I affirm that I have never given nor received aid on this examination. I understand that cheating in the exam will result in a grade F for the class.

Transcription

1 Che340 hysical Cheistry for Biocheists Exa 3 Apr 5, 0 Your Nae _ I affir that I have never given nor received aid on this exaination. I understand that cheating in the exa will result in a grade F for the class. Signature. Sec Multiple Choice [ /4] Sec Calculation/MC [ /8] Sec 3 Long Question [ /45] Sec 4 Derivation [ /4] Total [ /00] Total points are 9 points. If you score ore than 00, you will receive 00 points.

2 Multiple Choice Questions (Soe questions ay be siilar to those one in quiz, but not the sae) Each 3 points [ /43] Q. The figure (right) shows the teperature dependence of cheical potential for olecule X. Solid and dotted lines denote cheical potentials for 3 phases at = 0 and 0 +, respectively. In the case of this figure elting point T and boiling point T b changes are changed as follows when is increased fro 0 to 0 +. a) T and T b are both increased. b) T and T b are both decreased. c) T is increased while T b is decreased. d) T is decreased while T b is increased. T A T B T C T D Q, 3, 4 The diagra in the right shows a total vapor pressure pressure (Torr) for a given total olar fraction of benzene Z benzene for a benzene-toluene ixture. Q. How uch is X benzene at point c? Choose the closest. (a) 0.43 (b) 0.65 (b) 0.70 (c) 0.75 (d) 0.85 Q3. What is the ratio of liquid and vapor at point b? Choose the closest. (a) 7: (b) 3: (c) : (d) : 3 (e) :7 Q4. How uch is toluene *? Choose the closest. (a) 30 Torr (b) 50 Torr (c) 70 Torr (d) 90 Torr Teperature Q5 Choose two correct answers on the cheical potentials of stea and superheated water all at bar. For this proble, S H O,l 70.0 J ol K and S H O,g g, T) = (g, T) - (l, T) 88.8 J ol K. T = 0 ºC = 383K. (l a) (l g, T) < 0. b) (l g, T) > 0 c) (l g, T) = 0 d) (l g, T) = -(S 0 HO, g - S 0 HO, l) x0 ºC e) (l g, T) = (S 0 HO, g - S 0 HO, l) x 0 ºC f) (l g, T) = -(S 0 HO, g - S 0 HO, l) x 383 K g) (l g, T) = (S 0 HO, g - S 0 HO, l) x 383 K Q6. Choose 3 correct stateents on the right diagra. (a) V (sl) > 0 (b) V (sl) < 0 (c) S (sl) > 0 (d) S (sl) < 0 (e) Line b denotes phase transition fro liquid to solid through the freezing point. (f) Subliation can take place for this syste when the teperature is above that for triple point.

3 Q7. The vapor pressure fro pure CS liquid at 98 K is 0 = 0.4 bar. You want to calculate the vapor pressure of CS ( ) at 98 K at the equilibriu after He is added to the gas phase at a partial pressure of bar ( >00 bar). Choose TWO correct forulae that present the change in the cheical potential for CS (liquid or vapor phase) after the introduction of He. (Think about the change of cheical potential for each of the vapor and liquid phases). (a) ln( / 0 ) (b) ΔH vaporization/rt (c) 0 * 0 /( 0 + ) liquid liquid (d) RTln( / 0 ) (e) V ( - 0 ) (f) V ( - 0 ) Q8. Choose a forula that best represents a ± in ters of a + and a for CaCl a) a + a - b) a + a - c) a + a - d) ( a + a - ) 3 e) (a + a - ) 3 f) ( a + a - ) /3 f) (a + a - ) /3 Q9. Which properly represents K f in elting point depression upon ixing a solute? T f, pure M solvent T f, pure M solvent T f pure T, solute f, pure solute (a) R (b) R (c) R (d) R H H H H vap, fusion, vap, fusion, Q0. Which is a correct forula for a total pressure total for a given y in the vapor phase? (a) *+ * (b) * + y ( *- *) (c) * * /{ * +y ( *- *)} (d) * * /{ * +y ( *- *)} (e) * + y ( *- *) Q Which equation properly represents cheical potential for solvent in an ideal solution? Choose ALL. (a) i solution = i * + RTln(x i ) (b) i solution = i * + RTln( i / i 0 ) (c) i solution = i * + RTln( i / i * ) (d) i solution = i * + RTln(y i ) Q. What is the Debye-Huckel screening length fro the figure for =0.0? Choose the closest. (Hint: e - ) a) n b) 3 n c) 5 n d) 7n e) 9 n Q3. One sall bubble and large bubble ake contact. When the two bubble fuses, what is the direction of the air flow based on the pressure expected fro the surface tension? (a) Fro sall to large one (b) Fro large to sall one (c) No such a flow is expected 4 8 r (n) 3

4 Q4. When K 3 O 4 is dissolved in solvent, the relationship of the cheical potential and ean ionic cheical potential are written as follows: µ solute = [Q] µ Using µ = µ 0 + ln(a [Q] ) µ solute =4 µ 0 + ln(a [Q3] ) = µ solute RT ln(/ 0 ) + [Q3] RT ln( ) Choose the right choice for {[Q], [Q], [Q3]}. (a) {4, 4, 4} (b) {, 4, 4} (c) {4,, 4} (d) {4, 4, } (e) {,, } 4

5 . Calculation/Multiple Choice Question each 4 point [ /8 points].. For water, H vaporization is kj ol, and the noral boiling point is K. Calculate the boiling point for water in an autoclave pressurized at.0 at. a) kJol kJol. 00at R ln( ) R373. 5K. 0at b) kJol kJol. 0at R ln( ) K. 00at c) kJol K kJol. 00at R ln( ) R373. 5K. 0at d) R kJol. 0at R ln( ). 00at 3735, K e) R kJol. 00at R ln( ). 0at 3735, K f) R kJol. 00at R ln( ) 3735K. 0at,.. (Modified fro HW9 Q) The data in the Table below shows the vapor pressure of water (coponent A) and ethanol (B) at 39.9 C. x A y A total (Torr) The vapor pressure of pure water is Torr and that of ethanol is 55.6Torr at 39.9 C. Using the vapor pressures and the data fro the table above, calculate the activity coefficients ( B ) for Coponent B using a Raoult s law standard state at x A = Choose the closest. (a) 0.85 (b).00 (c).5 (d).50 (e).75 (f).00.3a For a protein denaturation for a utant protein (N D) at T = 30. K and =.00 bar, the enthalpy change is 9 kj ol and the entropy change is.950 kj K ol. Calculate the Gibbs energy change at T = 30.0 K and =.00 bar. Choose the closest (a) -8.5 kj ol - (b) -6.5 kjol - (c) -3.4 kjol - (d) -.5 kjol - (e) 0 kjol - (f) 9 kjol -.3B Which of D or N is ore stable at T =30K in.3? (a) D (b) N (c) The stability is the sae. ( point each) 5

6 .4 What is the ionic strength of.0 ol/kg Na 3 O 4 solution? (a) 0.5 ol/kg (b).0 ol/kg (c).0 ol/kg (d) 4.0 ol/kg (e) 5.0 ol/k (f) 6.0 ol/kg (g) 0.0 ol/kg (h).0 ol/kg.5 A and B for an ideal solution at 98 K, with x A = 0.400, A * = 60 Torr and B * = 00 Torr. A portion of the gas phase is reoved and condensed in a separate container. Calculate the partial pressures of B in equilibriu with this new liquid saple at 98 K. Choose the closest. (a) 5 Torr (b) 30 Torr (c) 50 Torr (d) 60 Torr (e) 75 Torr (f) 90 Torr.6 (a) Calculate the vapor pressure of water at 98.5 K. For the transforation H O(l) H O(g), use Table 3.. Hint: first, calculate G reaction 0. Choose the closest. (a) 0.03 bar (b) 0. bar (c) 0. bar (d) 0.53 bar (e).0 bar (f) 8.50 bar.7 What is the standard boiling point of water ( ext =.00 bar)? Assue that H f is independent of the teperature fro 98K to 398Kfor both H O(g) and H O(l). (a) 345 K (b) 358 K (c) 370K (d) 385 K (e) 398 K Table 3. Substance H O(g) H O(l) H 0 f (kjol - ) G f 0 (kjol - )

7 7

8 Calculation Question. [ /45] Choose 3 questions aong the following 4 questions. If you solve 4 without choosing, we will grade for 3 questions with the lowest scores. Write answers in the specified place. You should show calculations for full credit and partial credit. lease include units in calculations. 3. [Circle if you choose this] (Original Question 7.3) [ /5] Carbon tetrachloride elts at 50 K. The vapor pressure of the liquid is 0,539 a at 90 K and 74,58 a at 340 K. The vapor pressure of the solid is 70 a at 3 K and 09 a at 50 K. a. Calculate H vaporization and H subliation. (6 points) b. CalculateH fusion.(4 points) c. resent two equations needed to calculate the triple point pressure and teperature. Explain briefly how these paraeters can be calculated. (5 points) a) Calculate H vaporization and H subliation. vaporization f H ln i R Tf T i f R ln vaporization i H Tf T i a 8.34 J ol K ln vaporization 0539 a = J ol - H 340 K 90 K ( st eq. point; Last eq. with correct nubers point; Answer point) subliation f H ln i R Tf T i f R ln subliation i H Tf T i a 8.34 J ol K ln subliation 70 a = J ol - H 50 K 3 K ( st eq. point; Last eq. with correct nubers point; Answer point) a) H fusion = H subliation H vaporization = J ol J ol - = J ol -. ( st eq. 3 point; Answer point) b) Calculate the triple point pressure and teperature. Fro Exaple roble 7., 8

9 Subliation T H ln (*) ini = 70 a T ini = 3 K (or 09 a at 50 K). ( point) ini R TT Tini vap T H ln (**) ini = 0,539 a, T ini = 90 K (or 74,58 a at 340 K). ( points) ini R TT Tini (*)-(**) Solve it with respect to T T. Then, substitute T T in (*) to obtain T. ( points) 3. [Circle if you choose this] (Original Question 6.39) [ /5] You place.00 ol of NOCl(g) in a reaction vessel. Equilibriu is established with respect to the decoposition reaction NOCl g NOg Cl g. a. Assue that ol of NOCl out of ole is transfored into NO and Cl, present olar fractions of NOCl(g), NO(g), and Cl (g), where can change fro 0 to in this case. (4 points) b. Assuing that the total pressure is, derive an expression for K in ters of the extent of reaction. (3 points) c. Siplify your expression for part (b) in the liit that is very sall. (3 points) d. Assue that K p = 4.5 x 0-3. Calculate and the degree of dissociation of NOCl in the liit that is very sall at 375 K and a total pressure of bar. (4 points) a) Obtain an expression for K in ters of the degree of advanceent. NOCl(g) NO(g) + / Cl (g) Initial nuber of oles Moles present at equilibriu.00 / ( points) Mole fraction present.00 at equilibriu (b) artial pressure at equilibriu, i xi.00 ( point) ( point) We next express K in ters of and. K T eq eq NO Cl eq NOCl.00 9 (3 points)

10 0 (c) if 4 K T (3 points) (d) K K ( points eq with correct nuber. points for answer)

11 3.3 (Original 7.4) Calculate the factor by which the vapor pressure of a droplet of ethanol of radius at 45.0 C in equilibriu with its vapor is increased with respect to a very large droplet. At 45.0 ºC, a bulk vapor pressure 0 for a very large droplet is 6.0 x 0 4 a. The density of ethanol is 79 kg -3 and its olar ass is 3.04 g. The surface tension constant is =.07 x0-3 N - at 98 K. (a) How uch is the surface tension pressure for the sall droplet? (5 points) (b) How uch is the ratio of the vapor pressure of the sall droplet with respect to that for a bulk ethanol 0. (5 points) (c) How uch is actual vapor pressure of the droplet. ( points) (d) How uch is the pressure of the ethanol inside the droplet. (3 points) (a) = (/r) = (x.07x 0-3 N - )/(.63 x 0-9 ) = a (3 points for equation, point for calculation) (b) For a very large droplet, 0, and the vapor pressure is 0 = a. For the sall droplet, the vapor pressure is increased by the factor 3 M kgol 7 ( ) ( ) a 3 r 79. 4kg ln( / 0 ) RT 8. 34Jol K 35K 0 exp( ). 500 ( points for the too equations and point for correct units and points for answer in the botto) (c) =.50 0 = 9.0 x 0 4 a. ( point for answer) (d) inside = + = 9.0 x x 0 7 =.75 x 0 7 a ( point for equation & point for answer).

12 3.4 [Original 8.7] [ /5] Assue that the volatile liquid A and B for an ideal solution. At 73 K, A * =0.400 bar and B * = 0.00 bar. When only a trace of liquid is present at 73 K, y A = (a) Calculate the ole fraction of A (X A ) in the solution. (5 points) (b) Calculate the total pressure above the solution. (5 points) (c) What value would Z A have in order for there to be.0 ol of liquid and 3.0 ol of gas at a total pressure equal to (b)? Use the results fro (a and b) and the lever rule. State what is the lever rule with (Hint: n total liq /n total vap=(y A Z A )/(Z A x A ). (5 points) (a) Calculate the total pressure above the solution. A = y A total = x A * A B = (-X A ) B * y A = A /( A + B ) =X A A */{ X A A * + (-X A ) B *} ( points) x A = y A B */{( B * - A *)y A + A *} ( points; if the previous equation is not shown 4 points) = x 0.00 /{( )x } = 0.50 ( points) (b) total = x A A * + ( - x A ) B * ( 3 points) = 0.50 (0.40 bar) (0.0 bar) = 0.50 bar ( points) Alternatively, total = A * B */( A * + ( B * - A *)y A = 0.50 bar (eq 3 points, calc points) (c) The lever rule is n total liq /n total vap=(y A Z A )/(Z A x A ) or n total liq (Z A x A ) =(y A Z A ) n total vap.0 ol x (Z A x A ) = 3.0 ol x (y A Z A ) (3 points) Z A = (3.0 y A +.0 x A )/( ) = (3.0x x0.50)/( ) = 0.34 ( points)

13 4. Derivation Questions Q-4 points each Q5-6 3 points [ /4] Fill a forula or equation in [Q-Q4] and answer Q5-Q6. This section has soe hint for other questions. 4. We dissolve ole of K 3 O 4 into H O. Assuing that the olecule is copletely ionized in a solution, µ solute = ( + µ µ - ) = [Q] µ + + [Q] µ - Mean ionic cheical potential µ is given by µ = ([Q]µ + + [Q] µ - )/[Q3]. µ = {[Q]µ 0 ++ [Q]RT ln(a + ) + [Q]µ [Q]RT ln(a - )}/[Q3] = µ 0 + RT ln{ [Q4] (a - ) [Q]/[Q3] } = µ 0 + RT ln{a } Fill nubers in Q-Q3. [Q: 3 ] [Q: ] [Q3: 4 ] Fill a forula in Q4 [Q4: a + 3/4 ] 3

14 4. We discuss how vapor pressure can be affected by a radius of a droplet. Starting fro liq = (/r) + vap, we obtain the differential for d liq d vap = d(/r) = d(/r), [] which describes how the pressure change follow the radius change. In the equilibriu state, cheical potential of the two phases should be sae even if the radius of the droplet is changed. d liq = d vap. 0= V, liq d liq V,vap d vap [] By cobining [, ], we obtain [ Q5 ]d vap = d(/r) Using d = V d + [ Q6] dt, at a constant teperature, we obtain [3] Using V, vap >> V, liq, eq. [3] yields V,vap /V, liq d vap = d(/r) [4] V,vap d vap = V, liq d(/r) Assuing that the vapor behaves as an ideal gas, (RT/ vap )d vap = V, liq d(/r) [5] RT ( r ) ( r ) d vap vap V / r, liq 0 d( / r ' ) where the integration for the right side is taken fro 0 to /r and the right side is fro (r = ) to (r). Fill the right answers below. (Q5) (V, vap /V, liq ) (Q6) -S (or S) 4

15 Equations & Constants (You can detach this sheet, if you like) Differentials dln(x)/dx = /x dcos(x)/dx = -Sin(x) dsin(x)/dx = Cos(x) de -x /dx = -e -x Constants L = d 3 = d dt vap S V vap vap H RT vap 5