Chemistry 3411 MWF 9:00AM Spring 2009 Physical Chemistry I - Exam #2, Version A (Dated: February 27, 2009) 1 Name: GT-ID: NOTE: Partial Credit will be awarded! However, full credit will be awarded only if the correct answer is in marked boxes, when provided. (Do not write in the small boxes in the right margin; they are for grading purposes only.) Problem Max.Pts Actual Score 1 20 2 20 3 20 TOTAL: 60 You MUST sign the honor pledge: "On my honor, I pledge that I will not give or receive aid in examinations; I will not attempt to gain prior access to examinations; I will not represent the work of another as my own; and I will avoid any activity which will encourage others to violate their own pledge of honor." Your Signature: _ You may find the following information useful: Constant Symbol Value Units Speed of light in vacuum c 2.99792458 E+10 cm sec- 1 Electronic charge e 4.80298 E-I0 esu e 1.60219 E-19 C (Coulombs) Avogadro's number N A 6.02252 E+23 molecules mole- 1 Gas Constant R 8.31447 J K- 1 mole- 1 R 8.31447 E-2 L bar K- 1 mole- 1 R 8.20574 &-2 L atm K- 1 mole- 1 R 6.23637 E+l LTorr K- 1 mole- 1 Boltzmann constant k B 1.38065 E-23 J,K- 1 Electron mass me 5.48597 &-4 amu Proton mass m p 1.00727663 amu Neutron mass m n 1.0086654 amu Planck Constant h 6.626076 E-27 erg sec h 6.626076 &-34 J sec n 1.054573 E-27 erg sec Bohr radius ao 5.29177 E-ll m Atomic mass unit amu 1.66043 E-24 g Electron volt ev 1.60219 E-19 J ev 1.60219 E-12 erg Debye D 3.33564 E-30 em Calorie cal 4.184 J Rydberg Constant R 1.09737 E+5 cm- 1 A sheet of possibly useful formulas is provided at the end.
1. Concept Questions. Try to be concise, and correct! (5 pts) a. How are heat changes at constant temperature relevant to entropy along reversible paths? AND, how are they relevant to entropy changes along nonreversible paths?,,",0>-1 - H"V2.~ \~""t (C",",v,'., 1-.""I""'"'c.~) Aq nz-./ d.s :=.-- G c ~ I\s -to,l'.'\ -r l \ "",,o,-a.. V\Q...n:~.., f-\o~> ~ work ::> dv.> ~ ch,''>rq..j ::::.;> d C\ r t...j ~ d ot. e» ~> d5 ~ :=lcll.rl..ol ~ ~ j" '\ '1.t'\\Q..~ro,.'\~ o:~ CQ"~~o.,,-\ T t C\} \rilj '- C\ -, M:> - I -:::=-::> r::..~ :::. -:::r ~ -:r -- - T _S_:_ (5 pts) b. Does entropy increase, remain the same, or decrease at a phase transition from a liquid to a solid? AND, how does this relate to the change in molecular structure at a phase transition? (5 pts) c. What are the conditions for equilibria and stability for a 2-phase system at constant temperature and volume? EQ.v,L.\~v..\vt-'\. ~ r.,..:= rc L) c..~q...".,:. co..\ ~O~lt.I-..o..\ Is: (5 pts) d. Suppose that dg = -SdT - (Jd1 describes an interface. What other derivative is (Z;) IT related to? Is: clg ::. ;:;) dg... Scl:'\ tr c\ "f 0;:: -56"\ -+ () ci6" l) (%f)o - ~ -(~~JJ 3 Is: I [0
4 2. Gibbs Energy and Gases. SIt> (5 pts) a. What is the molar Gibbs energy relative to its standard value for a perfect gas of 145mg of CO 2 at standard temperature and pressure? MW :::. \')..0\\... 2 \5."~~ ";. 44. 00 ')31",,( "\ :::: 2. ~ 3. \'5 ~ (co '1- ) -'3 14),..\0.5 IAnswer: 0 k) ~o \ ~\ 11_8:_ (5 pts) b. What is the molar Gibbs energy relative to its standard value for a perfect gas of 145mg of CO 2 at 485.0K in a 1.000L container? -\,\ 0 '3 b').. \.. "~""'- ~...0\.. 48'5 '-r-.i 3.'t~,.,,)...0\ ~ 0.00 \ v \. :>00 L 9-\\1'"\. (.~.\'3'.I,~ ) G", -;:: G,...,. -t \,ot;)o o..~""" -0- \.3\'5 j,,~l"'o'... t G~ G"" -; G: r,\ 8."\')1"'C>\ \... ~' ~G ::::G~-G: ~ _gj~~)~ -, 4Q'j.O ~ ~ \" to., 3\ ),. I_A_n_sw_e_r_: -_8_,_'~_~_)_t'o'\D \ -_\ /1_ 8 :
5 (5 pts) c. What is the fugacity of 145mg of CO 2 at 485.0K in a 1.000L container if the gas is treated as perfect? <) f\ ~ 3. 2...,,. \0 ""'0\ -:> Lo.\c v \o..\~j... "or\- ~ 1 ~ 'tt s o : ~ \.000 L ~ (;\\.1 e,.j " ~~ G..\c.~\...\~.---:> oj '3> ~ ~ fy\ f ':. "0--\ b ~~ :;. \ '/- O.\3~ o.~~ 1 f"~o.c.a~,, cet...ff-~e.-l~\ IAnswer: 0.\ 3" o.~ry\ I-,-s_: (5 pts) d. What is the fugacity of 145mg of CO 2 at 485.0K in a 1.000L container if the molar Gibbs energy of the actual gas were to be.935 kj/mol less than the molar Gibbs energy of the corresponding perfect gas?" t _ '-..) GM." G:: ~ O. ~ ~ 5" ~J~ G", " G: ~ ~ ~ \" (+.) \ ~ I \ --..,!~,? 3."'""o\",.. 4g'5~,.,,, (i- f ) - D.9 3 5 'L..,) ""0-0 ::: 0.'" 0.\1"""\ IAnswer: 0."\ ~""""" II S: --------- LJ I
r'\ ~ 3. Coexistence Curves. An unknown one-component system exhibits the followin~ S ~L cp points on the phase diagram: T = 75.6K and P = 37.5kPa at the triple poin~~ () T = 756.0K and P = l101.0kpa at the critical@ and a solid-liquid coexistence point at T = 81.0K and P = 1303.0kP@ f 1, G C )1 (6 pts) a. What is the formula describing the coexistence curve between solid and liquid on a P-T phase diagram? (Make sure to provide values for all coefficients.) f -= f <l + \ ( ~1 \"',,- ~,0",-,ry "I' T? l'- T r~\o,'" 0 " 1 \,~~"":.'la.,,- ~ In,~ rw.""",'.) (VSt If ~ r~ t,\ +C \-;> 6~ @_:::> b:: f H - rt., --- = 8\.0 k - ':1'5. b ~ f>.v T:>L- Tie ::. 1. '3 4 ~(?o. t -\ 130:1.0l..~a. ::. ~'1.y \:~o.'t.-\ g,.o'{ + c. (4 pts) b. Provide an estimate of the melting temperature at standard pressure. "}, 0 t (11) -1'1 3"'lO ')~('q V l 0\.3 ~)"" ~G, ::. \g.'} I 0,,\Cl " (~.0 _------ 1 o _.~I ------- IL--An_sw_er:_1_7_.4_K. II-s:- 6
I Answer: 18: I D 7 (6 pts) c. What is the formula describing the coexistence curve between liquid and gas on a P-T phase diagram? (Make sure to provide values for all coefficients.) l~ (-f) ~ - ~>(~-~) fl- T T" ~ ( V ':>E If> o"-d Cf~) - - - ~, - - l.. - - l ~Ol. 0\, ~CL ) bl-\ \"tf!f') )" 31-'5 ~ fl. I \ \ - - -r Ttl :rrb '( ~") -(,l( -=- _2 84 ~ (t-or 0. -,.;,,~t- ro~~\ ~) (~\~ ckm>t./p) I ~lp4l= I" (3~ 5) - '28~ ~ ( -1: - ~ \<-) ~) l~(?/k~} 1-3~ - 2.g~ ~.~ / - 01"-1 Answer~~f.~ II, 1>13 "'''1' ~ ::. 2-~~" ~ V 1_ 8 : _ (4 pts) d. Provide an estimate of the boiling temperature at standard pressure..j+o,,\d... r d?rq :>~vre...; f -::. \ eli\-"'" :; 10'. 32.)" k p~ '2. ~ ~ 'i. -r -;::. ----- - :::. 103 ~0':1 i... \... (\0\. 3'l.5 )