Chemistry 192 Problem Set 2 Spring, 2018 Solutions

Transcription

1 Chemistry 192 Problem Set 2 Spring, 2018 Solutions 1. The gas phase species NO 2 and N 2 O 4 equilibrate according to the reaction N 2 O 4(g) 2NO 2(g), and it is found that at 298K in a reaction vessel of fixed volume the equilibrium concentrations of each species are [NO 2 ] M and [N 2 O 4 ] M. Under different nonequilibrum conditions in the same vessel at the same temperature, NO 2 and N 2 O 4 are added such that their partial pressures are P NO bar and P N2 O bar. Under the nonequilibrium conditions, predict whether the reaction will proceed to the right or left. K c [NO 2] 2 [N 2 O 4 ] ( ) K P K c (RT ) ngas ( )(298)( ) Q P P 2 NO 2 P N2 O 4 (0.456) so the reaction proceeds to the right. Q P < K P 2. For the reaction between solid iodine, hydrogen gas and gas-phase hydrogen iodide I 2(s) + H 2(g) 2HI (g) at 298 K, the equilibrium partial pressures of hydrogen and hydrogen iodide are measured to be respectively P H2 32. bar and P HI 4.0 bar. Suppose an initial nonequilibrium mixture of solid iodine, hydrogen gas and hydrogen iodide is prepared at 298 K in a closed 10.0 L container containing 68. grams of hydrogen gas, 352. grams 1

2 of hydrogen iodide gas and 500. grams of solid iodine (sufficient to be in excess). Calculate the concentration equilibrium constant K c for the reaction, and predict whether the reaction will proceed spontaneously to the right or left under the non-equilibrium conditions. K P P HI 2 (4.0) P H2 32. K c K P (RT ) ngas 0.50( ) ( ) mol 68. g 2.00 g [H 2 ] 3.4 M 10.0 L ( ) mol 352. g g [HI] M 10.0 L Q c > K c Q c [HI]2 [H 2 ] so reaction is spontaneous to the left 3. At 500.K and a total pressure of 5.57 bar, it is found that the degree of dissociation at equilibrium of gas-phase ammonia according to the reaction NH 3(g) 1 2 N 2(g) H 2(g) is α In a separate experiment at 500.K, a non equilibrium mixture is prepared by combing 1.00 moles each of gas-phase NH 3, N 2 and H 2 in a 1.00 L flask. Calculate first K P and then K c for the ammonia dissociation reaction, and predict the direction of the reaction for the non equilibrium mixture. Let n 0 the initial number of moles of ammonia. n NH3 n N2 n H2 initial n change αn 0 αn 0 /2 3αn 0 /2 equilibrium n 0 () αn 0 /2 3αn 0 /2 K P P 1/2 N 2 P 3/2 H 2 P NH3 n tot n 0 (1 + α) ( α/2 ) 1/2 ( 3α/2 ) 3/2 1 + α P 1 + α P 1 + α P 2

3 ( ) /2 ( ) 3/ K c K P (RT ) ngas (3.38)[( )(500.)] Q c 1 > K c 4. Consider the reaction at equilibrium reaction is spontaneous to the left PCl 5(g) PCl 3(g) + Cl 2(g). When a certain amount of PCl 5(g) is heated in a 10.0 liter flask at 275. C, analysis shows that at equilibrium the number of moles of each species is n P Cl mol, n P Cl mol and n Cl mol. Calculate K P and K c for the reaction at 275. C. ( ) K c [PCl 3][Cl 2 ] ( 10.0 ) [PCl 5 ] K P K c (RT ) ngas ( )[( )(548)] For the reaction given in problem 4, if for all species at 275. C, 1.00 moles of each species were placed in the 10.0 L flask, determine whether the reaction would be favored to the left or right. ( ) Q c ( 10.0 ) Q c < K c to right 6. Consider the reaction at equilibrium between gas-phase iodine, hydrogen and hydrogen iodide H 2(g) + I 2(g) 2HI (g). At 450.C the concentration equilibrum constant for the reaction is K c (a) Calculate K P at 450.C. K P K c (RT ) ngas K c (RT )

4 (b) If 2.0 moles each of iodine vapor and hydrogen are placed in a 5.0 L flask, and the gases are allowed to come to equilibrium at 450.C, calculate the final total pressure and partial pressures of each gas in the container. H 2 I 2 HI initial 2.0 mol 2.0 mol 0 mol change -x mol -x mol 2x mol equilibrium (2.0-x) mol (2.0 x) mol 2x mol K c [HI]2 [H 2 ][I 2 ] 50.0 ( ) 2x 2 ( 5.0 ) ( ) 2.0 x 2.0 x x 2 4 4x + x 2 46x 2 200x x 200 ± (200) 2 4(46)(200) (2)(46) 200 ± x 2.79, The first solution is > 2 and consequently unphysical. Then n H2 n I2 2.0 mol 1.55 mol 0.44 mol n HI 2x 3.1 mol P H2 P I2 n H 2 RT V 7. For the reaction (0.44 mol)( L bar mol 1 K 1 )(723 K) 5.0 L P HI (3.1 mol)( L bar mol 1 K 1 )(723 K) 37. bar 5.0 L P tot P H2 + P I2 + P HI 48. bar N 2 O 4(g) 2NO 2(g) 5.3 bar it is found that K P at 25.0 C. Calculate the degree of dissociation of N 2 O 4 at 25.0C and total pressures of 1.0 bar and 0.10 bar. N 2 O 4 NO 2 initial n 0 change -αn 2αn equilibrium ()n 2αn 4

5 K P (P NO 2 ) 2 (χ NO 2 P ) 2 P N2 O 4 χ N2 O 4 P n tot ()n + 2αn (1 + α)n χ NO2 n NO 2 n tot 2α 1 + α χ N2 O α 1.0 bar 0.10 bar ( 2α 1 + α P )2 ( 1 + α ) P 4α2 2 P α α α α α α The degree of dissociation (the fraction of the pure substance that dissociates at equilibrium) of NOCl (g) at 298K and a total pressure of 2.00 bar according to the reaction NOCl (g) NO (g) Cl 2(g) is α Calculate the pressure equilibrium constant, K P 298.K. Let n 0 be the initial number of moles of gas-phase NOCl. for the reaction at NOCl NO Cl 2 initial n change -αn 0 αn 0 αn 0 /2 equilibrium n 0 () αn 0 αn 0 /2 5

6 n tot n 0 (1 + α/2) K P P NOP 1/2 Cl 2 (χ NOP )(χ Cl2 P ) 1/2 P NOCl χ NOCl P (α/(1 + α/2))((α/2)/(1 + α/2))1/2 ()/(1 + α/2) P α(α/2) 1/2 ()(1 + α/2) 1/2 P ( /2) 1/2 ( )( /2) 1/ Predict the effects of increased pressure and temperature on the following reactions at equilibrium. (a) CO (g) + H 2 O (g) CO 2(g) + H 2(g) H 41.8 kj mol 1 (b) Answer increase P - no change increase T - to left 2SO 2(g) + O 2(g) 2SO 3(g) H kj mol 1 (c) Answer increase P - to right increase T - to left CaCO 3(s) Ca (s) + CO 2(g) H kj mol 1 Answer increase P - to left increase T - to right 10. At 400.K the concentration equilibrium constant for the reaction HCONH 2(g) NH 3(g) + CO (g) is K c If 10.0 grams of pure gas-phase HCONH 2 are placed in a 10.0 liter flask at 400.K, calculate the total pressure in the flask when equilibrium is reached g n initial mol ( ) g mol Let x be the number of moles of HCONH 2 that has reacted at equilibrium. 6

7 HCONH 2 NH 3 CO initial mol 0 mol 0 mol change -x mol x mol x mol equilibrium (0.222-x) mol x mol x mol [NH 3 ][CO] [HCONH 2 ] (x/10.0) 2 (0.222 x)/ x x 48.4 x x x 48.4 ± [(48.4)2 + 4(10.7)] 1/2 48.6, n tot mol x mol + 2x mol mol + x mol mol P n totrt V (0.442 mol)( L bar mol 1 K 1 )(400. K) 10.0 L 1.47 bar 11. When metallic lead is added to a solution of Cr 3+ (aq) the following reaction occurs Pb (s) + 2Cr 3+ (aq) Pb 2+ (aq) + 2Cr2+ (aq) with associated equilibrium constant K c (a) If solid lead is added to a M Cr 3+ aqueous solution, find the final concentrations of all ions in the system. K c [Pb2+ ][Cr 2+ ] 2 [Cr 3+ ] 2 [Cr 3+ ] [Pb 2+ ] [Cr 2+ ] initial M 0 M 0 M change -2x M x M 2x M equilibrium ( x) M x M 2x M x(2x) ( x) 2 Because K c is small, we can ignore the term 2x in the denominator. Then Then 4x x M [Cr 3+ ] M 2x 0.20 M to 2 significant figures, justifying our assumption. [Pb 2+ ] x M 7 [Cr 2+ ] 2x M

8 (b) If 100 ml of water are added to the solution at equilibrium, predict the direction that the equilibrium would be shifted. All concentrations are decreased, and by LeChâtelier s principle, the reaction shifts to the right. 12. At 145.K the the degree of dissociation of ozone in the gas-phase decomposition reaction O 3(g) 3 2 O 2(g) at a total pressure of P 1.00 bar is α Calculate the concentration equilibrium constant K c of the dissociation reaction. n O3 n O2 initial n 0 0 change -αn 0 (3/2)αn 0 equilibrium ()n 0 (3/2)αn 0 χ O2 (3/2)α 1 + α/2 ( (3/2)α 1 + α/2 P K P n tot n 0 (1 + α/2) ) 3/2 χ O3 1 + α/ α/2 P K c K P (RT ) ngas ( )( ) At a temperature of 452K gas-phase isopropyl alcohol dissociates into gas-phase acetone and hydrogen according to the reaction 3 (CH 3 ) 2 CHOH (g) (CH 3 ) 2 CO (g) + H 2(g). At P 2.00 bar and T 452K, the degree of dissociation isopropyl alcohol is measured to be α Calculate the concentration equilibrium constant K c for the reaction. n (CH3 )2CHOH n (CH3 ) 2 CO n H2 initial n change αn 0 αn 0 αn 0 equilibrium n 0 () αn 0 αn 0 8

9 n tot n 0 () + n 0 α + n 0 α n 0 (1 + α) K P P (CH 3 ) 2 COP H2 P (CH2 ) 2 CHOH ( )2 α 1 + α P ( ) 1 + α P α 2 P (0.182)2 1 (0.182) K c K P (RT ) n (0.0685)[( )(452)] The gas-phase decomposition of antimony pentachloride into gas-phase antimony trichloride and chlorine gas SbCl 5(g) SbCl 3(g) + Cl 2(g) has a concentration equilibrium constant K C at a temperature of 521. K. A sample of pure SbCl 5 gas is placed in a reaction vessel of fixed volume at T 521.K, and when the system attains equilibrium, the total pressure is measured to be 3.51 bar. Calculate the equilibrium degree of dissociation α (i.e. the fraction dissociated) of antimony pentachloride in the reaction vessel. K P K C RT ( )( )(521.) 1.08 Let n 0 be the initial number of moles of SbCl 5. n SbCl5 n SbCl3 n Cl2 initial n change αn 0 αn 0 αn 0 equilibrium n 0 () αn 0 αn 0 n tot n 0 (1 + α) K P P SbCl 3 P Cl2 χ SbCl 3 P χ Cl2 P P SbCl5 χ SbCl5 P α 1 + α P α 1 + α P α α P P 2 α 2 (3.51) 1.08 α

10 15. The equilibrium behavior of the gas-phase reaction P 4(g) 2P 2(g) is studied at 1325.K, and the concentration equilibrium constant is measured to be K C Calculate the equilibrium degree of dissociation α of P 4 at 1325.K and a total pressure of 2.00 bar. K P K C (RT ) ngas ( )[( )(1325)] n P4 n P2 initial n 0 0 change -αn 0 2αn 0 equilibrium ()n 0 2αn n tot n 0 (1 + α) ( )2 2α 1 + α P 1 + α P 4α 2 P 8.00α2 2 2 α α