Frst tw letters f yur last name Last ame Frst ame McGll ID Chem 204A, Fall 2004, Md-term (II) Read these nstructns carefully befre yu start tal me: 2 hurs 50 mnutes (6:05 PM 8:55 PM) 1. hs exam has ttal 8 pages. here are 5 sectns, wth ttal 100 pnts. 2. Only the answer shwn n the assgned bxes wll be graded. 3. When nstructed t use specfc cnstants n the questn fr calculatn purpse, fllw that nstructn. 4. Crrect answers must be accmpaned wth the crrect sgn and unt. 5. Frmula/cnstant sheet s gven at the end f the exam (page 8). 6. Yu are nt allwed t use any ther ntes/sheets n ths exam. 7. Yu can OLY use yur wn calculatr. 8. If yu wrte ths exam wth pencl, yu are nt elgble fr any re-grade. 9. Yu must shw all the ntermedate steps n hw yu wr ut the answers t the questns (except fr /F questns) t get yur pnts. 10. Yu are blgated t fllw the rules n McGll s Academc Integrty. Spend a mnute r tw t l ver the whle exam befre yu start, s yu can well plan yur tme. Gd Luc A Page 1 f 8
1. (30 pnts, 2 pnt fr each questn) Are the fllwng statements rue () r False (F)? (fr smethng t be true, t must be always true.) RUE FALSE a). When O 2 at the surface f earth and O 2 at 100 m abve the surface are n equlbrum, µ O ( g), surface] < µ [ O ( g),100 ] [ 2 2 m b). Maxmzng the multplcty f a system whle cnservng the ttal energy leads t the ltzmann dstrbutn. c). A yung cuple s tryng very hard t have a baby grl. After havng three baby bys f ther wn, ther prbablty f gettng a baby grl next tme s [1-(0.5) 3 ]. d). In the prten fldng prcess, the nly entrpy cntrbutn cmes frm the hydrphbc effect. e). Ins n meda f lwer delectrc cnstant wll be mre asscated than n water. f). he delectrc cnstant f water decreases wth ncreasng temperature. g). At cnstant temperature, pressure s the drvng frce fr vlume change. h). When a far dce s rlled twce, the prbablty f gettng a 1 n the frst rll OR a 2 n the secnd rll s (1/36). ). When tw systems f dfferent szes are brught tgether and the energy are allwed t exchange, the fnal equlbrum state wll be the case where bth systems have the same energy. ). At equlbrum, the value f parttn functn at hgher temperature s larger than that at lwer temperature. ). he electrstatc ptental f a charge s ndependent f dstance frm the charge. l). Chemcal ptental s the partal mlar Gbbs free energy. m). Fr an deal slutn f tw substances A and, µ A must be smaller n). ). than µ A. When 10 ml f 3 M sucrse aqueus slutn mxed wth 50 ml f 2 M sucrse aqueus slutn, the ttal fnal vlume s 55 ml. If ne cmpnent f a slutn beys Henry s law, then the ther cmpnent must bey Rault s law. A Page 2 f 8
2. (36 pnts, 6 parts, 6 pnts fr each part) Shrt Answers a). (6 pnts) Calculate <x 2 >, gven the prbablty dstrbutn functn: p(x) x when -a x a, and p(x) 0 therwse. b). (6 pnts) At cnstant temperature, a slutn cntanng 1 mle f mlecule A and 1 mle f mlecule has a cmbned partal pressure f 2.5 atm. When 1 mre mle f A s added t the prevus slutn, the cmbned partal pressure rses t 2.67 atm. Assumng that bth A and bey Rault s law, what s the vapr pressure f a pure slutn f A? c). (6 pnts) acterrhdpsn s respnsble fr lght-sensng n retnal. It has a all-trans frm and a 13-cs frm. he 13-cs frm s 10 J/ml hgher n energy than the alltrans frm. Calculate the rat f mlecules havng the 13-cs frm t the all-trans frm at 300K. A Page 3 f 8
d). (6 pnts) he K n cncentratn nsde a nerve cell s abut 400 mm, whle t s nly 20 mm n the extracellular space (utsde). he electrcal ptental nsde the cell s (80 mv) relatve t the utsde. Calculate the change n chemcal ptental fr transferrng 1 mle f K n ut f the nerve cell at 300K. e). (6 pnts) Calculate the change n entrpy fr mxng the fllwng three gases at cnstant pressure and temperature (300 K) under deal cndtns: 2 mles f hydrgen 5 mles f argn 3 mles f helum f). (6 pnts) Cnsder the fllwng reactns: H crystal A(crystal) H slutn A (g) (g) H slvatn A (aq) (aq) Gven the fllwng thermdynamc data, calculate H crystal f KI. acl ai KCl KI H crystal (J/ml) 787 700 716? H slutn (J/ml) 3.8-5.1 17.1 22.2 A Page 4 f 8
3. (12 pnts) Cnsderng an slated system cntanng 200 blac partcles and 100 whte partcles. Intally, chamber A cntans 100 whte partcles and 150 blac partcles, and chamber has 50 blac partcles. he tw chambers are separated by a parttn that s nly permeable t blac partcles. Each chamber s dvded nt 500 grd bxes, each f whch can tae at mst 1 partcle. Assumng partcles dn t nteract wth each ther, and 1 J/K, and use strg apprxmatn. Calculate the entrpy f A and separately, and then add them up. Yu wll need them n part (3). (1). (5 pnts) Calculate the ttal entrpy f the ntal system (n J/K). (2). (5 pnts) w, cnsder mvng 50 blac partcles frm A t. Calculate the ttal entrpy f the new system (n J/K) t verfy whether ths change ccurs spntaneusly. (3). (2 pnts) What s the chemcal ptental change (n unt f J/mlecule) at 300 K fr S blac partcles n chamber, gven µ. n A Page 5 f 8
4. (12 pnts) Durng a prten unfldng reactn ( Flded Unflded) : A prten s fund t have the fllwng unfldng thermdynamc prpertes: H 300 J/ml, S 1,000 J/ml-K (1). (3 pnts) What s the meltng temperature ( M ) f ths prten? (2). (3 pnts) Replacement f a bured yrsne resdue by a Glycne resdue lwers the meltng temperature t 292 K. Assumng that there s n effect n the entrpy change durng unfldng, what s the enthalpy f unfldng fr the Glycne mutant ( H mut)? (3). (6 pnts) What fractn f the Glycne mutant s unflded at the M f the wld-type prten (frm part 1)? A Page 6 f 8
5. (10 pnts) Streptavdn s a very stable vtamn-bndng prten f mlecular weght Mr 14,000 (14 Da). 56 g f pure streptavdn prten s dsslved n 1 lter f pure water and placed n the left sde f a dalyss apparatus, whle the rght sde cntans pure water. At equlbrum at 300 K, the smtc pressure Π n the left sde s measured t be 2486 Pascals (1 atm 1.01 x 10 5 Pa). Cnsder that streptavdn s O charged durng the measurement. (1). (3 pnts) Usng the defntn f mlarty (M, n ml/l), calculate the mlarty f streptavdn slutn. (2). (5 pnts) Usng the frmula fr smtc pressure t calculate the mlarty f streptavdn slutn at 300 K. (3). (2 pnts) Are the tw values f the mlarty the same? If nt, what s the mst reasnable explanatn? A Page 7 f 8
A Page 8 f 8 Φ > < F Z C R K R S H G dn VdP Sd dg dn dv P du ds e Q Q e p e x x x x n n W p p S W S p eq E E E γ µ µ µ µ 1,, 1) ( 3 2 1 1 2 2 1 Cnstants: R 8.314 J/ml-K0.082 atm-l/ml-k F 96500 J/V-ml 1.38 x 10-23 J/K 1 cal 4.184 J electrc charge 1.6 x 10-19 C 1 atm 760 trr 1.01 x 10 5 Pa 1 atm-l 101 J K b (water) 0.51 K-g/ml K f (water) 1.86 K-g/ml 1 atm 1.01 x 10 5 g/m-s 2