Determination of ionic product constant of water (K w ) Handout 2014

Transcription

1 Determinatin f inic rduct cnstant f water (K w ) andut 2014 Determinatin f inic rduct cnstant f water (Kw) frm equilibrium tential measurement f a hydrgen electrde Overview In this exeriment we use an electrchemical cell cnsisting f a hydrgen electrde and a saturated calmel electrde t find the inic rduct cnstant f water (Kw) at rm temerature. We set u five hydrgen electrdes using NaO slutins f different cncentratins t measure the electrmtive frce with a digital vltmeter with very high internal resistance. The electrmtive frce is the equilibrium tential f a articular hydrgen electrde relative t the saturated calmel electrde. KCl slutin salt bridges are alied t lwering the liquid junctin tential (diffusin tential) by the Bjerrum-methd. Once the cell reactin tential and the electrde reactin tential f calmel electrde are knwn, the electrde reactin tential f the investigated hydrgen electrdes may be fund. In terms f Nernst-equatin, the activity f hydrgen in can be btained. Knwledge f Debye-ückel thery is required fr calculatin f the mean inic activity f the NaO slutins. Thus the value f Kw can be calculated either numerically r grahically due t the rer frm f the Nernst equatin. Fr bth methds the cnfidence interval f the mean value shuld be determined. 1. Backgrund (i) Definitins By definitin, the inic rduct cnstant f water is K w = a + a O (1) In a NaO slutin, the charges n sitive and negative ins balance. S, it is nly ssible t determine the mean inic activity cefficient ± f the electrlyte slutin. ence, the mean inic activity f the NaO slutin can be exressed as a ± = γ ± c c (2) where c is the mlar cncentratin f the NaO slutin, c = 1 ml/dm 3. Accrding t the cmleted Debye-ückel law (which is valid u t 0.1 ml/dm 3 cncentratin) the mean inic activity cefficient f NaO slutin can be calculated as fllws: lgγ ± = c 1 2 1ml 1 2 dm c 1 2 (3)

2 Strictly the cnstant refers t 25 C. (ii) ydrgen electrde tentials Nernst equatins Since the half reactins in a hydrgen electrde in acid r neutral/alkaline slutin are + (aq) + e (4) r 2 O + e O - (5) therefre the electrde reactin tential f the hydrgen electrde can be exressed by the fllwing Nernst equatins: ln a F ln 2F 2 / 2 (6) r ln a F ln 2F 2 O / O 2O / 2, O O 2 2, (7) Inasmuch as the value f the abve tw equatins is equal, and with relatin (1), it easily derives that the standard electrde reactin tential in alkaline slutin (at unit value f hydrxide in activity) is determined by the Kw as fllws F ln K /, w 2O 2 O (8) R, T and F have the usual meanings, 2 is the artial ressure f hydrgen gas, = Pa. (iii) Reducing the liquid junctin tential with Bjerrum methd The intersitin between the tw slutins f a cncentrated slutin f sme salt bridges whse catin and anin mbility (e.g. saturated KCl slutin) are almst equal effectively reduces the magnitude f the diffusin tential. N. Bjerrum (1926) rsed an extralatin methd t estimate the diffusin tential. The Fig.1 shws the rincile f Bjerrum methd. 2

3 Fig.1 Eliminatin rincile f diffusin tential by Bjerrum extralatin methd. ES/2, ES are the measured electrmtive frce using half saturated then fully saturated KCl salt bridge. EMF is the estimated electrmtive frce. Bjerrum assumed that such a high residual diffusin tential still remains using first a half saturated KCl bridge slutin with which the measured electrde tential changes using sequentially a saturated KCl slutin fr intersitin. Frm Fig.1 it can be seen that the crrected electrmtive frce EMF can be calculated by the equatin (9): EMF = 2ES ES/2 (9) 2. Calculatin methds f Kw (i) numerical calculatin Use yur measured electrmtive frce results t calculate the crrected EMF by eq. (9). These vltage values are arximately eliminated frm the diffusin tential and can be cnsidered as the cell reactin tential f the investigated hydrgen-calmel electrchemical cell. The electrde reactin tential f the hydrgen electrde (eq (6)) can be calculated frm the fllwing equatin ε + / 2 = E MF + ε cal (10) knwing that the electrde reactin tential f a saturated calmel electrde is cal = V at 25 C. ere, we neglect the slight temerature deendence f cal. Assuming that the actual hydrgen ressure slightly deviates frm the standard value, the ressure deendence term n the right f equatin (6) tends t be zer. Therefre the a + can be calculated as: a + = 10 (E MF +ε cal ) F (11) 3

4 Imrtant nte! Observe and write dwn in the lg-bk the actual temerature in the lab. In all tential relatins used fr calculatin this actual temerature value shuld be used. Finally, ne can calculate the inic rduct cnstant f water fr every NaO cncentratin as fllws: K w = a + γ ± c c (12) (ii) grahical evaluatin Draw the calculated electrde reactin tentials f hydrgen electrde (eq.(10)) as a functin f the natural lgarithm f the calculated mean inic activity f NaO slutins (eq.(3)). In eq.(10) the ressure term is zer, s the intercet f the least-squares fit t a straight line bviusly gives the standard electrde reactin tential (eq. 8). Frm the intercet value, the Kw can be determined. 3. Aaratus On bench t the latinised Pt electrde f cylindrical shae and the saturated calmel electrde are sulied. The cnstructin f the hydrgen electrde and the galvanic cell can be seen in Fig. 2. Fig. 2 Scheme f the galvanic cell with hydrgen electrde and calmel reference electrde. A saturated r half-saturated KCl bridge slutin is used t cnnect half cells. The bx reresents a vltmeter f high internal resistance. Prir t inlet and after utlet the 2 gas is cnducted thrugh gas bubblers filled with distilled water. A digital vltmeter f Ohm internal resistance (tye f OP211/1 -meter) will serve t measure the cell EMF. 4. Prcedure The saturated KCl slutin as well as the 0.5 M NaO stck-slutin are als sulied. The range f NaO cncentratins and instructins fr rearatin are given in the enclsed Table 1. 4

5 All necessary glassware, burettes, iettes, measuring flasks f 100 ml vlume are sulied fr rearatin f the diluted NaO slutins, and fr titratin f a weighted amunt f xalic acid by the stck slutin with henlhthalein indicatr (titratin shuld be made nce f a week). 1.The first ste is t reare the necessary NaO dilutins as the teacher has instructed. Start the measurement with the slutin f lwest cncentratin. Befre filling, rinse the cell, its stcck and the Pt electrde nce with the test slutin. It is bviusly imrtant that the side-arm f the cell be filled withut air-bubbles. If yu gently at the tube f an en stcck abve a sink, then slutin the running ut will carry the air-bubbles away. Afterwards, during the tential measurement, the stcck is t be lsely clsed. 2. Preare the salt bridge slutins! Fill 40 ml saturated KCl slutin int a beakers. Fill 20 ml sat. KCl t a secnd beaker with similar diameter as the revius ne, and add 20 ml distilled water int it t make a half saturated slutin. 3. In setting u the cell, take care with hydrgen gas, use duble gas bubbler at the gas inlet t the electrde vessel, and cnnect a simle gas bubbler at the utlet t exclude air frm the electrde. Fill sme distilled water int the bubblers. It is bviusly essential that the liquid levels bth in the salt bridge and in the hydrgen electrde vessel are arximately the same s that n sihning ccurs int the test slutin. The saturatin f the slutin with hydrgen takes minutes. 4. Meanwhile cnnect the OP211/1 -meter f high internal resistance as instructed by the teacher. The reference electrde cable has t be cnnected t the R terminal, while that f hydrgen electrde t the G terminal. S that the larity dislayed refers t the hydrgen electrde. Find the true cell electrmtive frce by taking readings every 2 minutes fr at least minutes until the drift is less than 2 mv/min. 5. Nte the temerature f the cell. 6. Reeat the determinatins with the ther mre cncentrated slutins. Befre filling, thrughly rinse the cell, electrde and stcck with a little rtin f the new slutin (rinsing with water is nt necessary). 7. After having finished the measurement, all used glassware shuld be washed with distilled water. 4. T be rerted : 1. The measured and calculated hysical quantities shuld be listed in a table. Dente the crrectin factr f NaO stck slutin, and the lab temerature. 5

6 2. The mean value f the Kw and the standard errr fr 95% cnfidence limits f the student s t- distributin. 3. Draw the grah f the ε 2 O 2,O versus ln a O relatin with the measured data ints and fit a straight line. Give the fitted arameters f this line and calculate the Kw value frm the intercet. Determine the standard errr fr 95% cnfidence limits f the student s t-distributin. Table. 1 Cncentratin series reared with dilutin frm 0.5 M NaO stck slutin The lab-teacher dictates the slutin series t be measured I. set CNaO/M II. set CNaO/M III. set CNaO/M , , , , EMF V V V The first tw cncentratins in each clumn are reared with a burette. The fllwing tw slutins are reared with a 10 times dilutin f crresnding diluted slutin ured t the measuring flask f 100 ml with a iette f 10 ml. The last mst diluted slutin (grey-shaded) is nt t be reared, because its equilibrium tential wuld is rvided by the teacher. Titratin: The exact cncentratin f the NaO stck slutin f abut 0.5 M shuld be determined by acid-base titratin using NaO slutin as titrant, the weighted amunt f xalic acid diluted in an Erlenmeyer flask as analyte, and a henlhthalein indicatr. mewrk: Calculate the mass f C22O422O in grams necessary t get an abut 20 ml endint vlume f titrant. MC22O422O = g/ml. Prelab questins 1. What tye f galvanic cell shuld be set u fr determinatin f water in rduct cnstant? Write dwn the cell diagram and give the name f the electrdes, resectively! 6

7 2. What kind f instrument is suitable t measure the electrmtive frce f a galvanic cell? Is a lw r very high internal resistance f this instrument is needed t ensure an accurate electrmtive frce measurement? 3. What srt f salt bridge slutins are used fr lwering the liquid junctin tential f the electrdes and why? 4. What kind f reference electrde is used fr Kw determinatin and in what arrangement is it t be cnnected t the hydrgen electrde? Write dwn the half cell reactin! 5. w many cncentratins f NaO slutin and in what cncentratin range are used in the hydrgen electrde fr Kw determinatin? 6. w is the Bjerrum-methd is used t minimize the diffusin (liquid junctin) tential? 7. Deict determinatin f the cncentratin f the NaO stck slutin (methd, materials, and aaratus)! 8. w are the hydrgen in activity and the mean inic activity cefficient f NaO slutins determined: frm thery r frm tential measurement? 9. w much internal resistance shuld a digital -meter (vltmeter) have fr an accurate equilibrium tential measurement? 10. Draw hw a simle gas bubbler fits int a hydrgen electrde cell at the gas inlet and utlet, resectively, in rder t exclude air frm the electrde! 11. What tyes f electrdes and electrlytes are used fr Kw determinatin? Write dwn the halfcell reactins! 12. The DVM f tye OP 211/1 has tw inuts fr cnnectin f a galvanic cell: R (fr reference electrde) and G (fr glass electrde r ther articular investigated electrde). w are the electrdes f Kw galvanic cell t be cnnected t them, and hw is the cell larity dislayed then? 13. Why is the KCl slutin suitable fr lwering the liquid junctin tential? At what cncentratin des it give rise t the lwest liquid junctin tential? 14. What hysical quantity can be measured directly with a digital -meter f OP 211/1? Laura Sziráki 7