Physical Chemistry I for Biochemists. Lecture 2 (1/12/11) Yoshitaka Ishii. Gas Ch. 1 Non-Ideal Gas (Ch 1 & Raff p21-41) Announcement

Transcription

1 Physical Cheistry I for Biocheists Che340 Lecture (1/1/11) Yoshitaka Ishii Gas Ch. 1 No-Ideal Gas (Ch 1 & Raff p1-41) Aouceet HW 1 is due et Wedesday before the class (Fid HW1 at the web site) Attedace poits - Up to 15 poits for correctly aswerig a questio i the class - 1 poit/ aswer; liit oe per class - Effective today - Please clai the poit after the class Free Ecel/Google apps workshops at ACCC (registratio eeded!) 1

2 Correctio of Hoework (p1.30 i tet p13) P i = P i0 ep(-m i g/rt) P i = P i0 ep(-m i gz/rt) If you fid ay correctios eeded i your hoework, please let e kow it. Quiz A = 1 c h A colu of Hg (desity:d of g/l) of i height (h) yields a pressure of P o the base. What is P i Pa uits? Force fro Hg o 1 c of area = d (g/l) (h (c) 1 c ) g (/s ) = g/l c 1c 981/s 9.81 = (g c c )/(L s ) = (kg 10-3 )/(s ) = 10 kg/s P(Pa)= Force o 1 of area / =1.00? 10 5 Pa

3 Ideal Gas Eq. usig olar desity PV = RT P, T, : Itesive variable (variables that does ot deped o the size of the syste), V: Etesive variable (those that deped o the size) P = RT This depeds o oly three itesive variable. Is called olar desity 3

4 Isothers, isobars, isochores Isother: T = costat PV/ = cost Isobar: P =cost V/T = cost Isochore (or isovoluetric): V = cost P/T = cost P (Pa a) 40 T icrease /V (1/3) Hoework questio 5. Plot P (i bar) for a varied V (0.05 < V 10L)f 1.0 for oe ole of fideal gas at ttt = 80, 304 K, ad 500 K. Isother Display 3 graphs i oe figure usig Ecel or other software to draw graphs. Preset the equatios you used to draw the graphs ad eplai how you geerated each equatio. Use bar for the pressure uit. 4

5 Saple questio o isotheral process ) P (Pa) /V (1/3) Q1. The 4 lies shows isotheral plot represetig 1/V depedece of P for the sae ideal gas at T = 00K, 300K, 400K, 500K. Which graph shows that for 500 K? Q. Predict how ay oles of gas eists? Saple questio o isobaric plots V (^3) Series1 Series Series3 Series4 Isobaric plot of V vs T T (K) The plot shows plots for isobaric processes at P =, 4, 6, 8 Pa. Which plot idicate that for Pa? V = (R/P)T So the slope is greater whe P is saller. 5

6 A Mied Ideal Gas & Partial Pressure For a iture of ideal gasses, the partial pressure for olecule i is give by P i = i RT/V, where i deotes # of oles for the gas olecule i. The overall pressure of the ied gas is P = P i i = P i /P = i / is called olar fractio, where = i Saple Questio Here is a cotaier havig air that cosists of 1.0 ole of O ad 4.0 oles of N. Assuig the air pressure is 1.0 at at 300K, what is the pressure of O? What is the size of the cotaier at 300K? P O = 1.0/( )*1.0at = 0.0 at 6

7 No-ideal Gas Two assuptios for the ideal gas (1) No iteractios betwee gas olecules () The gas olecule ca be treated as a poit ass (o volue is cosidered) The assuptio is correct whe gas desity is low. (roughly speakig P < 10 bar ad T > 100K) Hoework Proble Q1.5) Paraeter a i the va der Waals equatio is greater for H O tha for He. What does this say about the for of the potetial fuctio i Figure 1.7 for the two gases? This eas that the depth of the attractive potetial is greater for H O tha for He. P RT V b V a P RT V 7

8 Isotheral P-V Plots for Real Gas (Eperiet for CO ) Liquid CO 50 C Codesatio fro gas to liquid below Tc 40 C 31.4 C (Tc) 0 C 0 C T c : Critical teperature Above Tc, G L trasitio is ot possible X deotes iflectio poit i isother (dp/dv = 0, d P/dV =0) P & V at this poit are aed P c ad V c. Raff (p1-41) No-ideal Gas: two types of iteractios r > r trasitio Po otetial Eergy r V < r < r trasitio r < r V V(r) < 0 V(r) > 0 8

9 Correlatio betwee T c ad Meltig Poit (T ) Higher T eas olecular iteractios strogly stabilizes the liquid syste T c ~ T but Why? How useful is a copressed gas? CO gas at just above the critical teperature ad pressure is kow to behave as super-critical fluid, which is useful, for eaple, for etractio of caffeie fro coffee. E. High desity as liquid offers efficiet etractio; Highly diffusible as gas; Easy to reove; (Not toic) 9

10 va der Waals Equatio of State RT P V b V a b: fiite size of 1 ol of the olecules a: attractive force costat P RT V b a V V V / 10

11 P (bar) How Does the Ter b Chage the Isother Plot P-V? Ne Ar ideal gas (b =0) No-ideal gas (b=0.03) No-dieal gas (b= ) P RT V b V (L) b Ne = Meaig of b RT a P V b V V RT P a / V b li( V P ) li P P RT a / V b b b is the iiu possible volue of the gas 11

12 P (bar) va der Waals Equatio for CO a = L bar ol - b = Lol P (bar) (ideal gas at 300K) 600 RT a P (CO) at 90K P 500 V b P (CO) 304.3K V P (CO) 315K P (CO) 350K V (Lol-1) P (bar) va der Waals Equatio for CO Well reproduces the eperietal curves above T c! 140 P (bar) (ideal gas at 300K) 10 P (CO) at 90K 100 P (CO) 304.3K 80 P (CO) 315K 60 P (CO) 350K Mawell costructio reproduces G-L trasitio V (Lol-1) Critical tep obtaied fro dp/dv = 0 ad d P/dV =0 1

13 Isotheral P-V Plots for Real Gas (CO ) 50 C Tc: Critical teperature Liquid CO Codesatio fro gas to liquid below Tc 40 C 31.4 C (Tc) 0 C 0 C X deotes iflectio poit i isother (dp/dv = 0, d P/dV =0) P & V at this poit are aed Pc ad Vc. Raff (p1-41) The eaig of a? a defies attractive force betwee gas olecules If a is high, eltig poit is also high. 13

14 14 Mawell Recostructio Correct the oscillatory behavior of vdw eq. to reproduce a trasitio fro gas to liquid Soe ath 1 ) / ( ) / ( a a ) ( ) / (

15 Calculate T c fro Va der Waals Eq. RT P V b a 6 4 V VC V C At Tc, the followig relatioships are epected. P V RT V c b a 3 V P RT 6 a c 3 4 V b V RT V b b C 3 C 6a RT V V a V C 4 C C b V 3 V c = 3b, T c = 8a/(7bR), P c = a/7b P V c c 3 RT / 8 c C Calculated critical costats Eperietal Tc (K) Ar K CO K Ne 44.4 K 15

16 Saple questio If you copare the desity of gas at critical poit, with that t of a ideal gas, which h oe has a lower desity? What is the ratio of the desities of the gas i the two states (ideal gas state ad gas at the critical state) at the sae teperature ad pressure? V 3 RT / 8P c c c V RT / P _ ideal VdW Eq for Reduced Paraeters Whe P R P/P c,v R V /V c, T R =T/T C 8T R 3 PR ( V 1/ 3) V 3 R R 16

17 Suary: va der Waals Equatio of State RT a RT a P V b V V b V V/ >> b, (a) 1/ The Equatio approaches the ideal gas eq. 1. va der Waals Eq. takes ito accout of attractive forces ad volue of gas olecules. Behavior aroud the critical teperature ca be well reproduced. Other Equatios of State 17

18 Virial Epasio 1 C ( T ) C3( T ) C( T ) RT V V V V P 3 P Redlich-Kwog RT a V b TV ( V b) a = R T c.5 /p c b = RT c /p c Boltza Distributio Populatio at eergy level j: p( j ) A ep( E / kt j ) E E 1 A N 1 / ep( E j / kt ) j 1 18