RATE LAWS AND STOICHIOMETRY (3) Marcel Lacroix Université de Sherbrooke
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1 RE LWS D SOIHIOMERY (3 Marcel Lacroix Uniersité de Sherbrooke
2 RE LWS D SOIHIOMERY: RELIOSHIS EWEE j D HUS R, WE HE SEE H I IS OSSILE O SIZE IDEL REORS I HE RE EQUIO IS KOW S UIO O OERSIO,i.e., r g( M. Lacroix Rate Laws and Stoichiometry 2
3 RELIOSHIS EWEE j D : OJEIE r g( I GEERL, IS O ILLE. ISED, r IS ERESSED I ERMS O HE OERIO O HE REIG SEIES: r f,,... ( HE OJEIE HERE IS O WRIE HE OERIO O HE RE SEIES j I ERMS O HE OERSIO, i.e., j hj ( SO S O ULIMELY RELE r O WHIH IS LL H IS EEDED O ELUE HE DESIG EQUIOS. M. Lacroix Rate Laws and Stoichiometry 3
4 SI DEIIIOS OR HEMIL REIOS: SUMMRY HOMOGEEOUS REIO: IOLES OE HSE. HEEROGEEOUS REIO: IOLES MORE H OE HSE D USULLY OURS OR ERY ER HE IERE EWEE HE HSES. IRREERSILE REIO: I ROEEDS I OLY OE DIREIO D OIUES I H DIREIO UIL HE RES RE EHUSED. REERSILE REIO: I ROEED I EIHER DIREIO, DEEDIG O HE OERIO O RES D RODUS RELIE O HE ORRESODIG EQUILIRIUM OERIO. M. Lacroix Rate Laws and Stoichiometry 4
5 HE REIO RE OS I HE HEMIL REIOS OSIDERED I HE RESE OURSE, WE KE S HE SIS O LULIO SEIES, WHIH IS OE O HE RES H IS DISERIG S RESUL O HE REIO. r HE RE O DISERE O,, DEEDS O EMERURE D OMOSIIO: r k ( f (,,... r HE LGERI EQUIO H RELES O HE SEIES OERIO IS LLED HE KIEI ERESSIO OR HE RE LW. HE SEII REIO RE (OR OS k I HE RE LW IS LMOS LWYS SROGLY DEEDE O EMERURE (I GS-HSE REIOS, I DEEDS O HE LYS; I LIQUID SYSEMS, I DEED O HE OL RESSURE. M. Lacroix Rate Laws and Stoichiometry 5
6 HE SEII REIO RE: EMERURE DEEDEE HE RRHEIUS EQUIO HS EE ERIIED EMIRILLY O GIE HE EMERURE EHIOR O MOS REIO RE OSS WIHI EERIMEL URY OER ILY LRGE EMERURE RGES: k ( exp( E / R HE LRGER HE IIO EERGY E, HE MORE EMERURE-SESIIE IS HE RE O REIO k 13 1 : OS(ex: 1 s E: IIO EERGY (J/mole OR cal/mole(ex: E 3kJ / mole : EMERURE (K R: GS OS (8.314 ka litre J cal mole K mole K mole K M. Lacroix Rate Laws and Stoichiometry 6
7 HE SEII REIO RE: DEERMIIO O HE IIO EERGY HE IIO EERGY IS DEERMIED EERIMELLY Y RRYIG OU HE REIO SEERL DIERE EMERURES. OR EMLE, ROM HE D k(s (K ln(k,295,3,35,31,315,32, y x + 38,925 WE ID: E R kj / mole; ln( s 16 1 ; 1/ M. Lacroix Rate Laws and Stoichiometry 7
8 SOIHIOMERI LE OW H WE HE SHOW H HE RE LW E ERESSED S UIO O OERIOS, i.e., r f (,,... WE EED OLY ERESS OERIO S UIO O OERSIO j hj ( I ORDER O RRY OU LULIOS SIMILR O HOSE RESEED I HE REIOUS LEURES O SIZE REORS. I HE RE LW DEEDS O MORE H OE SEIES, WE MUS RELE HE OERIOS O HE DIERE SEIES O EH OHER. HIS RELIOSHI IS ESLIHED WIH HE ID O SOIHIOMERI LE. HIS LE RESES HE SOIHIOMERI RELIOSHIS EWEE REIG MOLEULES OR SIGLE REIO, i.e., I ELLS US HOW MY MOLEULES O OE SEIES WILL E ORMED DURIG HEMIL REIO WHE GIE UMER O MOLEULES O OHER SEIES DISERS. M. Lacroix Rate Laws and Stoichiometry 8
9 SOIHIOMERI LE HE RELIOSHIS WILL E DEELOED OR HE REIO a + b c + dd I ORDER O U EERYHIG O SIS O ER MOLE O, WE SHLL KE SEIES S HE SIS O LULIO: b c + + a a WE SEE H OR EERY MOLE O H IS OSUMED, c/a MOLES O ER. I OHER WORDS, SIMILR RELIOSHIS RE DEELOED OR HE OHER SEIES. S RESUL, HE RELIE RES O REIO RE RELED Y r a r r b c ( r a r c M. Lacroix Rate Laws and Stoichiometry 9 r d D d a D
10 SOIHIOMERY OR H SYSEMS HERE WE OSIDER H HE REIO OLUME DOES O RY S HE REIO ROGRESSES. MOS H D LIQUID-HSE D SOME GS-HSE SYSEMS LL I HIS EGORY. IME t, HE REOR IS OEED D UMER O MOLES O SEIES,,, D D I (,,, D, I RE LED IO HE REOR. SEIES IS OUR SIS O LULIO. ER ( MOLES O HE REED, ( MOLES O REMI I HE SYSEM. M. Lacroix Rate Laws and Stoichiometry 1
11 SOIHIOMERY OR H SYSEMS O DEERMIE HE UMER O MOLES O EH SEIES REMIIG ER MOLES O HE REED, WE ORM HE SOIHIOMERI LE: M. Lacroix Rate Laws and Stoichiometry 11
12 SOIHIOMERY OR H SYSEMS: SEIES MOLES O IIILLY RESE I HE REOR; MOLES O RE OSUMED S RESUL O HEMIL REIO; MOLES O REMIIG I HE REOR ER OERSIO. M. Lacroix Rate Laws and Stoichiometry 12
13 SOIHIOMERY OR H SYSEMS: SEIES MOLES O IIILLY RESE I HE REOR; MOLES O H HE REED; OR EERY MOLE O H RES, b/a MOLES O MUS RE; HEREORE HE UMER O MOLES O H HE REED IS ( moles reacted moles reacted ( moles reacted ( moles reacted b ( a ( b / a MOLES O REMIIG I HE REOR ER OERSIO. M. Lacroix Rate Laws and Stoichiometry 13
14 SOIHIOMERY OR H SYSEMS: LL SEIES HE IRESE I HE OL UMER O MOLES ER MOLE O REED IS d c b δ + 1 a a a HE OL UMER O MOLES REMIIG ER OERSIO IS + δ M. Lacroix Rate Laws and Stoichiometry 14
15 SOIHIOMERY OR H SYSEMS: SOIHIOMERY OR H SYSEMS: OERIOS OERIOS WHERE (1 a b a b / ( ( / ( θ a c a c / ( ( / ( + + θ a d a d D D D D / ( ( / ( + + θ OERIO O IS HE UMER O MOLES O ER UI OLUME D RE DISERIG D D RE ERIG J J J J y y θ M. Lacroix Rate Laws and Stoichiometry 15
16 SOIHIOMERY OR H SYSEMS: OERIOS OR OS OLUME I HE REIG SYSEM UDERGOES O HGE I OLUME S HE REIO ROGRESSES,. I GS-HSE H SYSEMS, HE REOR IS SELED OS-OLUME ESSEL. I GS-HSE ISOHERML D ISORI REIO, HE UMER O MOLES O RODU EQULS HE UMER O MOLES O RE (E: O + H O O H 2 OR LIQUID-HSE REIOS KIG LE I SOLUIO, HE SOLE USULLY DOMIES HE SIUIO. S RESUL, HGES I HE DESIY O HE SOLUE DO O E HE OERLL DESIY O HE SOLUIO SIGIILY D HEREORE I IS ESSEILLY OS-OLUME REIO ROESS. M. Lacroix Rate Laws and Stoichiometry 16
17 SOIHIOMERY OR H SYSEMS: OERIOS OR OS OLUME (1 (1 ( θ ( b / a ( θ ( b / a ( θ ( c / a + ( θ ( d / a D D + M. Lacroix Rate Laws and Stoichiometry 17
18 EMLE o. 1: ERESSIG j h j ( OR LIQUID-HSE REIO SO OSISS O HE SODIUM D OSSIUM SLS O RIOUS Y IDS SUH S OLEI, SERI, LMII, D MYRISI IDS. HE SOIIIO OR HE ORMIO O SO ROM QUEOUS USI SOD D GLYERYL SERE IS: 3aOH ( aq + ( + OH 17 H35OO 33H5 317H35OOa 3H5( 3 LEIG RERESE HE OERSIO O SODIUM HYDROIDE (HE MOLES O SODIUM HYDROIDE REED ER MOLE O SODIUM HYDROIDE IIILLY RESE, SE U SOIHIOMERI LE ERESSIG HE OERIO O EH SEIES I ERMS O IS IIIL OERIO D HE OERSIO. M. Lacroix Rate Laws and Stoichiometry 18
19 SOIHIOMERY OR LOW SYSEMS HERE, WE RELE HE UMER O MOLES (moles Y HE MOLR LOW RE (moles/time OE: WE OSIDER HERE H HE REIO OLUME DOES O RY S HE REIO ROGRESSES. MOS LIQUID- HSE D SOME GS-HSE SYSEMS LL I HIS EGORY. EMLE: WER-GS SHI REIO I OL GSIIIO: O + H + 2O O2 H 2 M. Lacroix Rate Laws and Stoichiometry 19
20 SOIHIOMERY OR LOW SYSEMS M. Lacroix Rate Laws and Stoichiometry 2
21 SOIHIOMERY OR LOW SYSEMS: SOIHIOMERY OR LOW SYSEMS: OERIOS OERIOS OR LOW SYSEM, HE OERIO GIE OI E DEERMIED ROM HE MOLR LOW RE D HE OLUMERI LOW RE H OI: HE OERIOS O,, D D RE: ( ( / ( / ( liters moles time liters time moles ; / ( a b ; (1 ; / ( a d D D D + ; / ( a c + M. Lacroix Rate Laws and Stoichiometry 21
22 SOIHIOMERY OR LOW SYSEMS: SOIHIOMERY OR LOW SYSEMS: OERIOS OR LIQUIDS OERIOS OR LIQUIDS E. WIH (1 (1 / ( ( / ( a b a b θ y y θ M. Lacroix Rate Laws and Stoichiometry 22
23 SOIHIOMERY: OLUME HGE WIH REIO I HE REIOUS DISUSSIOS, WE OSIDERED RIMRILY SYSEMS I WHIH HE REIO OLUME OR OLUMERI LOW RE DID O RY S HE REIO ROGRESSED. MOS H D LIQUID-HSE D SOME GS-HSE SYSEMS LL IO HIS EGORY. HERE RE OHER SYSEMS I WHIH EIHER OR RY S HE REIO ROGRESSES. EMLE O RYIG LOW RE : SYHESIS O MMOI: GS-HSE REIO H DOES O HE EQUL UMER O RODU D RE MOLES 2 + H H 3 EMLE O RYIG H REOR OLUME : IERL OMUSIO EGIE. M. Lacroix Rate Laws and Stoichiometry 23
24 SOIHIOMERY: OLUME HGE WIH REIO IDIIDUL OERIOS E DEERMIED Y ERESSIG HE OLUME OR H SYSEM (OR OLUMERI LOW RE OR LOW SYSEM S UIO O OERSIO USIG HE EQUIO O SE: D RE DEIED S EORE; IS HE EMERURE (K, IS HE OL RESSURE (atm D R IS HE GS OS (.826 dm 3 atm/mole K. IME t, WHE HE REIO IS IIIED, IME t, HE OLUME IS HE R R M. Lacroix Rate Laws and Stoichiometry 24
25 SOIHIOMERY: OLUME HGE WIH REIO WE OW W O ERESS HE OLUME S UIO O OERSIO. RELLIG HE EQUIO OR HE OL UMER O MOLES, + δ,we GE: y 1+ δ 1+ δy WHERE IS HE MOLE RIO O IIILLY RESE. I LL HE SEIES I HE GEERLIZED REIO RE I HE GS HSE, ε WE DEIE S HE HGE I OL UMER O MOLES OR OMLEE OERSIO OER OL UMER O MOLES ED O HE REOR: ε ( d / a + c / a b / a 1 yδ M. Lacroix Rate Laws and Stoichiometry 25 δ d / a + c / a b / a 1
26 SOIHIOMERY: OLUME HGE WIH REIO SOIHIOMERY: OLUME HGE WIH REIO HEREORE, IME t, HE OLUME O GS OR H SYSEM EOMES: Y LOGY, OR RILE-LOW SYSEM, HE OL OERIO Y OI I HE REOR IS: HE ERE O HE REOR, KIG HE RIO O HE OE ERESSIOS YIELDS: (1 ε + R R (1 ε + M. Lacroix Rate Laws and Stoichiometry 26
27 OLUME HGE WIH REIO: OERIO OLUME HGE WIH REIO: OERIO WE OW ERES HE OERIO O SEIES j OR LOW SYSEM I ERMS O OERSIO: SUSIUIG HE ERESSIOS OR j D ROM HE REIOUS SOIHIOMERI LE D RERRGIG, WE OI: WHERE IS HE SOIHIOMERI OEIIE, WHIH IS EGIE OR RES D OSIIE OR RODUS. HE OERIOS I RILE-OLUME GS LOW SYSEM RE ROIDED I HE OLLOWIG LE. j j j j j j j j 1 ( + + ε ν θ ν j M. Lacroix Rate Laws and Stoichiometry 27
28 SOIHIOMERI LE: OLUME HGE WIH REIO M. Lacroix Rate Laws and Stoichiometry 28
29 Rate Laws and Stoichiometry 29
30 EMLE o. 2: DEERMIIG j h j ( OR GS-HSE REIO MIURE O 28% SO 2 D 72% IR IS HRGED O LOW REOR I WHIH SO 2 IS OIDIZED: 2SO SO 2 + O2 2 IRS, SE U SOIHIOMERI LE USIG HE SYMOLS θ j, j D HE ELUE UMERILLY HE OERIO O HE RES, RODU, D IER S UIO O OERSIO OR HE SE WHE HE OL RESSURE IS 1485 ka D HE EMERURE IS OS 5K. 3 M. Lacroix Rate Laws and Stoichiometry 3
31 DEERMIIG j h j ( OR GS-HSE REIO: RESULS,25 (mole/dm**3,2,15,1,5 SO2 O2 SO3 2,2,4,6,8 1 OERSIO ( M. Lacroix Rate Laws and Stoichiometry 31
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