Chem 1B, Test Review #2
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1 1. The following kinetics data were obtained for the reaction: Expt.# 2NO(g) + Cl 2 (g) 2NOCl(g) [NO] 0 (mol/l) [Cl 2 ] 0 (mol/l) Initial Rate, (mol/l.s) x x x ? (a) Determine the rate law for this reaction and calculate the rate constant, k (give appropriate unit). (b) What is the initial rate when the concentrations are [NO] 0 = 0.40 M and [Cl 2 ] 0 = 0.20 M? 2. The rate law for the reaction: 2NO(g) + 2H 2 (g) N 2 (g) + 2H 2 O(g), was studied by following the change in concentration of individual reactants as a function of time, and then appropriate linear plots were obtained for each reactant. When the starting concentrations of NO and H 2 were 2.0 x 10 3 M and 2.0 M, respectively, a plot of 1/[NO] versus time yields a straight line with slope = 3.2 x 10 3 M 1.s 1. However, when the starting concentrations of NO and H 2 were 2.0 M and 2.0 x 10 3 M, respectively, a plot of ln[h 2 ] versus time yields a straight line with slope = -6.4 x 10 3 s 1. Both experiments were carried out at the same and constant temperature. (a) Deduce the rate law for the above reaction. (b) Calculate the overall rate constant for the reaction and give appropriate unit for the rate constant. (c) Calculate the rate at the same temperature when the concentrations of NO and H 2 are both 0.10 M. 3. The re-arrangement of methyl isonitrile (CH 3 NC) to methyl cyanide (CH 3 CN): CH 3 NC CH 3 CN, follows first order rate law with rate constant, k = 3.3 x 10 3 s 1 at 250 o C. (a) What is the half-life for this reaction at 250 o C? (b) If the initial concentration of CH 3 NC is M, what are the concentrations of CH 3 NC and CH 3 CN after the reaction has occurred for 10.0 minutes? (c) How long would it take for 90.0% of the original amount of CH 3 NC to undergo re-arrangement? 4. The reaction: N 2 O 4 (g) 2NO 2 (g) has H o = 58 kj. This reaction follows first order rate law and the rate constants determined at two different temperatures are: k 1 = 4.5 x 10 2 s 1 at 315 K and k 2 = 1.0 x 10 1 s 1 at 324 K. (a) Calculate the activation energy, E a, for the decomposition of N 2 O 4. (b) What is the activation energy for the reversed reaction: 2NO 2 (g) N 2 O 4 (g)? (c) Assuming that the activation energy is independent of the reaction temperature, calculate the rate constant for the decomposition of N 2 O 4 at 25 o C. (R = J/mol.K) 5. The reaction: 2NOBr(g) 2 NO(g) + Br 2 (g) has the rate law: Rate = k[nobr] 2 (a) At a certain temperature it takes 45.0 s for the concentration of NOBr to decrease from M to M. Determine the rate constant k (with correct unit) for the decomposition of NOBr at that temperature. (b) What is the half-life for this reaction if [NOBr] 0 = M? 1
2 6. The following mechanism has been proposed for the reaction between NO and Cl 2 gases: Step 1: NO + Cl 2 NOCl 2 (fast, equilibrium) Step 2: NOCl 2 + NO 2NOCl (slow, rate-determining) (a) Write the net equation for the overall reaction. (b) What is the molecularity of the rate-determining step? (c) Identify all reaction intermediates. (d) Derive the rate law for the reaction. 7. A mL aliquot of saturated solution of calcium iodate, Ca(IO 3 ) 2, is titrated with M Na 2 S 2 O 3 solution in the presence of excess KI and H 2 SO 4, using starch as indicator. The reaction is as follows: IO 3 (aq) + 6 S2 O 3 2 (aq) + 6 H 3 O + (aq) I - (aq) + 3 S 4 O 6 2 (aq) + 9 H 2 O(l) (a) If ml of Na 2 S 2 O 3(aq) were needed to reach the end-point, calculate the concentration of IO 3 in the saturated solution? (b) What is the concentration of Ca 2+ in the solution? (c) Calculate the solubility (in mol/l) and K sp of Ca(IO 3 ) 2. Ca(IO 3 ) 2 (s) Ca 2+ (aq) + 2 IO 3 (aq) 8. A saturated solution of Ca(OH) 2 has ph = (a) Determine the solubility (in mol/l) and K sp of calcium hydroxide. (b) How many grams of Ca(OH) 2 will dissolve in 1.0 L of solution buffered at ph 12? 9. The solubility of silver phosphate, Ag 3 PO 4, is g/l. (a) What is the solubility of Ag 3 PO 4 in mole per liter? (b) Calculate the K sp of Ag 3 PO A 20.0-mL solution of 0.20 M Pb(NO 3 ) 2 is added to 30.0 ml of 0.20 M NaBr. (a) How many grams of PbBr 2 precipitate will be formed? (b) What is the concentrations of each of the following ions: Pb 2+, Br, Na +, and NO 3, in the solution saturated with PbBr 2 (K sp = 4.6 x 10 6 ) 11. Given that: AgCl(s) Ag + (aq) + Cl (aq); K sp = 1.6 x and Ag + (aq) + 2NH 3 (aq) Ag(NH 3 ) 2 + (aq); Kf = 1.7 x 10 7 (a) What is K c for the following equilibrium? AgCl(s) + 2NH 3 (aq) Ag(NH 3 ) 2 + (aq) + Cl (aq); (b) Will precipitate of AgCl form if 2.0 ml of 0.10 M AgNO 3, 2.0 ml of 0.10 M NaCl and 4.0 ml of de-ionized water are mixed in the same container? (c) Will precipitate of AgCl form if 2.0 ml of 0.10 M AgNO 3, 2.0 ml of 0.10 M NaCl and 4.0 ml of 2.0 M NH 3 are mixed in the same container? (d) How many grams of AgCl will dissolve in 500. ml of 2.0 M NH 3 solution? 2
3 12. Under what temperature conditions (high or low) is each of the following reactions spontaneous under standard conditions? (a) H 2 C CH 2 (g) + H 2 (g) CH 3 CH 3 (g); (b) CH 4 (g) + H 2 O(g) CO(g) + 3 H 2 (g); (c) N 2 (g) + 2H 2 (g) N 2 H 4 (l); (d) CH 4 (g) + 2 O 2 (g) CO 2 (g) + 2H 2 O(g); H o = -137 kj H o = +206 kj H o = +51 kj H o = -803 kj 13. Given the following Thermodynamic data: CO 2 (g) H 2 O(l) NH 3 (g) CO(NH 2 ) 2 (s) H o f (kj/mol): S o (J/K.mol): (a) Calculate H o, S o, and G o for the following reaction and predict if it is spontaneous at 25 o C. CO 2 (g) + 2NH 3 (g) CO(NH 2 ) 2 (s) + H 2 O(l) (b) Determine whether the reaction will become spontaneous at 75 o C when carried out under standard condition? (Assume H o and S o do not change with temperature.) 14. Given the following thermodynamic data for selected substances: Substances: H 2 (g) H 2 O(g) CH 4 (g) CO(g) H o f(kj/mol): S o (J/K.mol): (a) Calculate H o, S o, and G o for the following reaction at 25 o C and predict whether the reaction is spontaneous at 25 o C under standard partial pressure condition. CH 4 (g) + H 2 O(g) CO(g) + 3H 2 (g) (b) Calculate the transition temperature that would make the above reaction to become spontaneous above that temperature. 15. Given the following reactions: 2NO 2 (g) 2NO(g) + O 2 (g); 2SO 2 (g) + O 2 (g) 2SO 3 (g); G o = kj G o = kj Calculate G o and K p for the following reaction at 25 o C? Indicate whether the forward reaction is spontaneous or nonspontaneous at 25 o C under standard condition. SO 2 (g) + NO 2 (g) SO 3 (g) + NO(g); 3
4 16. For liquid-vapor equilibrium, such as CS 2 (l) CS 2 (g), the equilibrium constant K = P CS2, where P CS2 is G o the equilibrium vapor pressure of CS 2 at any given temperature. Given that lnk = ( ), derive a RT linear equation for lnp in terms of H o, S o, R and T, where R is the constant (=8.314 J/K.mol) and T is temperature in Kelvin. The vapor pressures of carbon disulfide are collected at various temperature, and a linear plot of lnp CS2 versus 1/T is obtained with slope = x 10 3 K and the intercept is (a) Calculate the enthalpy and entropy change ( H o vap and S o vap) for the following liquid-vapor equilibrium: CS 2 (l) CS 2 (g) (b) Determine the boiling point of carbon disulfide (in o C) at an atmospheric pressure of 1.00 atm. (c) What is the boiling point of CS 2 in Denver, Colorado, where the atmospheric pressure is atm? 17. For the reaction: 2NOCl (g) 2NO (g) + Cl 2(g), H o f (kj/mol): S o (J/mol.K): (a) Calculate H o, S o, G o, and the equilibrium constant, K p, at 298 K. (b) Is the reaction spontaneous at 25 o C? (c) At what temperature the reaction will become spontaneous when carried out under standard condition? 18. For the following reactions, their free energy ( G o ) are given as follows: C(s) + O 2 (g) CO 2 (g); CO(g) + ½ O 2 (g) CO 2 (g); 2Fe(s) + 3 / 2 O 2 (g) Fe 2 O 3 (s); G o = -394 kj G o = -257 kj G o = -740kJ Pb(s) + O 2 (g) PbO 2 (g); G o = -217 kj Determine whether or not each of the following reaction is spontaneous: (a) 2Fe 2 O 3 (s) + 3C(s) 4Fe(s) + 3CO 2 (g); (b) Fe 2 O 3 (s) + 3CO(s) 2Fe(s) + 3CO 2 (g); (c) PbO 2 (s) + C(s) Pb(s) + CO 2 (g); (d) PbO 2 (s) + 2CO(s) Pb(s) + 2CO 2 (g); (e) 2Fe 2 O 3 (s) + 3Pb(s) 4Fe(s) + 3PbO 2 (s); (f) 3PbO 2 (s) + 4Fe(s) 3Pb(s) + 2Fe 2 O 3 (s); 4
5 Answers: 1. (a) k = 0.32 L.mol 1.s 1 ; (b) Rate = 1.6 x 10 3 mol/l.s 2. (a) Rate = k[no] 2 [H 2 ]; (b) 1.6 x 10 3 L 2.mol 2.s 1 ; (c) Rate = 1.6 x 10 6 mol/l.s 3. (a) 210 s; (b) M; (c) 698 s = 11.6 minutes. 4. (a) E a = 75 kj/mol; (b) E ar = 17 kj; (c) k (298) = 8.8 x 10 3 s (a) k = L.mol 1.s 1 ; (b) 314 s 6. (a) 2NO + Cl 2 2NOCl; (b) bimolecular; (c) NOCl 2 ; (d) Rate = k[no] 2 [Cl 2 ] 7. (a) [IO 3 ] = M; (b) [Ca 2+ ] = M; (c) Solubility = 5.6 x 10 3 mol/l; K sp = 7.1 x Solubility = 6.9 x 10 3 ; K sp = 1.3 x 10 6 ; (b) 0.96 g 9. (a) 1.8 x 10 5 (b) K sp = 2.6 x (a) 2.2 g of PbBr 2 ; [Pb 2+ ] = M; [Br ] = M ; [Na + ] = 0.12 M; [NO 3 ] = 0.16 M; 11. (a) K c = 2.7 x 10 3 ; (b) AgCl ppt forms; Q sp = 6.3 x 10 4 > K sp ; (c) No AgCl ppt; Q c = 6.3 x 10 4 < K c ; (d) 6.8 g of AgCl 12. (a) spontaneous at low temperature; (b) spontaneous at high temperature; (c) not spontaneous at all temperature; (d) spontaneous at all temperature. 13. (a) H o = -133 kj; S o = -425 J/K; G o = kj at 25 o C; the reaction is spontaneous at 25 o C; (b) At 75 o C, G o = 14.9 kj; the reaction is not spontaneous at 75 o C.) 14. (a) H o = kj; S o = 216 J/K; G o (25) = kj; the reaction is not spontaneous at 25 o C; (b) Transition temperature, T r = K (681.5 o C); the reaction will become spontaneous above 682 o C) 15. G o = kj; K p = 1.48 x Spontaneous at 25 o C under standard condition) 16. (a) H o vap = 27.6 kj; S o vap = 86.5 J/K; (b) T b = 319 K = 45.9 o C; (c) T b = K = 40.4 o C. 17. (a) H o = 77.2 kj; S o = 121 J/K; G o = 41.1 kj; K p = 6.2 x 10 8 ; (b) Not spontaneous at 25 o C under standard condition. (c) T > 638 K (reaction becomes spontaneous at temperature above 638 K 18. (a) G o = 298 kj, not spontaneous; (b) G o = -31 kj, spontaneous; (c) G o = -177 kj, spontaneous; (d) G o = -297 kj, spontaneous; (e) G o = 829 kj, not spontaneous; (f) G o = -829 kj, spontaneous 5
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