Physics 400 Fall 2011 Problem Set 7

Due Thursday Nov 17 1159 pm

1 Diffusion

In this chapter we began with counting arguments One of the ways we will use counting arguments is in thinking about diffusive trajectories Consider eight particles four are black and four are white Four particles can fit left of a permeable membrane and four can fit right of the membrane Imagine that due to random motion of the particles every arrangement of the eight particles is equally likely Some possible arrangements are BBBB-WWWW BBBW-BWWW WBWB-WBWB the membrane position is denoted by -

(a) How many different arrangements are there

(b) Calculate the probability of having all four black particles on the left of the permeable membrane What is the probability of having one white particle and three black particles on the left of the membrane Finally calculate the probability that two white and two black particles are left of the membrane Compare these three probabilities Which arrangement is most likely

(c) Imagine that in one time instant a random particle from the left-hand side exchanges places with a random particle on the right-hand side Starting with three black particles and one white particle on the left of the membrane compute the probability that after one time instant there are four black particles on the left What is the probability that there are two black and two white particles on the left after that same time instant Which is the more likely scenario of the two

2 Elasticity of polymers

The thermodynamic identity for a one-dimensional system is

TdS dU Jdl (1)

where J is the external force exerted on the line and dl is the extension of the line (The direction of the force is opposite to the conventional direction of the pressure)

(a) Find an expression relating J to a derivative of the entropy

(b) Now consider a freely-jointed chain of N links each of length p with each link equally likely to be directed to the right and to the left How many arrangements give a headshyto-tail length of l = 2lslp You can write the result in terms of sand N

(c) Write the entropy of the chain as a function of l for lsi ltt N Your result should be of the form S(l) = Cl + c2l2 where q are constants

(d) Calculate the force at extension l

1

Youll see that the force is proportional to temperature The force arises because the polymer wants to curl up entropy is higher in a random coil than in an uncoiled configuration Wanning rubber makes it contract

3 Carbon monoxide poisoning

In carbon monoxide poisoning the CO replaces oxygen adsorbed on hemoglobin (Hb) molecules in the blood To show the effect consider a model for which each adsorption site on a heme may be vacant occupied by oxygen with energy fA or occupied by CO with energy fB Let N fixed heme sites be in equilibrium with oxygen and CO in the gas phases at concentrations such that the absolute activities are = 1 X 10-5 for oxygen and = 1 X 10-5 for CO

(a) Assuming the presence of oxygen alone evaluate fA such that 90 of the Hb sites are occupied by oxygen Express the answer in eV per oxygen molecule

(b) Now admit CO under the specified conditions Find fB such that only 10 of the Hb sites are occupied by oxygen What fraction is occupied by CO What fraction is unoccupied

4 Nordlund 149

5 Nordlund 1411

6 Nordlund 1416

2

P~~1 ofZ- LIJ1 twAch ~ lef

IJ

= (I( ]) (q gt 3) )( tf arJ r~

7n~~Ii~ of bAcL ~c4 I~ 11gtt I ~ldL Z

~I e I IJ

vJ v A rra ~4 (11] (laquo~) ( Itl 3) ~t ~ l ~( 70

1u+ I f F5 ~ VJ B Lv 8gt tJ

R ww 3 flt ~ I hteampJ~I amprW 8 f3 tJ ~ LHSmiddot ~ tNt- b 01shy

4J 3gt gLV ~~JP IN ampWB () lYl SvoL Fnht t)

so -bJ f~~ r b~ ~

1- acf J lr ~- --7tgt 70 ~sf II -L~ s~~

Youll see that the force is proportional to temperature The force arises because the polymer wants to curl up entropy is higher in a random coil than in an uncoiled configuration Wanning rubber makes it contract

3 Carbon monoxide poisoning

In carbon monoxide poisoning the CO replaces oxygen adsorbed on hemoglobin (Hb) molecules in the blood To show the effect consider a model for which each adsorption site on a heme may be vacant occupied by oxygen with energy fA or occupied by CO with energy fB Let N fixed heme sites be in equilibrium with oxygen and CO in the gas phases at concentrations such that the absolute activities are = 1 X 10-5 for oxygen and = 1 X 10-5 for CO

(a) Assuming the presence of oxygen alone evaluate fA such that 90 of the Hb sites are occupied by oxygen Express the answer in eV per oxygen molecule

(b) Now admit CO under the specified conditions Find fB such that only 10 of the Hb sites are occupied by oxygen What fraction is occupied by CO What fraction is unoccupied

4 Nordlund 149

5 Nordlund 1411

6 Nordlund 1416

2

P~~1 ofZ- LIJ1 twAch ~ lef

IJ

= (I( ]) (q gt 3) )( tf arJ r~

7n~~Ii~ of bAcL ~c4 I~ 11gtt I ~ldL Z

~I e I IJ

vJ v A rra ~4 (11] (laquo~) ( Itl 3) ~t ~ l ~( 70

1u+ I f F5 ~ VJ B Lv 8gt tJ

R ww 3 flt ~ I hteampJ~I amprW 8 f3 tJ ~ LHSmiddot ~ tNt- b 01shy

4J 3gt gLV ~~JP IN ampWB () lYl SvoL Fnht t)

so -bJ f~~ r b~ ~

1- acf J lr ~- --7tgt 70 ~sf II -L~ s~~

P~~1 ofZ- LIJ1 twAch ~ lef

IJ

= (I( ]) (q gt 3) )( tf arJ r~

7n~~Ii~ of bAcL ~c4 I~ 11gtt I ~ldL Z

~I e I IJ

vJ v A rra ~4 (11] (laquo~) ( Itl 3) ~t ~ l ~( 70

1u+ I f F5 ~ VJ B Lv 8gt tJ

R ww 3 flt ~ I hteampJ~I amprW 8 f3 tJ ~ LHSmiddot ~ tNt- b 01shy

4J 3gt gLV ~~JP IN ampWB () lYl SvoL Fnht t)

so -bJ f~~ r b~ ~

1- acf J lr ~- --7tgt 70 ~sf II -L~ s~~

(jiJ 1+ft1 ~ f ~ to t WAd c ltl (I lMl1 Cra If ) ~ $1VGpJ ft~ ~~ 4ft blAlt r Itf~ ~ A ~b- ~

(~ampw-l ~t~( e1- WL) I $1AI- tr J~ 8 ( flI Ai) (8 wy

$0 I If rosSI ~ 54J P =shy

~(($0i~ J Pigt11~ TJS -ampu-fcJJ is~~ +~O~~tC ~0

pound U f~-eJ ( ~- JV-=Ol ~ ~~ T J-S = - fcJJ

- T(H)UFI~J

IJ- ~ f-S ) ( i-s)

C9 fl4bW re cd2Q t~ JJedWoJL (-e f1v- PIlJ-r 0 OriifjJG~ ()shyr--b~ dls ~ t~ Lo)~ G~ sJf-r-cd-) f14 ~ raquos

IJ ~ QCtJr)(I) j

v~ f6JJlI

fn- f rtfmiddot Lwt- ~~JL~

C2 J ~ fer (~ tJ Coto L(l)

S2( ~1 ~ (-~) Vz JN eJpC-2 tJ

$ d +- cilsL

Vlru~ dI J

dLr - ~ k [A ~~J IJ ~ ____j loS l ~Jl

S oll ~ O--z (sect-)- J 4- J 1shy

- (I -I C1 J L If

V-~- C ( -= ~ I

pound _ ~ ~ _ 216 - - Ie 6 I - ~p~ J-fNpL ZAlp

G IoJ~ k t1cfr (A fj) fkrltl~ )

c - T CJfJ(J ~l( SI~CA

Els _ d ( CI I cl L) JJ- - iJ

- fa -1 tlfl

J =

(j) ~~(oX iJ Fampsffll (J

lZ(ce ~ j uw- ~s~ Q 51~ Gutsofh~ S~Q 1t- l- S f oSJltC shkJ uIocpHl) J ~middottl~J 1fI1i4 lt41

h lId ~ S~ C(J

~rr J lc tlt1-or ~ sh k )f(Dod

e-(e~ - rf)Ai tJ~ )(~r

1

s-pk A ~~

W C(oyc~J 0 c) 0 eO)

-~A-~T ) -pound4blOz fA I 0 e = 2 e ~ -poundtr

CO euro -(e-)ampcJr0 IJ i() (I e

~ 1o I

-~~re

6 A - k- T t[tl

T=- lt[1 II r TJC - 3(01lt

lev ~ 7 Xlb-SeV yen

ke r 002(7 e1 ~ 2 7 lID- eV

137[~1 J-[ i1~

eA- -~)7 X 2 7 ~ 1~2 -t y) - 03( of V

~~ Cfa 1-60h Aco I)-~ Js S tJflgtk lit fu pra~ sd- ~ J (t-r r Sb ~ct CO (pI(

~ ruJ-~ (I~rh~ ~~ ~ ~0rJ (+A

(~ A~L 4 - ~A It r

l --r~ 6- I ~ bull 1 -tkr + A e- L-r

gtt ~AIT~(0tJ ~ P - OLe

4- ~ If-eurocli-rf ~a e euroJ(

( t - Act-efA t1 r of- A(o e-EoI) r Aoz ( -fJgt1

()Ugt e- fl-r ) p - ~ e - EA~ T ( ( _ P) _ P

~ e- fjl1 - )Oze-~T( 1- P) - p

Aco P =-- shy

)aa r~~-r( L _ r) - -If ~ p p shy

------------- -

Jr p= 01 t -I = to- f ~

~r ~co ~~ fit f()~ ~~

pound8 -k I ( t-[ ~ e-f (~r_ lOr]

S-o Ea -- r h[ (ft) b r- IDrJ -s - t f J-[ ~O(ll1 - -ct r )J bull ( t ) if f = ~~ - 0lt128-1

f

( -- - 00 (( = I I 0-ff

Prohlm 149 Temperalute depeucIeot Equilibria

SoJutioos

(1) =- x~~nJ)=~( 72~X r()= 72Xeap( nx) where X =euthalpy cbaDae ia multiples of 1021 J

Typeofcbange -Euthalpy change

(uaits of Jeri J) d (HI)

dT HA _It

(I-J)

d(HBLdT HA It

(Kl)

Covalent hood 500 1-4 dOraquo 36 dOu1

louie 100 26 dO 2S dO~

Rhoad 30 17 dO) 79 dOu

Dipole-dipole IS 32 dO 21 dO

Loodcm 05 36 x 10 25 x1o-~

(2) At300K HI =exp( n46X)=713XIO NB amoun1stoO0713Oftbetotal N T

SioceA(Ha)=(H8) AT = (17 XlO-1C-1)(101C) = 17 X 10-5 bull theofB increases by HA dT NA lOOK

00011 (This is ampctor 0100017100713=0024 or Ul iacRase of24 over the iDitial

amount ofNa--tlOt very much)

Prohlm 1411 Mixing ED1ropy

Solution

(I)

Dilutioa oflhe water aCC01lDts for oaly +0 lOR oftb1s-about 1

AG =-TAS = -136RT = -34tJ I mole at 300It

AS =-k N [oooun0001 +01001110001 +SS5111 5S5 ] (2) bull Awt SS5 SS5 SSSOl

=-kNAwI [-Omiddot0109-0DI09-0001]=+O0228R

Water accooats flaquo OOOIRlaquo 4

ProbleJD 141 is UnimolecuJar Equilibria

Solution

AG=M-TAS=lL7kJmo1e-TbSs-l09kJmoIe

(1) -TbS=-226kJmo1e=entropic frIe eDer8Y (See Table S6)

22flX)Jmo1e=gt bS = = 7S8JK mole

298It

J (2) -TbS=-22600--( ~ )=370XIO-lOJ=9l6kBT

mole 602 xl moJec

(3) N = (_11700 + 7S8)= (_1410+912)=9140 (_1410)NalO ap 831ST 8315 eap T bull esp T

UIDO bull bullbull

I bull bull bullbull-shy ____

I bullbull

I -~ ---- f--- -I--- shybull U70 ~--- _ ~m__bullbull_ bullbullbullbullbull --bull shy _ubullbull_ __

4tI5 aD no 210 no SJO

T(IIII bull

~(($0i~ J Pigt11~ TJS -ampu-fcJJ is~~ +~O~~tC ~0

pound U f~-eJ ( ~- JV-=Ol ~ ~~ T J-S = - fcJJ

- T(H)UFI~J

IJ- ~ f-S ) ( i-s)

C9 fl4bW re cd2Q t~ JJedWoJL (-e f1v- PIlJ-r 0 OriifjJG~ ()shyr--b~ dls ~ t~ Lo)~ G~ sJf-r-cd-) f14 ~ raquos

IJ ~ QCtJr)(I) j

v~ f6JJlI

fn- f rtfmiddot Lwt- ~~JL~

C2 J ~ fer (~ tJ Coto L(l)

S2( ~1 ~ (-~) Vz JN eJpC-2 tJ

$ d +- cilsL

Vlru~ dI J

dLr - ~ k [A ~~J IJ ~ ____j loS l ~Jl

S oll ~ O--z (sect-)- J 4- J 1shy

- (I -I C1 J L If

V-~- C ( -= ~ I

pound _ ~ ~ _ 216 - - Ie 6 I - ~p~ J-fNpL ZAlp

G IoJ~ k t1cfr (A fj) fkrltl~ )

c - T CJfJ(J ~l( SI~CA

Els _ d ( CI I cl L) JJ- - iJ

- fa -1 tlfl

J =

(j) ~~(oX iJ Fampsffll (J

lZ(ce ~ j uw- ~s~ Q 51~ Gutsofh~ S~Q 1t- l- S f oSJltC shkJ uIocpHl) J ~middottl~J 1fI1i4 lt41

h lId ~ S~ C(J

~rr J lc tlt1-or ~ sh k )f(Dod

e-(e~ - rf)Ai tJ~ )(~r

1

s-pk A ~~

W C(oyc~J 0 c) 0 eO)

-~A-~T ) -pound4blOz fA I 0 e = 2 e ~ -poundtr

CO euro -(e-)ampcJr0 IJ i() (I e

~ 1o I

-~~re

6 A - k- T t[tl

T=- lt[1 II r TJC - 3(01lt

lev ~ 7 Xlb-SeV yen

ke r 002(7 e1 ~ 2 7 lID- eV

137[~1 J-[ i1~

eA- -~)7 X 2 7 ~ 1~2 -t y) - 03( of V

~~ Cfa 1-60h Aco I)-~ Js S tJflgtk lit fu pra~ sd- ~ J (t-r r Sb ~ct CO (pI(

~ ruJ-~ (I~rh~ ~~ ~ ~0rJ (+A

(~ A~L 4 - ~A It r

l --r~ 6- I ~ bull 1 -tkr + A e- L-r

gtt ~AIT~(0tJ ~ P - OLe

4- ~ If-eurocli-rf ~a e euroJ(

( t - Act-efA t1 r of- A(o e-EoI) r Aoz ( -fJgt1

()Ugt e- fl-r ) p - ~ e - EA~ T ( ( _ P) _ P

~ e- fjl1 - )Oze-~T( 1- P) - p

Aco P =-- shy

)aa r~~-r( L _ r) - -If ~ p p shy

------------- -

Jr p= 01 t -I = to- f ~

~r ~co ~~ fit f()~ ~~

pound8 -k I ( t-[ ~ e-f (~r_ lOr]

S-o Ea -- r h[ (ft) b r- IDrJ -s - t f J-[ ~O(ll1 - -ct r )J bull ( t ) if f = ~~ - 0lt128-1

f

( -- - 00 (( = I I 0-ff

Prohlm 149 Temperalute depeucIeot Equilibria

SoJutioos

(1) =- x~~nJ)=~( 72~X r()= 72Xeap( nx) where X =euthalpy cbaDae ia multiples of 1021 J

Typeofcbange -Euthalpy change

(uaits of Jeri J) d (HI)

dT HA _It

(I-J)

d(HBLdT HA It

(Kl)

Covalent hood 500 1-4 dOraquo 36 dOu1

louie 100 26 dO 2S dO~

Rhoad 30 17 dO) 79 dOu

Dipole-dipole IS 32 dO 21 dO

Loodcm 05 36 x 10 25 x1o-~

(2) At300K HI =exp( n46X)=713XIO NB amoun1stoO0713Oftbetotal N T

SioceA(Ha)=(H8) AT = (17 XlO-1C-1)(101C) = 17 X 10-5 bull theofB increases by HA dT NA lOOK

00011 (This is ampctor 0100017100713=0024 or Ul iacRase of24 over the iDitial

amount ofNa--tlOt very much)

Prohlm 1411 Mixing ED1ropy

Solution

(I)

Dilutioa oflhe water aCC01lDts for oaly +0 lOR oftb1s-about 1

AG =-TAS = -136RT = -34tJ I mole at 300It

AS =-k N [oooun0001 +01001110001 +SS5111 5S5 ] (2) bull Awt SS5 SS5 SSSOl

=-kNAwI [-Omiddot0109-0DI09-0001]=+O0228R

Water accooats flaquo OOOIRlaquo 4

ProbleJD 141 is UnimolecuJar Equilibria

Solution

AG=M-TAS=lL7kJmo1e-TbSs-l09kJmoIe

(1) -TbS=-226kJmo1e=entropic frIe eDer8Y (See Table S6)

22flX)Jmo1e=gt bS = = 7S8JK mole

298It

J (2) -TbS=-22600--( ~ )=370XIO-lOJ=9l6kBT

mole 602 xl moJec

(3) N = (_11700 + 7S8)= (_1410+912)=9140 (_1410)NalO ap 831ST 8315 eap T bull esp T

UIDO bull bullbull

I bull bull bullbull-shy ____

I bullbull

I -~ ---- f--- -I--- shybull U70 ~--- _ ~m__bullbull_ bullbullbullbullbull --bull shy _ubullbull_ __

4tI5 aD no 210 no SJO

T(IIII bull

C9 fl4bW re cd2Q t~ JJedWoJL (-e f1v- PIlJ-r 0 OriifjJG~ ()shyr--b~ dls ~ t~ Lo)~ G~ sJf-r-cd-) f14 ~ raquos

IJ ~ QCtJr)(I) j

v~ f6JJlI

fn- f rtfmiddot Lwt- ~~JL~

C2 J ~ fer (~ tJ Coto L(l)

S2( ~1 ~ (-~) Vz JN eJpC-2 tJ

$ d +- cilsL

Vlru~ dI J

dLr - ~ k [A ~~J IJ ~ ____j loS l ~Jl

S oll ~ O--z (sect-)- J 4- J 1shy

- (I -I C1 J L If

V-~- C ( -= ~ I

pound _ ~ ~ _ 216 - - Ie 6 I - ~p~ J-fNpL ZAlp

G IoJ~ k t1cfr (A fj) fkrltl~ )

c - T CJfJ(J ~l( SI~CA

Els _ d ( CI I cl L) JJ- - iJ

- fa -1 tlfl

J =

(j) ~~(oX iJ Fampsffll (J

lZ(ce ~ j uw- ~s~ Q 51~ Gutsofh~ S~Q 1t- l- S f oSJltC shkJ uIocpHl) J ~middottl~J 1fI1i4 lt41

h lId ~ S~ C(J

~rr J lc tlt1-or ~ sh k )f(Dod

e-(e~ - rf)Ai tJ~ )(~r

1

s-pk A ~~

W C(oyc~J 0 c) 0 eO)

-~A-~T ) -pound4blOz fA I 0 e = 2 e ~ -poundtr

CO euro -(e-)ampcJr0 IJ i() (I e

~ 1o I

-~~re

6 A - k- T t[tl

T=- lt[1 II r TJC - 3(01lt

lev ~ 7 Xlb-SeV yen

ke r 002(7 e1 ~ 2 7 lID- eV

137[~1 J-[ i1~

eA- -~)7 X 2 7 ~ 1~2 -t y) - 03( of V

~~ Cfa 1-60h Aco I)-~ Js S tJflgtk lit fu pra~ sd- ~ J (t-r r Sb ~ct CO (pI(

~ ruJ-~ (I~rh~ ~~ ~ ~0rJ (+A

(~ A~L 4 - ~A It r

l --r~ 6- I ~ bull 1 -tkr + A e- L-r

gtt ~AIT~(0tJ ~ P - OLe

4- ~ If-eurocli-rf ~a e euroJ(

( t - Act-efA t1 r of- A(o e-EoI) r Aoz ( -fJgt1

()Ugt e- fl-r ) p - ~ e - EA~ T ( ( _ P) _ P

~ e- fjl1 - )Oze-~T( 1- P) - p

Aco P =-- shy

)aa r~~-r( L _ r) - -If ~ p p shy

------------- -

Jr p= 01 t -I = to- f ~

~r ~co ~~ fit f()~ ~~

pound8 -k I ( t-[ ~ e-f (~r_ lOr]

S-o Ea -- r h[ (ft) b r- IDrJ -s - t f J-[ ~O(ll1 - -ct r )J bull ( t ) if f = ~~ - 0lt128-1

f

( -- - 00 (( = I I 0-ff

Prohlm 149 Temperalute depeucIeot Equilibria

SoJutioos

(1) =- x~~nJ)=~( 72~X r()= 72Xeap( nx) where X =euthalpy cbaDae ia multiples of 1021 J

Typeofcbange -Euthalpy change

(uaits of Jeri J) d (HI)

dT HA _It

(I-J)

d(HBLdT HA It

(Kl)

Covalent hood 500 1-4 dOraquo 36 dOu1

louie 100 26 dO 2S dO~

Rhoad 30 17 dO) 79 dOu

Dipole-dipole IS 32 dO 21 dO

Loodcm 05 36 x 10 25 x1o-~

(2) At300K HI =exp( n46X)=713XIO NB amoun1stoO0713Oftbetotal N T

SioceA(Ha)=(H8) AT = (17 XlO-1C-1)(101C) = 17 X 10-5 bull theofB increases by HA dT NA lOOK

00011 (This is ampctor 0100017100713=0024 or Ul iacRase of24 over the iDitial

amount ofNa--tlOt very much)

Prohlm 1411 Mixing ED1ropy

Solution

(I)

Dilutioa oflhe water aCC01lDts for oaly +0 lOR oftb1s-about 1

AG =-TAS = -136RT = -34tJ I mole at 300It

AS =-k N [oooun0001 +01001110001 +SS5111 5S5 ] (2) bull Awt SS5 SS5 SSSOl

=-kNAwI [-Omiddot0109-0DI09-0001]=+O0228R

Water accooats flaquo OOOIRlaquo 4

ProbleJD 141 is UnimolecuJar Equilibria

Solution

AG=M-TAS=lL7kJmo1e-TbSs-l09kJmoIe

(1) -TbS=-226kJmo1e=entropic frIe eDer8Y (See Table S6)

22flX)Jmo1e=gt bS = = 7S8JK mole

298It

J (2) -TbS=-22600--( ~ )=370XIO-lOJ=9l6kBT

mole 602 xl moJec

(3) N = (_11700 + 7S8)= (_1410+912)=9140 (_1410)NalO ap 831ST 8315 eap T bull esp T

UIDO bull bullbull

I bull bull bullbull-shy ____

I bullbull

I -~ ---- f--- -I--- shybull U70 ~--- _ ~m__bullbull_ bullbullbullbullbull --bull shy _ubullbull_ __

4tI5 aD no 210 no SJO

T(IIII bull

G IoJ~ k t1cfr (A fj) fkrltl~ )

c - T CJfJ(J ~l( SI~CA

Els _ d ( CI I cl L) JJ- - iJ

- fa -1 tlfl

J =

(j) ~~(oX iJ Fampsffll (J

lZ(ce ~ j uw- ~s~ Q 51~ Gutsofh~ S~Q 1t- l- S f oSJltC shkJ uIocpHl) J ~middottl~J 1fI1i4 lt41

h lId ~ S~ C(J

~rr J lc tlt1-or ~ sh k )f(Dod

e-(e~ - rf)Ai tJ~ )(~r

1

s-pk A ~~

W C(oyc~J 0 c) 0 eO)

-~A-~T ) -pound4blOz fA I 0 e = 2 e ~ -poundtr

CO euro -(e-)ampcJr0 IJ i() (I e

~ 1o I

-~~re

6 A - k- T t[tl

T=- lt[1 II r TJC - 3(01lt

lev ~ 7 Xlb-SeV yen

ke r 002(7 e1 ~ 2 7 lID- eV

137[~1 J-[ i1~

eA- -~)7 X 2 7 ~ 1~2 -t y) - 03( of V

~~ Cfa 1-60h Aco I)-~ Js S tJflgtk lit fu pra~ sd- ~ J (t-r r Sb ~ct CO (pI(

~ ruJ-~ (I~rh~ ~~ ~ ~0rJ (+A

(~ A~L 4 - ~A It r

l --r~ 6- I ~ bull 1 -tkr + A e- L-r

gtt ~AIT~(0tJ ~ P - OLe

4- ~ If-eurocli-rf ~a e euroJ(

( t - Act-efA t1 r of- A(o e-EoI) r Aoz ( -fJgt1

()Ugt e- fl-r ) p - ~ e - EA~ T ( ( _ P) _ P

~ e- fjl1 - )Oze-~T( 1- P) - p

Aco P =-- shy

)aa r~~-r( L _ r) - -If ~ p p shy

------------- -

Jr p= 01 t -I = to- f ~

~r ~co ~~ fit f()~ ~~

pound8 -k I ( t-[ ~ e-f (~r_ lOr]

S-o Ea -- r h[ (ft) b r- IDrJ -s - t f J-[ ~O(ll1 - -ct r )J bull ( t ) if f = ~~ - 0lt128-1

f

( -- - 00 (( = I I 0-ff

Prohlm 149 Temperalute depeucIeot Equilibria

SoJutioos

(1) =- x~~nJ)=~( 72~X r()= 72Xeap( nx) where X =euthalpy cbaDae ia multiples of 1021 J

Typeofcbange -Euthalpy change

(uaits of Jeri J) d (HI)

dT HA _It

(I-J)

d(HBLdT HA It

(Kl)

Covalent hood 500 1-4 dOraquo 36 dOu1

louie 100 26 dO 2S dO~

Rhoad 30 17 dO) 79 dOu

Dipole-dipole IS 32 dO 21 dO

Loodcm 05 36 x 10 25 x1o-~

(2) At300K HI =exp( n46X)=713XIO NB amoun1stoO0713Oftbetotal N T

SioceA(Ha)=(H8) AT = (17 XlO-1C-1)(101C) = 17 X 10-5 bull theofB increases by HA dT NA lOOK

00011 (This is ampctor 0100017100713=0024 or Ul iacRase of24 over the iDitial

amount ofNa--tlOt very much)

Prohlm 1411 Mixing ED1ropy

Solution

(I)

Dilutioa oflhe water aCC01lDts for oaly +0 lOR oftb1s-about 1

AG =-TAS = -136RT = -34tJ I mole at 300It

AS =-k N [oooun0001 +01001110001 +SS5111 5S5 ] (2) bull Awt SS5 SS5 SSSOl

=-kNAwI [-Omiddot0109-0DI09-0001]=+O0228R

Water accooats flaquo OOOIRlaquo 4

ProbleJD 141 is UnimolecuJar Equilibria

Solution

AG=M-TAS=lL7kJmo1e-TbSs-l09kJmoIe

(1) -TbS=-226kJmo1e=entropic frIe eDer8Y (See Table S6)

22flX)Jmo1e=gt bS = = 7S8JK mole

298It

J (2) -TbS=-22600--( ~ )=370XIO-lOJ=9l6kBT

mole 602 xl moJec

(3) N = (_11700 + 7S8)= (_1410+912)=9140 (_1410)NalO ap 831ST 8315 eap T bull esp T

UIDO bull bullbull

I bull bull bullbull-shy ____

I bullbull

I -~ ---- f--- -I--- shybull U70 ~--- _ ~m__bullbull_ bullbullbullbullbull --bull shy _ubullbull_ __

4tI5 aD no 210 no SJO

T(IIII bull

(j) ~~(oX iJ Fampsffll (J

lZ(ce ~ j uw- ~s~ Q 51~ Gutsofh~ S~Q 1t- l- S f oSJltC shkJ uIocpHl) J ~middottl~J 1fI1i4 lt41

h lId ~ S~ C(J

~rr J lc tlt1-or ~ sh k )f(Dod

e-(e~ - rf)Ai tJ~ )(~r

1

s-pk A ~~

W C(oyc~J 0 c) 0 eO)

-~A-~T ) -pound4blOz fA I 0 e = 2 e ~ -poundtr

CO euro -(e-)ampcJr0 IJ i() (I e

~ 1o I

-~~re

6 A - k- T t[tl

T=- lt[1 II r TJC - 3(01lt

lev ~ 7 Xlb-SeV yen

ke r 002(7 e1 ~ 2 7 lID- eV

137[~1 J-[ i1~

eA- -~)7 X 2 7 ~ 1~2 -t y) - 03( of V

~~ Cfa 1-60h Aco I)-~ Js S tJflgtk lit fu pra~ sd- ~ J (t-r r Sb ~ct CO (pI(

~ ruJ-~ (I~rh~ ~~ ~ ~0rJ (+A

(~ A~L 4 - ~A It r

l --r~ 6- I ~ bull 1 -tkr + A e- L-r

gtt ~AIT~(0tJ ~ P - OLe

4- ~ If-eurocli-rf ~a e euroJ(

( t - Act-efA t1 r of- A(o e-EoI) r Aoz ( -fJgt1

()Ugt e- fl-r ) p - ~ e - EA~ T ( ( _ P) _ P

~ e- fjl1 - )Oze-~T( 1- P) - p

Aco P =-- shy

)aa r~~-r( L _ r) - -If ~ p p shy

------------- -

Jr p= 01 t -I = to- f ~

~r ~co ~~ fit f()~ ~~

pound8 -k I ( t-[ ~ e-f (~r_ lOr]

S-o Ea -- r h[ (ft) b r- IDrJ -s - t f J-[ ~O(ll1 - -ct r )J bull ( t ) if f = ~~ - 0lt128-1

f

( -- - 00 (( = I I 0-ff

Prohlm 149 Temperalute depeucIeot Equilibria

SoJutioos

(1) =- x~~nJ)=~( 72~X r()= 72Xeap( nx) where X =euthalpy cbaDae ia multiples of 1021 J

Typeofcbange -Euthalpy change

(uaits of Jeri J) d (HI)

dT HA _It

(I-J)

d(HBLdT HA It

(Kl)

Covalent hood 500 1-4 dOraquo 36 dOu1

louie 100 26 dO 2S dO~

Rhoad 30 17 dO) 79 dOu

Dipole-dipole IS 32 dO 21 dO

Loodcm 05 36 x 10 25 x1o-~

(2) At300K HI =exp( n46X)=713XIO NB amoun1stoO0713Oftbetotal N T

SioceA(Ha)=(H8) AT = (17 XlO-1C-1)(101C) = 17 X 10-5 bull theofB increases by HA dT NA lOOK

00011 (This is ampctor 0100017100713=0024 or Ul iacRase of24 over the iDitial

amount ofNa--tlOt very much)

Prohlm 1411 Mixing ED1ropy

Solution

(I)

Dilutioa oflhe water aCC01lDts for oaly +0 lOR oftb1s-about 1

AG =-TAS = -136RT = -34tJ I mole at 300It

AS =-k N [oooun0001 +01001110001 +SS5111 5S5 ] (2) bull Awt SS5 SS5 SSSOl

=-kNAwI [-Omiddot0109-0DI09-0001]=+O0228R

Water accooats flaquo OOOIRlaquo 4

ProbleJD 141 is UnimolecuJar Equilibria

Solution

AG=M-TAS=lL7kJmo1e-TbSs-l09kJmoIe

(1) -TbS=-226kJmo1e=entropic frIe eDer8Y (See Table S6)

22flX)Jmo1e=gt bS = = 7S8JK mole

298It

J (2) -TbS=-22600--( ~ )=370XIO-lOJ=9l6kBT

mole 602 xl moJec

(3) N = (_11700 + 7S8)= (_1410+912)=9140 (_1410)NalO ap 831ST 8315 eap T bull esp T

UIDO bull bullbull

I bull bull bullbull-shy ____

I bullbull

I -~ ---- f--- -I--- shybull U70 ~--- _ ~m__bullbull_ bullbullbullbullbull --bull shy _ubullbull_ __

4tI5 aD no 210 no SJO

T(IIII bull

~ 1o I

-~~re

6 A - k- T t[tl

T=- lt[1 II r TJC - 3(01lt

lev ~ 7 Xlb-SeV yen

ke r 002(7 e1 ~ 2 7 lID- eV

137[~1 J-[ i1~

eA- -~)7 X 2 7 ~ 1~2 -t y) - 03( of V

~~ Cfa 1-60h Aco I)-~ Js S tJflgtk lit fu pra~ sd- ~ J (t-r r Sb ~ct CO (pI(

~ ruJ-~ (I~rh~ ~~ ~ ~0rJ (+A

(~ A~L 4 - ~A It r

l --r~ 6- I ~ bull 1 -tkr + A e- L-r

gtt ~AIT~(0tJ ~ P - OLe

4- ~ If-eurocli-rf ~a e euroJ(

( t - Act-efA t1 r of- A(o e-EoI) r Aoz ( -fJgt1

()Ugt e- fl-r ) p - ~ e - EA~ T ( ( _ P) _ P

~ e- fjl1 - )Oze-~T( 1- P) - p

Aco P =-- shy

)aa r~~-r( L _ r) - -If ~ p p shy

------------- -

Jr p= 01 t -I = to- f ~

~r ~co ~~ fit f()~ ~~

pound8 -k I ( t-[ ~ e-f (~r_ lOr]

S-o Ea -- r h[ (ft) b r- IDrJ -s - t f J-[ ~O(ll1 - -ct r )J bull ( t ) if f = ~~ - 0lt128-1

f

( -- - 00 (( = I I 0-ff

Prohlm 149 Temperalute depeucIeot Equilibria

SoJutioos

(1) =- x~~nJ)=~( 72~X r()= 72Xeap( nx) where X =euthalpy cbaDae ia multiples of 1021 J

Typeofcbange -Euthalpy change

(uaits of Jeri J) d (HI)

dT HA _It

(I-J)

d(HBLdT HA It

(Kl)

Covalent hood 500 1-4 dOraquo 36 dOu1

louie 100 26 dO 2S dO~

Rhoad 30 17 dO) 79 dOu

Dipole-dipole IS 32 dO 21 dO

Loodcm 05 36 x 10 25 x1o-~

(2) At300K HI =exp( n46X)=713XIO NB amoun1stoO0713Oftbetotal N T

SioceA(Ha)=(H8) AT = (17 XlO-1C-1)(101C) = 17 X 10-5 bull theofB increases by HA dT NA lOOK

00011 (This is ampctor 0100017100713=0024 or Ul iacRase of24 over the iDitial

amount ofNa--tlOt very much)

Prohlm 1411 Mixing ED1ropy

Solution

(I)

Dilutioa oflhe water aCC01lDts for oaly +0 lOR oftb1s-about 1

AG =-TAS = -136RT = -34tJ I mole at 300It

AS =-k N [oooun0001 +01001110001 +SS5111 5S5 ] (2) bull Awt SS5 SS5 SSSOl

=-kNAwI [-Omiddot0109-0DI09-0001]=+O0228R

Water accooats flaquo OOOIRlaquo 4

ProbleJD 141 is UnimolecuJar Equilibria

Solution

AG=M-TAS=lL7kJmo1e-TbSs-l09kJmoIe

(1) -TbS=-226kJmo1e=entropic frIe eDer8Y (See Table S6)

22flX)Jmo1e=gt bS = = 7S8JK mole

298It

J (2) -TbS=-22600--( ~ )=370XIO-lOJ=9l6kBT

mole 602 xl moJec

(3) N = (_11700 + 7S8)= (_1410+912)=9140 (_1410)NalO ap 831ST 8315 eap T bull esp T

UIDO bull bullbull

I bull bull bullbull-shy ____

I bullbull

I -~ ---- f--- -I--- shybull U70 ~--- _ ~m__bullbull_ bullbullbullbullbull --bull shy _ubullbull_ __

4tI5 aD no 210 no SJO

T(IIII bull

------------- -

Jr p= 01 t -I = to- f ~

~r ~co ~~ fit f()~ ~~

pound8 -k I ( t-[ ~ e-f (~r_ lOr]

S-o Ea -- r h[ (ft) b r- IDrJ -s - t f J-[ ~O(ll1 - -ct r )J bull ( t ) if f = ~~ - 0lt128-1

f

( -- - 00 (( = I I 0-ff

Prohlm 149 Temperalute depeucIeot Equilibria

SoJutioos

(1) =- x~~nJ)=~( 72~X r()= 72Xeap( nx) where X =euthalpy cbaDae ia multiples of 1021 J

Typeofcbange -Euthalpy change

(uaits of Jeri J) d (HI)

dT HA _It

(I-J)

d(HBLdT HA It

(Kl)

Covalent hood 500 1-4 dOraquo 36 dOu1

louie 100 26 dO 2S dO~

Rhoad 30 17 dO) 79 dOu

Dipole-dipole IS 32 dO 21 dO

Loodcm 05 36 x 10 25 x1o-~

(2) At300K HI =exp( n46X)=713XIO NB amoun1stoO0713Oftbetotal N T

SioceA(Ha)=(H8) AT = (17 XlO-1C-1)(101C) = 17 X 10-5 bull theofB increases by HA dT NA lOOK

00011 (This is ampctor 0100017100713=0024 or Ul iacRase of24 over the iDitial

amount ofNa--tlOt very much)

Prohlm 1411 Mixing ED1ropy

Solution

(I)

Dilutioa oflhe water aCC01lDts for oaly +0 lOR oftb1s-about 1

AG =-TAS = -136RT = -34tJ I mole at 300It

AS =-k N [oooun0001 +01001110001 +SS5111 5S5 ] (2) bull Awt SS5 SS5 SSSOl

=-kNAwI [-Omiddot0109-0DI09-0001]=+O0228R

Water accooats flaquo OOOIRlaquo 4

ProbleJD 141 is UnimolecuJar Equilibria

Solution

AG=M-TAS=lL7kJmo1e-TbSs-l09kJmoIe

(1) -TbS=-226kJmo1e=entropic frIe eDer8Y (See Table S6)

22flX)Jmo1e=gt bS = = 7S8JK mole

298It

J (2) -TbS=-22600--( ~ )=370XIO-lOJ=9l6kBT

mole 602 xl moJec

(3) N = (_11700 + 7S8)= (_1410+912)=9140 (_1410)NalO ap 831ST 8315 eap T bull esp T

UIDO bull bullbull

I bull bull bullbull-shy ____

I bullbull

I -~ ---- f--- -I--- shybull U70 ~--- _ ~m__bullbull_ bullbullbullbullbull --bull shy _ubullbull_ __

4tI5 aD no 210 no SJO

T(IIII bull

Prohlm 149 Temperalute depeucIeot Equilibria

SoJutioos

(1) =- x~~nJ)=~( 72~X r()= 72Xeap( nx) where X =euthalpy cbaDae ia multiples of 1021 J

Typeofcbange -Euthalpy change

(uaits of Jeri J) d (HI)

dT HA _It

(I-J)

d(HBLdT HA It

(Kl)

Covalent hood 500 1-4 dOraquo 36 dOu1

louie 100 26 dO 2S dO~

Rhoad 30 17 dO) 79 dOu

Dipole-dipole IS 32 dO 21 dO

Loodcm 05 36 x 10 25 x1o-~

(2) At300K HI =exp( n46X)=713XIO NB amoun1stoO0713Oftbetotal N T

SioceA(Ha)=(H8) AT = (17 XlO-1C-1)(101C) = 17 X 10-5 bull theofB increases by HA dT NA lOOK

00011 (This is ampctor 0100017100713=0024 or Ul iacRase of24 over the iDitial

amount ofNa--tlOt very much)

Prohlm 1411 Mixing ED1ropy

Solution

(I)

Dilutioa oflhe water aCC01lDts for oaly +0 lOR oftb1s-about 1

AG =-TAS = -136RT = -34tJ I mole at 300It

AS =-k N [oooun0001 +01001110001 +SS5111 5S5 ] (2) bull Awt SS5 SS5 SSSOl

=-kNAwI [-Omiddot0109-0DI09-0001]=+O0228R

Water accooats flaquo OOOIRlaquo 4

ProbleJD 141 is UnimolecuJar Equilibria

Solution

AG=M-TAS=lL7kJmo1e-TbSs-l09kJmoIe

(1) -TbS=-226kJmo1e=entropic frIe eDer8Y (See Table S6)

22flX)Jmo1e=gt bS = = 7S8JK mole

298It

J (2) -TbS=-22600--( ~ )=370XIO-lOJ=9l6kBT

mole 602 xl moJec

(3) N = (_11700 + 7S8)= (_1410+912)=9140 (_1410)NalO ap 831ST 8315 eap T bull esp T

UIDO bull bullbull

I bull bull bullbull-shy ____

I bullbull

I -~ ---- f--- -I--- shybull U70 ~--- _ ~m__bullbull_ bullbullbullbullbull --bull shy _ubullbull_ __

4tI5 aD no 210 no SJO

T(IIII bull

Dilutioa oflhe water aCC01lDts for oaly +0 lOR oftb1s-about 1

AG =-TAS = -136RT = -34tJ I mole at 300It

AS =-k N [oooun0001 +01001110001 +SS5111 5S5 ] (2) bull Awt SS5 SS5 SSSOl

=-kNAwI [-Omiddot0109-0DI09-0001]=+O0228R

Water accooats flaquo OOOIRlaquo 4

ProbleJD 141 is UnimolecuJar Equilibria

Solution

AG=M-TAS=lL7kJmo1e-TbSs-l09kJmoIe

(1) -TbS=-226kJmo1e=entropic frIe eDer8Y (See Table S6)

22flX)Jmo1e=gt bS = = 7S8JK mole

298It

J (2) -TbS=-22600--( ~ )=370XIO-lOJ=9l6kBT

mole 602 xl moJec

(3) N = (_11700 + 7S8)= (_1410+912)=9140 (_1410)NalO ap 831ST 8315 eap T bull esp T

UIDO bull bullbull

I bull bull bullbull-shy ____

I bullbull

I -~ ---- f--- -I--- shybull U70 ~--- _ ~m__bullbull_ bullbullbullbullbull --bull shy _ubullbull_ __

4tI5 aD no 210 no SJO

T(IIII bull