Final Exam Chem 260 (12/20/99) Name (printed) Signature

Final Exam Chem 260 (12/20/99) Name (printed) Signature

1. For the reaction, (14 pts total) C(graph) + CO 2 (g) 2 CO(g) (a) Write the equilibrium constant expression: (2 pts) K = P CO 2 P CO2 (b) Using the following thermodynamic data, calculate the equilibrium constant at 298 K: f H f G S C p,m kj/mol kj/mol J-mol -1 -K -1 J-mol -1 -K -1 CO(g) -110.52-137.15 197.56 29.14 C(graph) 0.0 0.0 5.74 8.53 CO2(g) -393.51-394.36 213.63 37.11 rg = + 120.06 kj rg = - RT lnk = -8.314 * 298 * ln K= + 120.06 x10 3 J K = 9.0 x10-22 (6 pts) (c) In a non-equilibrium reaction mixture, PCO2=0.23 bar and PCO = 12.2 bar. What is r G for this mixture? (6 pts) rg = rg + RT ln Q = 120.06 x10 3 + 8.314*298*Ln (12.2 2 / 0.23) =136. 10 kj.

2. NO 2 (g), N 2 O(g), O2(g), and NO(g) react as shown below. The following initial partial pressures of reactants and products are placed in a reaction vessel at T=450 K, where they come to equilibrium. Calculate the equilibrium partial pressures if K=0.009 at 450 K. (10 pts) NO 2 (s) + 1/2 N 2 O(g) NO(g) + 1/2 O 2 (g) K = 0.009 p(initial): 2.00 bar 1.00 bar 0.50 bar 0.2 bar p(eq): 2.00-2x 1.00-x 0.50+2x 0.2+x x = increase in pp of O2 at equilibrium (You may give as your answer an algebraic expression for an unknown x. You do not need to solve for the numerical values of the partial pressures, but you must give a proper definition of x, and a correct equilibrium expression in terms of x.).009 = (0.50+2x) (0.2+x) 1/2 / (2.00-2x) (1.00-x) 1/2 This form (or its equivalent) is sufficient for full credit. Solving gives x=-0.18. (Minus sign means P(O 2 ) decreases). P(O 2 ) = 0.182 bar, etc.

3. A closed container holds a solution of salt water (aqueous NaCl), NaCl(s), ice, and water vapor in equilibrium with each other (see below). (a) How many components (C), phases (P), and degrees of freedom (F) does this system have? (Graded right-wrong: 3 max, 0 min) C = 2 P = 4 F = 0 (3 pts) (b) What is true concerning chemical potentials in this system? (Graded Right-Wrong, 2 pts each part) (4 pts) T _x F µ(h 2 O,vapor) = µ(h 2 O,solution) = µ(h 2 O,ice) T F _x µ(na + (aq)) = µ(cl - (aq)) = µ(h 2 O(solution)) (3 pts) (c) A small amount of solid NaCl is added to this system. After this addition, the system is brought to equilibrium. The container is thermally insulated from the surroundings. (Graded right-wrong: 3 pts max, 0 min) Which of the following occurs? T F _x The pressure of the vapor phase increases. T F _x The concentration of NaCl(aq) in solution increases. T F _x The temperature increases. vapor ice Aqueous NaCl solution NaCl(s)

4. The boiling point diagram for a HCl/ water mixture at p=1 bar is shown below. (10 pts total) A mixture that is 65 mol% HCl is fractionally distilled: a) What name is given to the liquid mixture of composition labelled "A" in the plot? (the name is on the list of terms) azeotrope (2 pt) b) What is the composition of the liquid that remains in the distillation flask at the end of the distillation process? (2pts) circle one: (a) pure HCl (b) pure water (c) liquid "A" c) What is the composition of the distillate (the liquid that distills off and is collected by the condenser? (2pts) circle one: (a) pure HCl (b) pure water (c) liquid "A" d) Show on this plot how X HCl and T b of the boiling liquid in the distillation flask change during the distillation process. ( Label this curve "B") (2pts). (In other words, show how the boiling point and composition of the liquid change during distillation.) e) A X HCl =0.65 mixture of HCl/water starts to boil at 1 bar pressure. What is the approximate composition of the vapor phase that is in equilibrium with the boiling mixture? (2pts) T b ( C) i) XHCl = 0.00 ii) XHCl = 0.31 120 A iii) XHCl = 0.65 iv) XHCl = 0.88 v) XHCl = 1.00 100 80 H 2 O X HCl HCl

5. Consider the following two changes of state: (i) CaCO 3 (s, 220K,1 bar) -> (ii) CaCO 3 (s, 298K,1 bar) -> (iii) CaO(s, 298K,1 bar) + CO 2 (g, 298K,1 bar) Give signs and magnitudes of the indicated thermodynamic quantities. You may assume that gases are ideal, and that solids and liquids have negligible molar volumes. Relevant thermodynamic data: f H f G S C p,m kj/mol kj/mol J-mol -1 -K -1 J-mol -1 -K -1 CaCO 3 (s) -1206.9-1128.8 92.9 81.88 CaO(s) -635.09-604.03 39.75 42.80 CO 2 (g) -393.51-394.36 213.63 37.11 (a) For (i)->(ii), give signs for: (8 pts) w 0 q + H + S + (b) For (ii)->(iii), give signs for: (10 pts) w - q + U + S + G + (c) For (ii)->(iii), is U (more positive, equal to, more negative) than H? (circle one, 2 pts)

(d) Calculate H for process (i) -> (ii): (6 pts) H = n C p,m T = 1 * 81.88 * (298-220) = +6.39 kj (e) Calculate w for process (ii) -> (iii). (6 pts) w = - p ext * V = - p(co 2 ) * V = - n R T = -1 * 8.314 * 298 = - 2.50 kj (f) Calculate S for process (ii) -> (iii) (6 pts) S = (+39.75) + (+213.63) - (+92.9) = +160.48 J-mol -1 -K -1

6. The Lennard-Jones equation is V = 4ε{(σ/R) 12 - (σ/r) 6 }. (3 pts) The term containing -(σ/r) 6 describes which interaction? a) repulsion of atoms b) dispersion forces c) hard sphere potential d) permanent dipole forces e) ionic attraction 7. For each of the following equations, give the name of the indicated symbol. (All names are listed with the terms in bold. The equations are among the numbered eqns.) (8 pts total, 2 pts each) Give the name of: (i) V = (1/2) k (R-Re) 2 (ii) E J = h c B J(J+1) (iii) Ev = (v +1/2) h ν (iv) I = µ R 2 k: force constant B: rotational constant h: Planck's constant I: moment of inertia 8. For the wavefunction of an electron in a quantum mechanical atom, which is always true? (graded right - wrong, 4 pts max, 0 pts min) T F x the wavefunction is proportional to the electron density T F x the principal quantum number is proportional to energy T x F the number of angular nodes is given by l T F x the wavefunction must go to zero at the nucleus and at r=infinity

9. The experimental isotherms of CO 2 are shown at several temperatures. A sealed 0.16 Liter vessel contains 1.00 mole of CO 2 at a pressure of 60.0 bar. Find this point on the plot of isotherms. Which best describes the contents of the vessel? (6 pts) a) CO 2 gas only b) CO 2 liquid only c) CO 2 critical fluid d) CO 2 gas plus CO 2 liquid e) not defined without a temperature 10. An enclosed container of V=1.60 L contains a mixture of 1.00 g CO 2 (g) plus an unknown amount of H 2 (g). If the total pressure is 720 torr and T=0 C, how many grams of H 2 (g) are in the flask? (8 pts) a) 0.072 g b) 0.090 g c) 0.128 g d) 0.144 g z) 0.180 g p V = (nh2 + nco2) * R * T (720/760) atm * (1.01325 bar/atm) *(10 5 Pa/bar)* 1.60 L * (10-3 m 3 /L) = (nh2 + (1.00/44.0)) *8.314 * 273 nh2 = 0.045 moles = 0.090 grams

11. The IR spectrum of HCl has one intense band at 2890 cm -1. (8 pts) (a) From the equation sheet, write down the equation(s) you would need to analyze the Raman spectrum in terms of the molecular information it contains. (4 pts) Eq. 24 or 27 from Chapter 11 (b) What molecular property(ies) can be calculated from this number? (4 pts) (Assume that you have the physical constants provided on the front page of this exam.) (graded right - wrong, 4 max; more than one response may be correct.) yes: no: x the moment of inertia yes: no: x the O 2 bond length yes:_x no: the force constant of the O=O bond yes:_x no: the vibrational frequency in Hertz 12. The microwave spectrum of CO(g) contains a sequence of four sharp lines at (5 pts) ν = 4.20 cm -1, 8.40 cm -1, 12.60 cm -1, 16.80 cm -1. From the equation sheet, write down the equation(s) you would need to analyze this spectrum in terms of the molecular information it contains. For full credit, you need: (all from Chapt 11) eq. 14 (or eq. 17, or eq 19, or eq 20) plus eq 15 plus eq 16 2 pts for one correct eqn, 4 pts for two correct eqns, 5 pt for 3 correct eqns.

13. Draw the following diagrams. (12 pts, 4 pts each) a) contour surface for 3d xy b) cloud picture of a 3s orbital (label the axes) y spherically symmetric cloud with two internal radial nodes; falls off exponentially toward infinity - + + - x c) Radial wavefunction of a 3 p x orbital ψ x 14. The molecule to the right contains: (4 pts) a) How many σ-bonds? 10 ; π-bonds? 2 :O: b) How many sp 3 hybrid orbitals are there (total) H C O H \ / on all C, N, O atoms? 8 (4 on N, 4 on O) C=C / \ c) How many sp 2 are there (total) H :N H on all C, N, O atoms? 12 (3 on each of 3 C+1 O) H

15. The MO energy level diagram of a certain diatomic molecule is shown. (14 pts total) 2p 2p 2s 2s X atom 1 MO's atom 2 a) Which diatomic is described by this MO diagram? (3 pts) (i) N 2 (ii) NO (iii) O 2 (iv) CO (v) C 2 b) Is the orbital marked X bonding or anti-bonding? bonding (2 pts) c) The molecule has unpaired electrons. What physical property results from this fact? (this is one of the terms in bold) _paramagnetic (2 pts) d) What is the orbital symbol of the LUMO (e.g., 1σ g )? 2π g * (3 pts) e) Sketch the boundary surface for the MO labelled "X" (4 pts) +

16. For the cell reaction (28 pts total) 2 Ag (s) + 1/2 O 2 (g, 0.2 bar) + 2 H + (ph 4.0) + 2 Cl - (0.013 M) H 2 O (l) + 2 AgCl (s) a) Write the balanced half reactions (4 pts) 2e - + 1/2 O 2 (g, 0.2 bar) + 2 H + (ph 4.0) H 2 O (l) 2 Ag (s) + 2 Cl - (0.013 M) 2 AgCl (s) + 2 e - Identify the oxidizing agent: O2(g) ; the reducing agent: Ag(s) (2 pts) b) Sketch a cell in which this cell reaction occurs: (8 pts) Ag(s) Pt electrode O 2 (g), 0.2 bar AgCl(s) coating Cl - (0.013 M) spectator ions not shown H + (10-4 M)

c) Diagram the cell: (4 pts) Ag(s) AgCl(s) Cl - (0.013 M) H + (1.0 x10-4 M) O 2 (g, 0.2 bar) Pt d) What is E for the cell? (5 pts) E cell = E R - E L = +1.23 - (+0.22) = +1.01 V e) Calculate the equilibrium constant for the cell reaction. (5 pts) G = -RT ln K = - F E cell = 2 ln K = F E cell / RT = 2*96485*(+1.01) / (8.314*298) = 78.6 K = 1.5 x10 34

Chemical Kinetics 17. The rate of the reaction 2 Ce 4+ + Sn 2+ + 4 OH - 2 Ce 3+ + SnO 2 (s) + 2 H 2 O has been measured at various initial concentrations (in molarity) of the reactants: [Ce 4+ ] [Sn 2+ ] [OH - ] Initial Rate 1.1 x10-5 1.8 x10-5 1.0 x10-6 2.4 x10-3 3.3 x10-5 1.8 x10-5 1.0 x10-6 7.2 x10-3 3.3 x10-5 3.6 x10-5 1.0 x10-6 7.2 x10-3 3.3 x10-5 1.8 x10-5 1.0 x10-7 7.2 x10-2 From these data, find the experimental rate law for this reaction. (5 pts) a) rate = k expt [Ce 4+ ] 1 [Sn 2+ ] 0 [OH - ] 1 b) rate = k expt [Ce 4+ ] 1 [Sn 2+ ] 1 [OH - ] 1 c) rate = k expt [Ce 4+ ] 2 [Sn 2+ ] 1 [OH - ] 1 d) rate = k expt [Ce 4+ ] 2 [Sn 2+ ] 2 [OH - ] 1 e) rate = k expt [Ce 4+ ] 1 [Sn 2+ ] 0 [OH - ] -1 f) rate = k expt [Ce 4+ ] 1 [Sn 2+ ] 2 [OH - ] -1 18. The reaction rate can be defined by two of the following quantities, but not by the other two. Which two define the rate? (Both responses must be correct for credit) (4 pts) a) rate = d[ce 4+ ] dt c) rate = (1/2) d[ce3+ ] dt b) rate = (1/2) d[ce3+ ] dt d) rate = (1/ 4) d[oh ] dt

19. For the reaction Cl 2 (g) + CHCl 3 (g) CCl 4 (g) + HCl (g) (8 pts) the following mechanism is proposed: k 1, k -1 Cl2 2 Cl fast, eq k 2 CHCl 3 + Cl CCl 3 + HCl slow k 3 CCl 3 + Cl CCl4 fast What rate law is consistent with this,mechanism? rate = k 2 [CHCl 3 ] [Cl] K eq = k 1 /k -1 = [Cl] 2 / [Cl 2 ] Ans: rate = k 2 K eq 1/2 [CHCl 3 ] 1 [Cl2] 1/2 20. For a second order reaction, what are the correct units of the rate constant, k? (3 pts) A + B -> products, rate = k [A] [B] a) mol-l -1 b) L-mol -1 c) mol 2 -:L -1 -s d) mol 2 -L -2 -s -1 e) L-mol -1 -s -1