Gasometric Determination of NaHCO 3 in a Mixture

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1 Temperature ( o C) 9/28/16 Gasometrc Determnaton of NaHCO 3 n a Mxture apor Pressure (mm Hg) apor Pressure of Water 1 NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g) 2 Ths exercse can be approached at two very dfferent levels. 1. Cookbook: Jump to page 24 of these notes Follow the procedure descrbed n the lab manual. Collect the prescrbed data Substtute the data n the relevant equatons Report the result 2. Explore the underlyng prncples and assumptons Lsten to pre-lab lecture and/or read pre-lab notes Learn how the procedure & calculatons are establshed Derve the relevant equatons - yourself ew the exercse as an opportunty to expand your knowledge about the behavor of gases and ther practcal applcatons. 3 Contents Questons Addressed n the Exercse 5 The Reacton Condtons 17 Objectves, Concepts, Technques 6 Summary of Relevant olumes 18 Overvew of Exercse 7 Gas Mxtures - Partal Pressures 19 Outlne of Proposed Procedure 8 Partal Pressure of Water The Expermental Arrangement 9 Calculaton of n g CO2 and P CO2 21 Intrnsc Lmtatons of Apparatus Revew of Complcatons 23 Constrants Due to the Syrnge 11 Adjusted Fnal Procedure 24 The Reacton - What s n the System 12 Fnal Calculaton Scheme 25 CO 2 Solublty- Henry s Law 13 Sample Calculatons 26 Can we treat CO 2 and Ar as Ideal Gases? 14 Some Notes on the Procedure 29 What about the Product Water? 15 What s on the Web Apparatus Set-up 16 4? QUESTIONS? Can we determne the composton of a mxture from the amount of gas evolved when the mxture undergoes a chemcal reacton? What reacton should we conduct? What prncples can we apply to determne the amount of gas lberated? What addtonal concerns must we consder? What wll we need to measure? What accuracy and precson can we expect n our determnaton? 5 Objectve: Determne the amount of, and from that, the percent NaHCO 3 n a mxture by Gasometry Gasometry: An analytcal technque whch Concepts: depends on measurng an evolved gas. Stochometry Lmtng Reagents Ideal Gas Law Gas Non-dealty Partal Pressure apor Pressure Henry s Law Technques: Capture Gaseous Product Determne System olume Determne Dssolved Gas Apparatus: Gas Syrnge Thermometer [Barometer] Balance Cylnder 6 1

The Exercse s Conceptually Smple The unknowns consst of unform mxtures of sold NaHCO 3 and NaCl contanng between 50-0 NaHCO 3 1. Wegh Sample, w sample 2. Conduct reacton to lberate gas 3.

2 The Exercse s Conceptually Smple The unknowns consst of unform mxtures of sold NaHCO 3 and NaCl contanng between 50-0 NaHCO 3 1. Wegh Sample, w sample 2. Conduct reacton to lberate gas 3. Measure moles of lberated gas 4. Use reacton stochometry to get moles & weght and from that, of NaHCO 3 Our Proposed Procedure & Assumptons 1. Wegh unknown sample What determnes how much we should wegh? Whch balance wll we need to use? Depends on desred precson 2. React unknown wth HCl (aq) a) NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g) b) NaCl(s) Na + (aq) + Cl - (aq) How much HCl shall we use? 3. Capture and measure the volume of lberated CO 2 Wll all of the CO 2 be n the gas phase? What else s n the gas phase? 4. Determne pressure, P and temp, T 7 5. Use Ideal Gas Law, P = n R T, to calculate n CO2 Can CO 2 be consdered deal? What pressure, P, goes n the deal gas law? What s the relevant volume,? 8 The Basc Expermental Arrangement Large (0 mm) Test Tube Small (60mm) Test Tube Gas Syrnge n CO2 = ( )/ RT???? Intrnsc Precson/Accuracy- Apparatus Syrnge: Maxmum capacty s 60 ml Instead of Syrnge can be read to ± 0.5 ml ( 1 ±0.2 precson ml at ~50 ml ) Balance: On whch balance shall we wegh the unknown? Depends on desred precson & how much unknown we wll wegh. Top Loadng Balance can be read to 0.01 g ( at 0.1 g ) Analytcal Balance can be read to g ( 0.1 at 0.1 g ) Barometer: Can be read to 0.1 Torr ( at 1 atm = 760 Torr ) Thermometer: Can be read to 0.2 o C But T (K) = T ( o C) ( 0.8 at 25 o C ) ( 0.07 at 298 K ) HCl NaHCO 3 / NaCl 9 The Syrnge olume measurements have the least precson ~ 1 Other Lmtatons Due To The Syrnge Capacty of syrnge lmts maxmum weght of NaHCO 3 /unknown < 60 ml means < 60/24 = 2.5 mmol CO 2 max at Room Temp and 1 atm That means 2.5 mmol NaHCO 3 max (2.0 mmol s a practcal lmt) max weght of 0 NaHCO 3 = 2.0 X 84 = 168 mg (can wegh up to 336 mg f unknown s 50 NaHCO 3 ) For ~50 ml of CO 2, the weght range of unknown s mg Everyone does a TRIAL RUN (~ 0 mg) to determne weght of unknown requred to produce 40 ± ml of CO 2 Procedure requres unknown to be the lmtng reagent Weght range of mg determnes analytcal balance must be used to wegh unknown f we want ~1 accuracy. Capacty also determnes mnmum amount of 1.0 M HCl requred To nsure that NaHCO 3 s lmtng for any unknown we must add at least 2.0 mmol of HCl. For 1.0 M HCl, ths means 2.0 ml We actually add ml whch s a large excess! < x < 2.00 We need to determne x. To do so, we need z What Substances are n the System? Speces Intal (mmol) Fnal (mmol) Ar (g) w mmol w mmol H 2 O (l) 556 mmol x mmol HCl (aq) mmol x mmol NaHCO 3 (s) x mmol 0 mmol NaCl (s) y mmol 0 mmol NaCl (aq) 0 mmol x + y mmol CO 2 (g) 0 mmol x - z mmol CO 2 (aq) 0 mmol z mmol.0 ml of 1.00 M HCl contans: X 1.0 = mmol HCl.0 ml H 2 O =.0 g H 2 O.0 g =,000 mg / 18.0 mg/mmol = 556 mmol H 2 O NaHCO 3 (s) + H + (aq) + Cl - (aq) Na + (aq) + H 2 O (l) + CO 2 (g) + Cl - (aq) 12 2

How Much CO 2 Dssolves n the HCl (aq)? Henry s Law: for a gven solvent, at a gven temperature, the equlbrum concentraton of a gas n soluton, C x, s proportonal to the p partal pressure of a gas, P x.

2 X -2 mol/l-atm In the typcal lab setup, the total gas volume after the CO 2 s generated, v f s ~ 125 ml. If we generate 2.

2 X -2 * 0.39 = 0.012 M ml of soluton contans 0.012 * = 0.12 mmol of CO 2 whch s 0 * 0.12 / 2 = 6.0 of the CO 2 moles n the gas phase. 13 Can CO 2, Ar and Water be treated as Ideal Gases?

3 How Much CO 2 Dssolves n the HCl (aq)? Henry s Law: for a gven solvent, at a gven temperature, the equlbrum concentraton of a gas n soluton, C x, s proportonal to the p partal pressure of a gas, P x. Henry s Law: C CO2 = K H P CO2 K H s called the Henry s Law constant For CO 2 and water at And, n CO2l = C CO2 HCl = K H P CO2 HCl room temperature, K H = 3.2 X -2 mol/l-atm In the typcal lab setup, the total gas volume after the CO 2 s generated, v f s ~ 125 ml. If we generate 2.0 mmol of CO 2, the partal pressure of CO 2 at Room Temperature wll be: P CO2 = n CO2g RT/ f = 2.0 * * 298/125 ~ 0.39 atm From Henry s Law, the concentraton of CO 2 n the water/hcl s CCO2 = 3.2 X -2 * 0.39 = M ml of soluton contans * = 0.12 mmol of CO 2 whch s 0 * 0.12 / 2 = 6.0 of the CO 2 moles n the gas phase. 13 Can CO 2, Ar and Water be treated as Ideal Gases? We can estmate the devatons from dealty by examnng the van der Waals constants. ( P + n 2 a / 2 ) ( n b ) = n R T At Room Temperature (298 K), the constants are: For: P CO2 ~ 0.4 atm, n CO2 ~ 2.0 mol P AIR ~ 0.6 atm, n AIR ~ 3.3 mol T ~ 298 K ~ ml Producng correctons of: Ideal Gas Approxmaton a L 2 atm-mol -2 b Lmol -1 CO Ar H 2 O n 2 a/ 2 nb atm ml CO X X Ar 9.5 X X Accuracy and Reproducblty Product Water NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g) The reacton produces water. 1 mol NaHCO 3 1 mol H 2 O Stll, consderng pure NaHCO 3, (0 mg NaHCO 3 = 2.0 mmol) We produce at most 2.4 mmol of lqud H 2 O Is ths volume sgnfcant compared to the ~ ml of HCl? 1 drop = 0.05 ml 2.0 mmol X 18 mg/mmol = 36 mg; olume = ml About 1 drop of water s produced ( 0.036/. = 0.36 ) 15 EXTENSION CLAMP INGE The Apparatus More Detal RIGHT ANGLE ELBOW LARGE TEST TUBE SMALL TEST TUBE 16 Reacton Condtons Reacton s conducted n a closed system -no mass n or out mult-component, mult-phase - gas, lqud, sold -ar, H 2 O, HCl, NaHCO 3, NaCl, CO 2 at constant external pressure - atmospherc ( P ~ 1 atm ) at constant temperature - room temperature ( T ~ 25 o C) at changng volume - ncreases from ~ 85 ml to ~ 125 ml What are the varous volumes n the exercse? f We desgnate the gas phase* volume of the entre closed system before & after the reacton. and = TUBE + = TUBE + HCl HCl 17 *We must exclude the volume of the lqud HCl ( ml ) but we can gnore the ntal sold unknown ( ~ 0.1 ml) 18 3

4 Gas Mxtures Partal Pressure Intally: System contans ar & water (HCl) Pressure n system s potentally due to: water (from HCl) P H2O the ar n the system P AIR * P H2O + P AIR = Intal volume of gas s: = TUBE + - HCl After reacton, pressure s due to water (from HCl) P H2O P H2O + P f AIR + P CO2 = the ar n the system P AIR f * CO 2 n gas phase P CO2 Fnal volume of gas s: = TUBE + - HCl * P AIR ncludes the partal pressure of any HCl n the gas phase 19 Table showng vapor pressure of water as a functon of temperature s posted n lab. P H2O s a functon of Temperature What s the Magntude of P H2O? apor Pressure (mm Hg) apor Pressure of Water Temperature ( o C) Over the range o C o C, P H2O ncreases from: 17.5 to 31.8 mm Hg (0.023 to atm) 2.3 to 4.2 for P ~1 atm T, P H2O, n AIR,P AIR H 2 O/HCl (l) Intally, we have = P AIR + P H2O P AIR + P H2O T, P H2O, n AIR,P f AIR, n CO2g, P CO2 n l CO2 H 2 O/HCl (l) Fnally, we have = P f AIR + P H2O + P CO2 = P f AIR + P H2O + P CO2 P CO2 = P AIR P f AIR = n AIR RT (1/v tot 1/v f tot ) But, P AIR = n AIR RT/ = P H2O So, n AIR = ( - P H2O ) / RT and, P CO2 P= f [( - P H2O ) / RT] (1/ 1/ AIR = n AIR RT/ f f ) RT P CO2 = ( - P H2O ) (1 / ) 21 n CO2g P CO2 = ( - P H2O ) (1 / f ) = P CO2 f /RT = ( - P H2O ) (1 / f ) f /RT = ( - P H2O ) ( f ) /RT But, f = f - n CO2g = ( - P H2O ) ( f - ) / RT Equaton 3 We have determned n CO2g. We also need n CO2l. To calculate n CO2l, we use Henry s Law n CO2l = K H P CO2 HCl So, we need P CO2, the partal pressure of CO 2! P CO2 = n CO2g RT / Equaton 5 22 Correctons Revew Assumng P and T do not change durng a run. Affected arable Effect Include? olume of H 2 O Produced HCl ~ 0.5 X olume Change of Sold Unknown ~ 0.1 X Non -Idealty of CO 2 P CO2 ~ 0.01 X apor Pressure of Water P CO2 ~ 3.0 Solublty of CO 2 n CO2 l ~ 6.0 Adjusted Fnal Procedure 1. Measure volume of tube assembly, TUBE 2. Do a test run to determne approprate unknown weght 3. Wegh unknown sample, w sample 4. Measure Temperature and convert to Absolute, T 5. Look up apor Pressure of water n table, P H2O 6. Record Atmospherc Pressure n atm, P 7. Measure Intal Syrnge Readng, 8. Measure volume of HCl accurately, HCl 9. React Unknown wth.0 ml 1.00 M HCl (aq), HCl If we seek accuracy to ~ 1 n the NaHCO Measure Fnal Syrnge Readng, 24 4

5 Our Fnal Calculaton Scheme 1. Calculate approprate weght range of unknown ( / test ) * w test < w sample < (50 / test ) w test 2. Use deal gas law to calculate moles of CO 2 n gas phase n CO2g = ( P P H2O ) ( f ) / RT 3. From deal gas law, Calculate P CO2 P CO2 = n CO2g RT / ( f + TUBE HCl ) 4. Use Henry s Law to calculate moles of CO 2 n lqud phase n l CO2 = P CO2 K H HCl 5. Calculate weght of NaHCO 3 n sample w NaHCO3 = ( n CO2g + n l CO2 ) Calculate NaHCO 3 n unknown NaHCO 3 = 0 * w NaHCO3 / w sample 25 Calculatons Calculated vmeasured fnal Posted -v nt Intal Small Test Tube g Fnal Small Test Tube g Weght of Sample g olume of HCl.0 ml Tube olume, TUBE 0.0 ml Intal Syrnge 5.0 ml Fnal Syrnge 50.7 ml olume of gaseous CO 2, 45.7 ml Pressure, P = 752 mm Hg = atm Temperature, T = 23.3 o C = K P 23.3 o C (from Table) 21.9 mm Hg atm mmol CO 2 (g= (P - P H2O )( )/RT 1.81 mmol mmol CO 2 (lqud) (Henry s Law)??? 0. mmo1 mmol 26 To calculate the Henry s Law correcton, we need the partal pressure of CO 2 & the fnal total gas volume, v f The fnal gas volume s, = = ml P CO2 = n CO2g R T / = ( 1.81 * * 296 ) / 140.7) = atm Henry s Law gves us the CO 2 concentraton: c CO2 = 3.2 X -2 mol/l-atm * atm = 0.0 M whch n.0 ml of water/hcl contans n CO2 l =.0 ml * 0.0 mmol/ml = 0. mmol 27 Calculatons Weght of Sample g olume of gaseous CO ml Pressure, P = 752 mm Hg = atm Temperature, T = 23.0 o C = 296. K P 23 o C (from Table) 21 mm Hg atm mmol CO 2 (gas)=(p - P H2O )( )/RT 1.81 mmol mmol CO 2 (lqud) (Henry s Law) 0. mmol Total CO mmol mmol NaHCO 3 (from stochometry) 1.91 mmol Weght of NaHCO X g NaHCO 3 = 0 X / = Procedure - Notes Everyone should wegh ~ 0 mg = 0.2 g ACCURATELY for ther tral run - Dependng on your sample, you must adjust the weght n subsequent runs to nsure that you get between 35 and 50 ml of CO 2, but not more than 50 ml. ( Calculate the expected volume before dong the run! ) Test that system s ar-tght before usng Set syrnge at 5.0 ml ntally read to ± 0.5 ml remember to subtract ntal volume from fnal volume Use proper unts for calculatons - E.g., P n atm, T n K, R = L-atm/mol-K = ml-atm/mmol-k What s on the Web? Do test run - then up to 4 whch you report. 29 5

If two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9.

If two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9. 9.9 Real Solutons Exhbt Devatons from Raoult s Law If two volatle and mscble lquds are combned to form a soluton, Raoult s law s not obeyed. Use the expermental data n Table 9.3: Physcal Chemstry 00 Pearson