Chemistry 431 Problem Set 8 Fall 2018 Solutions

Transcription

1 Chemistry 43 Problem Set 8 Fall 208 Solutions. Use able 4. of the text to calculate the equilibrium constant of the reaction NO g + 2 O 2g NO 2g at 25. C and 35. C. r,m G f,m G NO 2g f,m G NO g At 25 C 2. Consider the reaction 5.3 kj mol 87.6 kj mol 36.3 kj mol r,m H f,m H NO 2g f,m H NO g 33.2 kj mol 9.3 kj mol 58. kj mol { K P exp r,mg } { J mol } exp J mol K K K P 2 K P r,mh 2 K P J mol J mol K 298 K 308 K K p PCl 5g PCl 3g + Cl 2g a Show that if one starts with pure PCl 5 and a fraction, α, dissociates, the reaction quotient will be given by α 2 P Q P α 2 P

2 Let n the initial number of moles of PCl 5g n P Cl5 n P Cl3 n Cl2 initial n 0 0 change αn αn αn equilibrium n α αn αn hen n total 2αn + αn + αn P P Cl5 χ P Cl5 P α + α P P P Cl3 P Cl2 χ Cl2 α + α P Q P P P Cl 3 /P P Cl2 /p P P Cl5 /p [α/ + αp/p ] 2 [ α/ + αp/p ] α2 α 2 P P b At 250. C the equilibrium constant for the reaction is K P.78. Calculate α for P 0. bar and P.0 bar at equilibrium. K P α2 P α 2 P α 2 K P α 2 P P P α 2 P + K P K P /2 K P α K P + P/P.78 /2 α /2 α

3 c Calculate r,m G for an equimolar mixture at bar pressure and 250. C. r,m G r,m G + Q P K P + Q P K P + P P Cl 3 /P P Cl2 /P P P Cl5 /P P /3/3 K P + P / J mol K 523K[.78 /3] 7285J mol d Calculate r,m G for 20 per cent dissociation at 250. C and bar pressure. Q P G r,m 8.344J mol K 523K[ ] 6323J mol 3. he following results were obtained for the degree of dissociation, α, of CO 2 in the reaction CO 2g CO g + 2 O 2g at a pressure of.0 bar: K α x x x 0 2 Calculate r,m S for the reaction at 400. K. Let n initial number of moles of CO 2g n CO2 n CO n O2 initial n 0 0 change αn αn αn/2 equilibrium n α αn αn/2 n total αn + αn + 2 αn + α 2 n 3

4 hen hen P O2 2 α P CO2 2 + α P P CO 2α 2 + α P /2α + /2α P α 2 + α P K P P CO/P P O2 /P /2 P CO2 /P 2α/[2 + α]α/[2 + α]/2 2 α/2 + α P P /2 α 3/2 P /2 α2 + α /2 P K P 000K K P 400K K p 2000K r,m G 400K K P 8.344J mol K400K kJ mol K P 400K K P 000K r,mh r,m H 8.344J mol K 000K r,m H 28.7kJ mol r,m S r,mh r,m G J mol 400K 400K 000K 400K 86.43J mol K 4. Gvien the following table for the thermodynamic properties of bromine at 298K f,m H kj mol f,m G kj mol Br 2l 0 0 Br 2g Br g

5 calculate the degree of dissociation α of gas-phase Br 2 at 2000.K and a total pressure of 5.00 bar according to the reaction Br 2g 2Br g. r,m G kj mol 3. kj mol 6.7 kj mol { K P 298 e r,mg / 6700 J mol } exp J mol K K r,m H 2.9 kj mol 30.9 kj mol 92.9 kj mol K 2 K r,mh K J mol J mol K K K 2000 K n Br2 n Br initial n 0 change αn 2αn equilibrium n α 2αn K P P Br/P 2 P Br2 /P n tot n + α 2α/ + α2 P α/ + α 4α α2 α α α2 5. Hydrogen bromide dissociates according to the reaction HBr g 2 H 2g + 2 Br 2g Use able 4. of the text to find the degree of dissociation of HBr at 35. C and 2.0 bar pressure. r,m G 2 3. kj mol 53.4 kj mol kj mol 5 P

6 r,m H kj mol 36.3 kj mol 5.75 kj mol { K P 298 exp r,mg } { J mol } exp J mol K K K P J mol J mol K 298 K 308 K K P Let ninitial number of moles of HBr n HBr n H2 n Br2 initial n 0 0 change αn αn/2 αn/2 equilibrium n α αn/2 αn/2 α n total αn + αn n P HBr αp P H2 P Br2 α 2 P K P [α/2/2 ] 2 α α 2 α 2K P K P Hydrogen iodide gas dissociates according to the reaction HI g 2 H 2g + 2 I 2g At 0. C and.0 bar pressure, the degree of dissociation is α.40, and at 00. C, α.88. Assuming r,m H to be independent of temperature, calculate r,m H, r,m G and r,m S for the reaction at 0. C. As in the previous problem α K P 2 α K P K P

7 r,m G K P J mol K 273 K J K P 2 K P r,mh r,m H J mol K 273 K 373 K r,m H 2038 J mol r,m S r,mh r,m G 2038 J mol 2496 J mol 273 K 7. he gas NO 2 dissociates according to the reaction NO 2g NO g + 2 O 2g J mol K One mole of NO 2g is placed in a vessel, and the gas is allowed to come to equilibrium such that the total pressure is kept fixed at.0 bar. he ratio P NO /P NO2 is measured as a function of temperature and equals.872 at 700K and 2.50 at 800K. Calculate r,m H, r,m G and r,m S for the reaction at 700K. Let r P NO P NO2 n NO2 n NO n O2 initial n 0 0 change αn αn αn/2 equilibrium n α αn αn/2 hen or hen n tot n α + αn + α 2 n + α 2 n P NO α + α/2 P P NO 2 α + α/2 P r α α α r + r at 700 K α 0.47 and at 800 K α 0.7 7

8 Now hen K P P O 2 /P /2 P NO /P P NO2 /P α/2 /2 α P /2 + α/2 /2 α P K P K P r,m G K P J mol K 700 K J r,m H J mol K 700 K 800 K r,m H 5680 J r,m S 5680 J mol 563 J mol 700 K 72.7 J mol K 8. he standard molar enthalpy of formation and molar Gibbs free energy of formation of solid sodium hydride NaH at 298K are given by Given the reaction f,m H 56.3 J mol f,m G 33.5 J mol. NaH s Na s + 2 H 2g Calculate the temperature at which the pressure of hydrogen in equilibrium with NaH s and Na s is 0.0 bar. K P /2 PH2 K P 298 K exp f,mg J mol exp J mol K K K2 r,mh K / J mol J mol K 298 K P 589 K 9. Solid ammonium chloride at 600.K is allowed to come to equilibrium with equimolar amounts of gas phase hydrogen chloride HCl and ammonia NH 3 according to the reaction NH 4 Cl s NH 3g + HCl g. Given the table of thermodynamic data valid at 298.K 8

9 Substance f,m H kj mol f,m G kj mol NH 3g HCl g NH 4 Cl s calculate the partial pressures of ammonia and hydrogen chloride gas in equilibrium with the solid ammonium chloride at 600K. r,m H f,m H NH 3g + f,m H HCl g f,m H NH 4 Cl s 45.9 kj mol 92.3 kj mol 34.4 kj mol 76.2kJ mol r,m G f,m G NH 3g + f,m G HCl g f,m G NH 4 Cl s 6.5 kj mol 95.3 kj mol kj mol 9.kJ mol 900 J mol K P 298 K exp J mol K K K 2 r,mh K 2 K P 600 K J mol J mol K 298 K 600 K K P 600 K 0.38 P HCl P NH3 P P P HCl P NH3 P P P P HCl P NH3 P 0.62 bar 0. he equilibrium pressure of hydrogen gas in the presence of solid lithium hydride and lithium metal according to the reaction LiH s Li s + 2 H 2g is bar at 000. K and 0.80 bar at 200. K. Assuming the enthalpy change for the process is temperature independent, calculate the equilibrium pressure of H 2g in the presence of of solid LiH and Li at 00. K. K P P /2 K P P K P

10 r,mh K P 2 K P r,mh K P K 200. K K 2 r,m H 000. K 00. K K P P P /2 P 0.54 bar. When gas phase molecular iodine dissociates according to the reaction K I 2g 2I g at a total pressure of 0.50 bar, the degree of dissociation of the molecular iodine at equilibrium is α at 000K and α 0.55 at 200K. Assuming the standard enthalpy change for the reaction is independent of temperature, calculate r,m H, r,m G and r,m S for the dissociation reaction at 000K. n I2 n I initial n 0 change αn 2αn equilibrium n α 2αn n tot + αn K P P I/P 2 P I2 /P 2α/ + αp/p 2 α/ + αp/p 4α2 α 2 P P K P 000 K K P 200 K K200 K K000 K r,mh 000 K 200 K r,mh K 200 K r,m H 529 J mol r,m G K P J mol K 000 K J mol r,m S r,mh r,m G 529 J mol J mol 000 K 00.9 J mol K 0

11 2. Phosphorous trihydride dissociates according to the gas-phase reaction PH 3g 4 P 4g H 2g. Measurements of the amount of phosphorous trihydride at equilibrium find that the degree of dissociation is α at 25.0 C and α at 50.0 C when the total pressure in each case is 2.00 bar. Calculate the entropy change for the reaction at 25.0 C assuming the enthalpy change for the reaction is temperature independent. Let n be the initial number of moles of PH 3. hen n P H3 n P4 n H2 initial n 0 0 change αn αn/4 3αn/2 equilibrium n α αn/4 3αn/2 n tot n P H3 + n P4 + n H2 n + 3α/4 K P P 4/P /4 P H2 /P 3/2 P P H3 /P /4 3/2 α/4 3α/2 + 3α/4 + 3α/4 P 3/4 α/ + 3α/4 P K P K P K 2 r,mh K r,mh 298 K r,m H 9733 J mol 323 K r,m G K P J mol K 298 K J mol r,m S r,mh r,m G 9733 J mol 7385 J mol 298. K 57.4 J mol K 3. Liquid nitric acid dissociates into liquid-phase water and gas-phase nitrogen dioxide and oxygen according to the reaction HNO 3l 2 H 2O l + NO 2g + 4 O 2g Pure nitric acid is injected into an evacuated flask, and it is found that at equilibrium, the total pressure of the gas phase species is bar at 323. K and 2.77

12 0 2 bar at 308. K. Assuming the enthalpy change for the reaction is independent of temperature, calculate the entropy change r,m S for the reaction at 308. K. /4 PNO2 PO2 K P P P P tot P NO2 + P O2 5P O K : P O2 5 P tot bar P NO2 4P O bar K P / K : P O2 5 P tot bar P NO2 4P O bar K P / K P 2 K P r,mh r,mh 2 r,m H J mol 308. K 323. K r,m G K P J mol K 308. K J mol r,m S r,mh r,m G J mol 3070 J mol 308. K 34.8 J K 4. At 750.K the pressure of atomic I g in equilibrium with solid iodine according to the reaction I 2s 2I g is 0.30 bar, and the pressure of atomic iodine associated with the same reaction at 850.K is bar. Calculate the pressure of atomic, gas-phase iodine in equilibrium with solid I 2 at 800.K. K750 P K850 P K 2 K r,mh r,mh K r,m H 2760 K 850 K K K K K K P 800 K800 / bar 2

13 5. For the dissociation reaction of gas-phase tungsten hexafluoride into liquid tungsten and fluorine gas WF 6g W l + 3F 2g when the total pressure is 2.00 bar, the degree of dissociation of WF 6g is measured to be α 0.22 at 5650K and α at 5700K. Calculate the entropy change for the reaction at K. n W F6 n F2 initial n 0 change αn 3αn equilibrium n α 3αn χ F2 n tot n + 2α 3α + 2α K P F 2 /P 3 P W F6 /P χ W F6 α + 2α 3α 3 + 2α P 2 α P + 2α K K K 2 K r,mh r,m H J mol K 5650 K r,m H J mol 5700 K r,m G K J mol K 5650 K J mol r,m S r,mh r,m G J mol 5430 J mol 5650 K 299 J mol K 3