nernst-equation, the activity of hyrogen ion can be obtaine an K can be calculate either numerically or grahically. ) Theoretical backgroun In this hanout the most relate knolege of the exeriment are summerize. The basic electrochemical efinitions can be foun in the hanout of Measurement of the electromotive force of an electrochemical cell exeriment..1) Ionic rouct constant of ater The chemically ure ater is usually not hanle as electrolyte, but there is a issociation so calle autorotolysis: H O H O OH (1) Here one of the ater molecules act as aci the other as basis. The equilibrium constant ( K ) for the self issociation can be ritten as: K a a =, () + H3O OH aho here a + is the activity of the oxonium ions, a is the activity of the hyroxie ions, a H 3 O OH H O is the activity of the ater molecules. From the equilibrium constant the ionic rouct constant of ater (K ) can be erive as: K (3) = K ah O = a + a OH H3O K an a O are constant at a given temerature K is also constant. H For examle in a NaOH solution having a given concentration the ionic rouct constant of ater can be aroximate ith the folloing: c = + γ, (4) NaOH K a H O ±,NaOH 3 0 c

2 here c is the concentration of the NaOH solution, c 0 = 1 mol/m 3. Base on the Debye-Hückel la the logarithm of the mean activity coefficient ( γ ± ) in the mol/m 3 interval can be escribe ith the 1/ 0.509c lgγ = (5) 1/ -3/ 1/ 1mol m c ± equation. Strictly the constant refers to 5 o C..) The use galvanic cell For the etermination of the ionic rouct constant of ater e assemble the folloing cell: Hg(l) Hg Cl, KCl(aq.) c KCl..1) The calomel electroe Salt brige (KCl-solution) H saturate NaOH solution Pt(s) (C.1.) In the calomel electroe mercury is in contact ith the saturate solution of its oorly soluble salt (calomel, Hg Cl ). It is an electroe of the secon kin, often use as reference electroe. The electroe reaction is: Hg Cl (s) + e Hg(l) + Cl (aq.) (6) The electroe reaction otential ( ε ) can be ritten as: r, HgCl/Hg RT εr, Hg - Cl/Hg = ε o r, HgCl/Hg ln a (7) Cl F o here ε is the stanar electroe reaction of the calomel electroe, R is the universal gas r, Hg Cl /Hg constant, T is the temerature, F is the Faraay constant. The otential of the calomel electroe (see equation (7)) eens on the chlorie ion concentration of the electrolyte solution. In the ractice usually saturate solution of KCl is use. In this case the electroe reaction otential of the calomel electroe ε o 5 C 0.40 V. r,hg Cl /Hg =..) The hyrogen electroe The hyrogen electroe contains inert metal (e.g. latinum) immerse into H saturate, hyrogen ion containing solution. It is an electroe of the first kin, a gas electroe. Since the half reactions in a hyrogen electroe in aci (8) or neutral/alkaline (9) solution are: H + (aq) + e 0.5 H (8) H O + e 0.5 H + OH (9) therefore the electroe reaction otential of the hyrogen electroe can be exresse in aci (10) or neutral/alkaline (11) solution by the folloing Nernst-tye equations:

3 RT RT H ε + = lna + ln r,h /H H F F (10) o RT RT H ε = ε ln a ln r,h O/H,OH r,h O/H,OH OH F F (11) Inasmuch as the value of the above to equations is equal, an ith relation (3), it easily erives that the stanar electroe reaction otential in alkaline solution (at unit value of hyroxie ion activity) is etermine by the K as follos: here o RT ε = ln K r, H O/H,OH, (1) F H is the artial ressure of hyrogen gas, = Pa..3) Reucing the liqui junction otential ith Bjerrum metho The interosition beteen the to solutions of a concentrate solution of some salt briges hose cation an anion mobility (e.g. saturate KCl solution) are almost equal effectively reuces the magnitue of the iffusion otential. N. Bjerrum (196) roose an extraolation metho to estimate the iffusion otential. The Fig.1 shos the rincile of Bjerrum metho. Fig.1 Elimination rincile of iffusion otential by Bjerrum extraolation metho. E, E are the measure electromotive force using half saturate then fully saturate KCl salt brige. 1/sat sat E is the estimate electromotive force. Bjerrum assume that such a high resiual iffusion otential still remains using first a half saturate KCl brige solution ith hich the measure electroe otential changes using sequentially a saturate KCl solution for interosition. From Fig.1 it can be seen that the ecte electromotive force.4) Calculation methos of K.4.1) Numerical calculation E can be calculate by the equation (13): E sat 1/sat E E = (13) Use your measure electromotive force results to calculate the ecte E by eq. (13). These voltage values are aroximately eliminate from the iffusion otential an can be consiere as the cell reaction otential of the investigate hyrogen-calomel electrochemical cell. The cell 3

4 reaction otential is the ifference of the right an the left electroe reaction otentials, therefore the electroe reaction otential of the hyrogen electroe can be calculate from the folloing equation: ε E + (14) + = cell + ε r, H /H r,hg Cl,Hg E ε r,hg Cl,Hg knoing that the electroe reaction otential of a saturate calomel electroe is at 5 o C. Neglecting the slight temerature eenence of r, HgCl, Hg ε r, HgCl, Hg = 0.40 V ε an assuming that the actual hyrogen ressure slightly eviates from the stanar value, the ressure eenence term on the right of equation (11) tens to be zero. Therefore the activity of the hyrogen ions can be calculate as: ( E +ε r,hg Cl,Hg ) F ln RT + = 10 (15) 10 ah Imortant note! The activity of the hyrogen ions eens on the temerature! Finally, calculate the ionic rouct constant of ater for every NaOH concentration base on the equation (4)..4.) Grahical evaluation Dra the calculate electroe reaction otentials of hyrogen electroe (eq.(14)) as a function of the natural logarithm of the calculate mean ionic activity of NaOH solutions (eq.(5)). (The logarithm of the mean activity coefficient of the NaOH can be calculate from equation (5). The rouct of the mean activity coefficient an the exact solution concentration gives the mean activity of the hyroxi ions.) In eq.(11) the ressure term is zero, so the intercet of the least-squares fit to a straight line obviously gives the stanar electroe reaction otential. From the intercet value (eq. 1), the K can be etermine. 3) Exerimental roceure 3.1) Aaratus On bench to the latinise Pt electroe of cylinrical shae an the saturate calomel electroe are sulie. The construction of the hyrogen electroe an the galvanic cell can be seen in Fig.. 4

5 3.) Solution rearation Fig. Electrochemical cell for the etermination of the ionic rouct constant of ater The saturate KCl solution as ell as the 0.5 M NaOH stock-solution is sulie. The range of NaOH concentrations are given in Table 1. The teacher selects the solution series to be measure. The ecte electromotive force ata for the most ilute solutions are given, these are not to be measure, but use this ata for the calculation. The first to concentrations in each column are reare ith a burette. The folloing to solutions are reare using a iette (use ball!) of 10 ml ith a 10 times ilution of esoning ilute solution. Practical orer of rearation: n, 4 th (ut this to the cell an uring saturation reare the others) 1 st, 3 r. Rea the temerature an rite to your lab reort! The exact concentration of the NaOH stock solution of about 0.5 M shoul be etermine once a eek by aci-base titration using NaOH solution as titrant the eighte amount of oxalic aci ilute in an Erlenmeyer flask as analyte, an henolhthalein inicator. Write the factor to the atasheet at the measuring lace too! II. set C NaOH /(mol/m 3 ) I. set C NaOH /(mol/m 3 ) III. set C NaOH /(mol/m 3 ) E = V E = V E = V Table. 1 Concentration series reare ith ilution from 0.5 M NaOH stock solution 5

6 3.3) Stes of the measurement Maniulation ith the hyrogen gas valve is alloe to the instructor only or uner his suervision! Hanling of the gas ressure regulator is not alloe for the stuents! 1. Take the latinum from the electroe vessel! Take care for the cleanness of the latinize latinum surface, o not ut on anything an o not soil it!. Start the measurement ith the solution of loest concentration. Before filling, rinse the cell, its stocock an the Pt electroe once ith the test solution. It is obviously imortant that the sie-arm of the cell is fille ithout air-bubbles. During the otential measurement the stocock is to be close. Do not use grease at the stocock not to block the ionic migration! 3. Preare the salt brige solutions by iluting about 10 cm 3 saturate KCl ith 10 cm 3 x istille ater. 4. Put the latinum to the solution in the electroe vessel. At least one half of the latinum late of the hyrogen electroe must be immerse in the measure solution. Use ouble gas bubbler at the gas inlet to the electroe vessel, an connect a simle gas bubbler at the outlet to exclue air from the electroe. Fill some istille ater into the bubblers. 5. Immerse the sie arm of the hyrogen electroe an the saturate electroe into a baker containing half saturate KCl solution. 6. Connect the electroes to the OP11/1 voltmeter of high internal resistance (10 1 Ohm) as instructe by the teacher. The reference electroe cable has to be connecte to the R terminal, hile that of hyrogen electroe to the G terminal. So that the olarity islaye refers to the hyrogen electroe. 7. Ask the teacher to check the set u, an to set the hyrogen flo. The hyrogen gas no bubbles gently through the measure solution. To saturate the solution ith the hyrogen takes about 10 minutes. Wear safety glasses uring the exeriment ith gas! 8. Rea the electromotive force from the islay of otentiometer hen its value is stable ithin 0. mv an recor it in your lab reort. 9. Measure the electromotive force using both saturate an half saturate KCl salt brige. 10. Reeat the eterminations ith the other more concentrate solutions. Before filling, thoroughly rinse the cell, electroe an stocock ith a little ortion of the ne solution (rinsing ith ater is not necessary). 11. After having finishe the measurement by the hel of the teacher close the gas ith the neele valves! 6

7 13. All use glassare shoul be ashe ith x istille ater. Put back the calomel electroe to its container. Rinse the latinum late ith x istille ater an ut back to the x istille ater fille electroe-vessel. Do not fill the sie arm, ut filtering aer into the stocock! 4) Data evaluation Calculate the activity of the hyrogen ions base on the equation (15) an estimate the mean activity coefficient base on the Debye-Hückel theory (equation (5)) an using these values give the ionic rouct constant of ater for all NaOH solutions! Otional task is the ata evaluation by grahical metho (chater.4.). 5) Results The measure electromotive forces an calculate hysical quantities shoul be liste in a table. the laboratory temerature the factor of NaOH stock solution The mean value of the K an the stanar error for 95% confience limits of the stuent s t- istribution. Otional: Dra the grah of the ε versus ln a relation ith the measure ata oints r, H O/H,OH an fit a straight line. Give the fitte arameters of this line an calculate the K value from the intercet. Determine the stanar error for 95% confience limits of the stuent s t-istribution. Homeork: Calculate the mass of C H O 4 H O in grams necessary to get an about 0 ml enoint volume of titrant. M ( ) = 16.07g/mol COOH HO OH 7

The extreme case of the anisothermal calorimeter when there is no heat exchange is the adiabatic calorimeter.

The extreme case of the anisothermal calorimeter when there is no heat exchange is the adiabatic calorimeter. .4. Determination of the enthaly of solution of anhydrous and hydrous sodium acetate by anisothermal calorimeter, and the enthaly of melting of ice by isothermal heat flow calorimeter Theoretical background