The Advanced Placement Examination in Chemistry. Part II - Free Response Questions & Answers 1970 to Equilibrium

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1 The Advanced Placement Examination in Chemistry Part II - Free Response Questions & Answers 1970 to 005 Equilibrium Teachers may reproduce this publication, in whole or in part, in limited print quantities for non-commercial, face-to-face teaching purposes. This permission does not apply to any third-party copyrights contained within this publication. Advanced Placement Examination in Chemistry. Questions copyright by the College Entrance Examination Board, Princeton, NJ Reprinted with permission. All rights reserved. apcentral.collegeboard.com. This material may not be mass distributed, electronically or otherwise. This publication and any copies made from it may not be resold. Portions copyright by Unlimited Potential, Framingham, MA Compiled for the Macintosh and PC by: Harvey Gendreau Framingham High School 115 A Street Framingham, MA (fax) (home office) hgendrea@framingham.k1.ma.us hgendreau@rcn.com Requests for copies of these questions and answers as attachments for either the Macintosh or the PC (MS-Office files) should be sent to: apchemfiles@apchemistry.com. Please include your name, school, school phone, name of principal/headmaster and school website address. Don t forget to include the file format you want, Mac or PC.

2 1977 D For the system SO (g) + O (g) SO 3 (g), H is negative for the production of SO 3. Assume that one has an equilibrium mixture of these substances. Predict the effect of each of the following changes on the value of the equilibrium constant and on the number of moles of SO 3 present in the mixture at equilibrium. Briefly account for each of your predictions. (Assume that in each case all other factors remain constant.) (a) Decreasing the volume of the system. (b) Adding oxygen to the equilibrium mixture. (c) Raising the temperature of the system. (a) As volume decreases, pressure increases and the reaction shifts in the direction of fewer molecules (less volume; more SO 3 ) to relieve the stress. Value of K eq does not change. (b) Additional O disturbs the equilibrium and SO 3 is formed to relieve the stress. Value of K eq does not change. (c) Increase in temperature shifts the reaction to the left to use up some of the added heat. Less SO 3 remains. Value of K eq decreases due to the relative greater increase in the rate of the endothermic reaction (reaction to the left) D NH 4 Cl(s) NH 3 (g) + HCl(g) H +4.1 kilocalories Suppose the substances in the reaction above are at equilibrium at 600K in volume V and at pressure P. State whether the partial pressure of NH 3 (g) will have increased, decreased, or remained the same when equilibrium is reestablished after each of the following disturbances of the original system. Some solid NH 4 Cl remains in the flask at all times. Justify each answer with a one-or-two sentence explanation. (a) A small quantity of NH 4 Cl is added. (b) The temperature of the system is increased. (c) The volume of the system is increased. (d) A quantity of gaseous HCl is added. (e) A quantity of gaseous NH 3 is added. Equilibrium page (a) P NH3 does not change. Since NH 4 Cl(s) has constant concentration (a 1), equilibrium does not shift. (b) P NH3 increases. Since the reaction is endothermic, increasing the temperature shifts the equilibrium to the right and more NH 3 is present. (c) P NH3 does not change. As V increases, some solid NH 4 Cl decomposes to produce more NH 3. But as the volume increases, P NH3 remains constant due to the additional decomposition. (d) P NH3 decreases. Some NH 3 reacts with the added HCl to relieve the stress from the HCl addition. (e) P NH3 increases. Some of the added NH 3 reacts with HCl to relieve the stress, but only a part of the added NH 3 reacts, so P NH3 increases A Ammonium hydrogen sulfide is a crystalline solid that decomposes as follows: NH 4 HS(s) NH 3 (g) + H S(g) (a) Some solid NH 4 HS is placed in an evacuated vessel at 5ºC. After equilibrium is attained, the total pressure inside the vessel is found to be atmosphere. Some solid NH 4 HS remains in the vessel at equilibrium. For this decomposition, write the expression for K P and calculate its numerical value at 5ºC. (b) Some extra NH 3 gas is injected into the vessel containing the sample described in part (a). When equilibrium is reestablished at 5ºC, the partial pressure of NH 3 in the vessel is twice the partial pressure of H S. Calculate the numerical value of the partial pressure of NH 3 and the partial pressure of H S in the vessel after the NH 3 has been added and the equilibrium has been reestablished. (c) In a different experiment, NH 3 gas and H S gas are introduced into an empty 1.00 liter vessel at 5ºC. The initial partial pressure of each gas is atmospheres. Calculate the number of moles of solid NH 4 HS that is present when equilibrium is established. (a) K P (P NH3 )(P HS ) P NH3 P HS 0.659/ atm atm

3 K P (0.330) (b) P NH3 P HS (x)(x) ; x 0.33 atm P HS P NH atm (c) Equilibrium pressures of NH 3 and H S are each atm. Amounts of each NH 3 and H S that have reacted correspond to ( ) atm. n mol of each reactant mol of solid product n PV ( atm )(1. 00L ) RT ( L _ atm )( 98 K ) mol mol _ K 1983 A Sulfuryl chloride, SO Cl, is a highly reactive gaseous compound. When heated, it decomposes as follows: SO Cl (g) SO (g) + Cl (g). This decomposition is endothermic. A sample of grams of SO Cl is placed in an evacuated 1.00 litre bulb and the temperature is raised to 375K. (a) What would be the pressure in atmospheres in the bulb if no dissociation of the SO Cl (g) occurred? (b) When the system has come to equilibrium at 375K, the total pressure in the bulb is found to be 1.43 atmospheres. Calculate the partial pressures of SO, Cl, and SO Cl at equilibrium at 375K. (c) Give the expression for the equilibrium constant (either K p or K c ) for the decomposition of SO Cl (g) at 375K. Calculate the value of the equilibrium constant you have given, and specify its units. (d) If the temperature were raised to 500K, what effect would this have on the equilibrium constant? Explain briefly. (a) P nrt V g 1 mol _ I 135.0g ( L _ atm mol _ K ) ( 375 K ) 1. 00L atm (b) P SOCl ( y) atm P SO P Cl y atm P T P SOCl + P SO + P Cl Equilibrium page atm ( y + y + y) atm y 0.63 atm P SO P Cl P SOCl ( ) atm 0.17 atm ( P SO )( P K Cl ) ( 0. 63atm ) p. 3 atm P SO (c) Cl 0. 17atm (d) Heat is absorbed during the dissociation and so K 500 > K 375. A stress is place on the system and K increases, which reduces the stress associated with the higher temperature A At 5ºC the solubility product constant, K sp, for strontium sulfate, SrSO 4, is The solubility product constant for strontium fluoride, SrF, is (a) What is the molar solubility of SrSO 4 in pure water at 5ºC? (b) What is the molar solubility of SrF in pure water at 5ºC? (c) An aqueous solution of Sr(NO 3 ) is added slowly to 1.0 litre of a well-stirred solution containing 0.00 mole F - and 0.10 mole SO 4 - at 5ºC. (You may assume that the added Sr(NO 3 ) solution does not materially affect the total volume of the system.) 1. Which salt precipitates first?. What is the concentration of strontium ion, Sr +, in the solution when the first precipitate begins to form? (d) As more Sr(NO 3 ) is added to the mixture in (c) a second precipitate begins to form. At that stage, what percent of the anion of the first precipitate remains in solution? (a) SrSO 4 (s) Sr + (aq) + SO 4 - (aq) At equilibrium: [Sr + ] X M [SO 4 - ] X K sp X mol/l, solubility of SrSO 4 (b) SrF (s) Sr + (aq) + F - (aq) At equilibrium: [Sr + ] X M [F - ] X M K SP [Sr + ][F - ] (X)(X) X mol/l, solubility of SrF

4 (c) Solve for [Sr + ] required for precipitation of each salt. K sp [Sr + ][F - ] ( mol ) _ ( x ) I ; x M 1. 0 L K sp [Sr + - ][SO 4 ] ( y ) 0. 10mol ) _ I ; y M 1. 0 L Since M < M, SrF must precipitate first. When SrF precipitates, [Sr + ] M (d) The second precipitate to form is SrSO 4, which appears when [Sr + ] M (based on calculations in Part c.) When [Sr + ] M, [F - ] is determined as follows: K sp [Sr + ][F - ] ( )(z) ; z M - % F still in solution % A At elevated temperatures, SbCl 5 gas decomposes into SbCl 3 gas and Cl gas as shown by the following equation: SbCl 5 (g) SbCl 3 (g) + Cl (g) (a) An 89.7 gram sample of SbCl 5 (molecular weight 99.0) is placed in an evacuated 15.0 litre container at 18ºC. 1. What is the concentration in moles per litre of SbCl 5 in the container before any decomposition occurs?. What is the pressure in atmospheres of SbCl 5 in the container before any decomposition occurs? (b) If the SbCl 5 is 9. percent decomposed when equilibrium is established at 18ºC, calculate the value for either equilibrium constant K p or K c, for this decomposition reaction. Indicated whether you are calculating K p or K c. (c) In order to produce some SbCl 5, a 1.00 mole sample of SbCl 3 is first placed in an empty.00 litre container maintained at a temperature different from 18ºC. At this temperature, K c, Equilibrium page 4 equals How many moles of Cl must be added to this container to reduce the number of moles of SbCl 3 to mole at equilibrium? g S bcl 1 mol g mol SbCl 5 (a) (1) mol [ SbCl 5 ] init M 15.0L () T 18ºC K P nrt V atm ( mol )( L _ atm mol _ K )( 455 K ) L OR L 73 K L mol 455 K at std. temp. mol 1 atm f(.4 L/mol,30.0 L/mol) atm (b) [SbCl 3 ] [Cl ] (0.000 mol/l)(0.9) M [SbCl 5 ] (0.000 mol/l)(0.708) M K c [ SbCl 3 ][ Cl ] [ SbCl 5 ] ( ) OR P SbCl3 P Cl (0.747 atm)(0.9) 0.18 atm P SbCl5 (0.747 atm)(0.708) 0.59 atm ( P SbCl )( P K 3 Cl ) ( ) P P SbCl K [ SbCl 3 ][ Cl ] [ SbCl (c) 5 ] ( ) mol [ SbCl 5 ] equil M. 00L mol [ SbCl 3 ] equil M. 00L [Cl ] equil. X M ( )( X ) K C ; X M [ Cl ] Moles Cl (equil.) ( mol/l)(.00l) 0.10 mol Cl Moles Cl needed to make mol SbCl 3 into SbCl mol Moles Cl that must be added 0.40 mol

5 1988 D NH 4 HS(s) NH 3 (g) + H S(g) Hº +93 kilojoules The equilibrium above is established by placing solid NH 4 HS in an evacuated container at 5ºC. At equilibrium, some solid NH 4 HS remains in the container. Predict and explain each of the following. (a) The effect on the equilibrium partial pressure of NH 3 gas when additional solid NH 4 HS is introduced into the container (b) The effect on the equilibrium partial pressure of NH 3 gas when additional solid H S is introduced into the container (c) The effect on the mass of solid NH 4 HS present when the volume of the container is decreased (d) The effect on the mass of solid NH 4 HS present when the temperature is increased. (a) The equilibrium pressure of NH 3 gas would be unaffected. K P (P NH3 )(P HS ). Thus the amount of solid NH 4 HS present does not affect the equilibrium. (b) The equilibrium pressure of NH 3 gas would decrease. In order for the pressure equilibrium constant, K P, to remain constant, the equilibrium pressure of NH 3 must decrease when the pressure of H S is increased. K P (P NH3 )(P HS ). (A complete explanation based on LeChatelierÆs principle is also acceptable.) (c) The mass of NH 4 HS increases. A decrease in volume causes the pressure of each gas to increase. To maintain the value of the pressure equilibrium constant, K p, the pressure of each of the gases must decrease. The decrease is realized by the formation of more solid NH 4 HS. K p (P NH3 )(P HS ). (A complete explanation based on LeChatelier s principle is also acceptable.) (d) The mass of NH 4 HS decreases because the endothermic reaction absorbs heat and goes nearer to completion (to the right) as the temperature increases. Equilibrium page 5 (a) A sample of 100. grams of solid NaHCO 3 was placed in a previously evacuated rigid 5.00-liter container and heated to 160ºC. Some of the original solid remained and the total pressure in the container was 7.76 atmospheres when equilibrium was reached. Calculate the number of moles of H O(g) present at equilibrium. (b) How many grams of the original solid remain in the container under the conditions described in (a)? (c) Write the equilibrium expression for the equilibrium constant, K P, and calculate its value for the reaction under the conditions in (a). (d) If 110. grams of solid NaHCO 3 had been placed in the 5.00-liter container and heated to 160ºC, what would the total pressure have been at equilibrium? Explain. n PV ( atm )( 5. 00L ) gas RT L _ atm 1. 09mol ( mol _ K )( 433 K ) (a) mol H O ( 1 / )(1.09 mol) mol H O(g) (b) mo l H O mo l NaHCO 3 1 mo l H O 91.9 g NaHCO 3 decomposed remaining 100.g g 8.4g OR g NaHCO 3 1 mol molh O g 1 mol molco g _ I 1 mol 100g g 66g (or 66.g) [includes Na CO 3 solid in this mass] (c) K p (P HO )(P CO ) (3.88)(3.88)atm 15.1 atm (d) Pressure would remain at 7.76 atm. Since some solid remained when 100.g was used (and there has been no temperature change), then using 110g will not affect the equilibrium. 199 A NaHCO 3 (s) Na CO 3 (s) + H O(g) + CO (g) Solid sodium hydrogen carbonate, NaHCO 3, decomposes on heating according to the equation above A MgF (s) Mg + (aq) + F - (aq) In a saturated solution of MgF at 18ºC, the concentration of Mg + is molar. The equilibrium is represented by the equation above.

6 (a) Write the expression for the solubility-product constant, K sp, and calculate its value at 18ºC. (b) Calculate the equilibrium concentration of Mg + in liter of saturated MgF solution at 18ºC to which mole of solid KF has been added. The KF dissolves completely. Assume the volume change is negligible. (c) Predict whether a precipitate of MgF will form when milliliters of a molar Mg(NO 3 ) solution is mixed with 00.0 milliliters of a.00 l0-3 -molar NaF solution at 18ºC. Calculations to support your prediction must be shown. (d) At 7ºC the concentration of Mg + in a saturated solution of MgF is molar. Is the dissolving of MgF in water an endothermic or an exothermic process? Give an explanation to support your conclusion. (a) K sp [Mg + ][F - ] ( )( ) (b) X concentration loss by Mg + ion X concentration loss by F - ion [Mg + ] ( X) M [F - ] ( X) M since X is a small number then ( X) K sp ( X)(0.100) X [Mg + ] M (c) [Mg + ] M ml/300.0 ml M [F - ] M 00.0 ml/300.0 ml M trial K sp ( )( ) trial K sp < , no ppt. 18ºC, M MgF 7ºC, M MgF dissolves MgF Mg + + F - + heat dissolving is exothermic; if heat is increased it forces the equilibrium to shift left (according to Equilibrium page 6 LeChatelier s Principle) and less MgF will dissolve A CO (g) + H (g) H O(g) + CO(g) When H (g) is mixed with CO (g) at,000 K, equilibrium is achieved according to the equation above. In one experiment, the following equilibrium concentrations were measured. [H ] 0.0 mol/l [CO ] 0.30 mol/l [H O] [CO] 0.55 mol/l (a) What is the mole fraction of CO(g) in the equilibrium mixture? (b) Using the equilibrium concentrations given above, calculate the value of K c, the equilibrium constant for the reaction. (c) Determine K p in terms of K c for this system. (d) When the system is cooled from,000 K to a lower temperature, 30.0 percent of the CO(g) is converted back to CO (g). Calculate the value of K c at this lower temperature. (e) In a different experiment, 0.50 mole of H (g) is mixed with 0.50 mole of CO (g) in a 3.0-liter reaction vessel at,000 K. Calculate the equilibrium concentration, in moles per liter, of CO(g) at this temperature. (a) CO f(0.55 mol, 1.6 mol) 0.34 (b) K c ([H O][CO])/([H ][CO ]) ( )/( ) 5.04 (c) since n 0, K c K p (d) [CO] % M [H O] M [H ] M [CO ] M K (0.385) /( ) 0.87 (e) let X [H ] to reach equilibrium [H ] 0.50 mol/3.0l - X X [CO ] 0.50 mol/3.0l - X X [CO] +X ; [H O] +X K X /( X) 5.04 ; X [CO] 0.1 M

7 1998 D C(s) + H O(g) CO(g) + H (g) Hº +131kJ A rigid container holds a mixture of graphite pellets (C(s)), H O(g), CO(g), and H (g) at equilibrium. State whether the number of moles of CO(g) in the container will increase, decrease, or remain the same after each of the following disturbances is applied to the original mixture. For each case, assume that all other variables remain constant except for the given disturbance. Explain each answer with a short statement. (a) Additional H (g) is added to the equilibrium mixture at constant volume. (b) The temperature of the equilibrium mixture is increased at constant volume. (c) The volume of the container is decreased at constant temperature. (d) The graphite pellets are pulverized. Answer (a) CO will decrease. An increase of hydrogen gas molecule will increase the rate of the reverse reaction which consumes CO. A LeChatelier Principle shift to the left. (b) CO will increase. Since the forward reaction is endothermic (a H > 0) an increase in temperature will cause the forward reaction to increase its rate and produce more CO. A LeChatelier Principle shift to the right. (c) CO will decrease. A decrease in volume will result in an increase in pressure, the equilibrium will shift to the side with fewer gas molecules to decrease the pressure,, a shift to the left. (d) CO will remain the same. Once at equilibrium, the size of the solid will affect neither the reaction rates nor the equilibrium nor the concentrations of reactants or products. 000 A Required 1. H S(g) H (g) + S (g) When heated, hydrogen sulfide gas decomposes according to the equation above. A 3.40 g sample of H S(g) is introduced into an evacuated rigid 1.5 L Equilibrium page 7 container. The sealed container is heated to 483 K, and mol of S (g) is present at equilibrium. (a) Write the expression for the equilibrium constant, K c, for the decomposition reaction represented above. (b) Calculate the equilibrium concentration, in mol L -1, of the following gases in the container at 483 K. (i) H (g) (ii) H S(g) (c) Calculate the value of the equilibrium constant, K c, for the decomposition reaction at 483 K. (d) Calculate the partial pressure of S (g) in the container at equilibrium at 483 K. (e) For the reaction H (g) + 1 S (g) H S(g) at 483 K, calculate the value of the equilibrium constant, K c. (a) K c [H ] [S ] [H S] (b) (i) mol S 1.5 L M H mol H 1 mol S (ii) g H S 1 mol mol S mol H S 34.0 g 1 mol S 1.5 L M H S (c) K c [ ] 1. 5 (d) PVnRT 1.18 (e) K c 1 K c.00 [ ] 0.51