Chem Kinetics Homework Key

Kinetics - Objectives in concentration with 1 . Express the rate of a given reaction In terms of the • change • time of a reactant or a product. 2. List the factors that affect the rate of reaction. 3. Outline the collision theory as it pertains to kinetics. 4. Describe the concept of activation energy and show how it explains the variation of reaction rate with temperature. 5. Draw an energy diagram for an exothermic or endothermic reactions which indicate the activation energy and AH for the reaction under study. 6. Discuss the role that temperature plays in determining the rate of reaction. 7. Determine the order of reactions with respect to each reactant given a set of experimental data. 8. Write a rate equation (rate law or rate expression) after determining the order of the reaction. 9. Calculate the rate constant, k, by using experimental data and express it with the proper units •)dentlfy the factor that changes the value of the rate constant. 1 D. Use the rate equation to calculate the rate of reaction given the initial concentrations of the reactants. 11. Describe what is involve in radio active decay and determine the age of an object by analyzing data. -13. Determine the order of a reaction by oonductiiig an experiment. 14. Determine the instantaneous rate of reaction by using the tangent method. 15. Define the term reaction mechanism and discuss the role of the rate determining step. 16. Given the overall reaction and two to the three steps of the reaction mechanism determine the missing step of the reacti_on mechanism. 17 Discuss the role of a catalyst on the reaction mechanism. 18. Using a given reaction mechanism could you explain how a particular reactant of a reaction could be zero order. Readl• Rates sedion 1&.1 A Model for Reaction Rates In your textbook, read about expressing reaction rates and explaining reactions and their rates. Use each of the tenns below just once to complete the passage. collision theory activation energy activated complex reaction rate According to the (1) to)\1S I IY\ mol/(l•s) +V\fory , atoms, ions, and molecules must collide in order to react. Once formed, the (2) OJ,hvec+cc\ C.o""pleK is a temporary, unstable arrangement of atoms that may then form products or may break apart to reform the reactauts. Every chemical reaction requires energy, and the minimum amount of energy that reacting particles must have to fonn the activated complex is the (3) 0.(j,veµ, � chemical reaction, the (4) ft 0,t .n.t>I) -evie.:n:iv. In a rovre,. is the change in concentration of a reactant or product per unit time, It may be expressed using the units of (5) Mo 1 / L 'S Use the energy diagram for the rearrangement reaction of methyl isonitrile to acetoni­ trile to answer the following questions. 6. What kind of reaction is represented by this diagram, . endothermic or exothermic? ,l,)( o¼I\U iV'\ I C.., 7. What is the chemical struct�re identified at the top of the curve on the diagram? <;\, vo..tc d OJIY1 p I x; °' e. 8. What does the symbol E0 represent? 0-.e,,k, vcu\, Ln e.,\l'\e,.rq, 1.../ 9. What does the symbol AE represent? \"" -e.,1A-€.4"''1 I-( CY\C-.)A_* Reaction Progress The potential-energy diagram for the reaction A+ B ➔ C + D is 3 C+D 4 Reaction coordinate ➔ What interval represents the activation energy for this reaction? I What Interval represents the net energy change for this reaction? L\ Is this reaction, as written, endothermic or exothermic? c:-rom the given information, would you hypothesize that this reaction is spontaneous orjnonspontaneou;J? IVhat are the answers to these same questions for the reverse reaction? 3, 4, e.,xo, s pon+ . 'his ngure represents potential energy diagrams of two different mechanisms for one chemical reaction. t �· ;J_ E D . jlij Reaction Coordinate ➔ A , activation energy for the un-catalyzed reaction is represented by: activation energy for the catalyzed reaction is represented by: d I:) C e...:xo�e rrn ic.. rse In activation energy when using a catalyst ls represented by: is reaction, as written, endothermic or exothermic? Kinetics In class problems .. _ 6icients and rate The coefficients of a chemical equation give us some insight as to the relative rates of consumption of reactants and production of products, but absolute amounts. Example: consider the reaction 2 A + B ➔ 3 C + 2 D What does this tell us? a) it takes 2 A's for every single B that reacts, so A is "disappearing" twice as fast as Bis b) there are 2 D's produced for every Band every 2 A's that are "consumed", so D is appearing at the same rate A is disappearing and t wice as fast as B is disappearing c) C is being produced 3 times faster than B Is being used up, and 3/2 times faster that A is being used up Concrete now .. .is the rate if appearance of D Is 0.01 moles/second (molls), then ... A is disappearing at a rate of , 0 I molls C is appearing at a rate of ,Ol S molls B is disappearing at a rate of ,OD<; molls A Rate Law is an equation that describes how a change in concentration affects the reaction rate. Example: for the reaction A + B ➔ products The rate law would be: rate = k[Airo[B]" k = the rate constant ➔ depends on the temperature, different for each reaction m = the "order ofreaction" with respect to A n = the "order of reaction" with respect to B note: m and n have to be experimentally determined; they are not the same as the reaction coefficients except by coincidence. Once k, m, and n are known, the rate can be determined for any set of Initial concentrations at a given temperature. Example: for the reaction 2 NO + 02 ➔ 2 N02 it is known that at 25°C, rate= k[N0]2[02], and that k = 7.1x109L2mol-2s· 1. What does the size of the rate constant indicate? -t w1 I oo� II @. e1.1 u.,J d::>n i.,� ..u / What information do the "orders of reaction" indicate? \!'161.N 4-lile CCV' (".e_v1•·\ r ,�, -J·ic.v·i, cr1I::, r ;.,:v1 %f)-ec1, What is the rate when the initial concentration of [NO] = 0.0035mol/L and [02] = 0.005mol/L? r0-J·t � :: \.:: [NO] 1. \ X ID 01 \;4p;� 1---l; 2 �✓, [C):t] 2 ( I5 ( , 003 s M) 7- (' C5DS fvl) Determining the orders of reaction from lab data 1) NH4•c•qJ + NOicaqJ ➔ N2c9i + 2 H20co I n[lial co��ntrations (M) __LlNOiJ2_ __ _[NH4'];i__ ""-,- . I, o:0100 '\ 0.200 Xl 0.200 i. 0.0200 ,J rate /Mis) 5.4Jff0'7 \ )( 2. 10.ax10·1 J,, 1 21.5x10· 7 1 . 0.8x10" '\ 21.6x1ff7 it �- 0.200 0.0202 '}. 0.0400 A /Q.2000' 0.0494 s.. 0.2000 •[ liz. l<'l. 2) For the reaction A + B + C ➔ products the following data is collected: 1 '!, C\ s _[A]_ o.01o l 1 0.020 � _[BJ_ 0.010 0.030 0.020 0.030 0.010 0.03.0 0.030 y. 2 write the rate law: rate = 0.010 \( [A] [6] . 0.40 0.60 0.010 0.010 0.010 1� 1 0.020 0.030 0.030 0.030 a) J p:630 o.63o "1 0.010 _[CJ_ 0.01() rcde; k'. [AJ" [BJ' [c] arate {Mis} ' X =- I 0.200 -:: 2 '/i l xz. 2.40 5.40 5.40 5.40 :i J X � J x\ 2" ;"\ \ =2? � =- 2. c-=-0 1 b) what is �e reaction rate when the initial concentrations of [A]= 0.005M, [BJ= 0.0025M, and [CJ = 0.10M? •t, / Al '? 1"' .•A l ;_ ( S ) • .·:;, ,vi), , -l 1 2110 )v'lo r,;1 ) 2. ' 01 M · .!.:.! • S \. • S ( ) ( 2 """k .01 M K ( \)(\D-lo 3 \ irllr� M 3L roJ-e;;, ,oos \) ) /Qnefies (/uMlions and Problems (j For a certain reaction, Ea is 50 kJ and to AH is -100 kJ. In the presence of a catalyst• the activation ene rgy is lowered • 30 kJ. Draw a an energy diagram for this reaction: 1<:} ' A➔B :;I •. '3,C,\t,J 3 ·. .;. I oO \".l I, s o 2 .. What is the only factor that will change the value of the rate constant? +e\'lf\ '\}er et} L,Lr· e 3. Consider the reaction is: 2 N02 ➔ 2 NO + 02. At 600 °C the decomposition of N02 is second order. The rate constant is 0.002 M"1s·1 a) Write the rate expression: :::: [NO 2] -z \"C\.Je b) What is the rate when [N02] = 0.02 M? rQ If =- , 00 2 M ·' S • 1 \( (, 0 2 tvt J ';/.., ,0.\-e .- B )( I 0· 7 rvl Is /7/\7 ';rhe greatest increase In rate for the reaction between X and Z where R = k[X][Z]2 will be caused by: �I (d). lowerlng the temperature ; (a)doubling[Z] (b) doubling [X] (c) tripling [X] 5. Given: R = k[A]2 [B] . What effect will doubling the [A] while cutting the [BJ in fourth have on the rate of reaction ? ( Will the rate double, triple,. ..... ?) A -i- [ 13 dOLl...b\,nc.i A: 4' x4 :,. ::; \<. (,;t) X '/'i c\r\CL109€' . ('C\t(_. vJ1II V\D-\ x4 t�'M:,v'\"1 e, 11•1: "1/ -, " x'\ 6. Complete the following data table for the reaction 2 A + Z ➔ Products, which is first order in both reactants. = \:'.. [ J v exneriment 1 exoeriment 2 exneriment 3 Experiment 1 : '(o-..,'tf.. ::: A Experiment 2: ,01i 1� r� 0.45 ? 0.75 rz11M, 0.30 0.053 0.80 '0 l'\-'3 -( '!.\$ fiM"'s''l 4.0 0.32 ? Rate /Mis\ ? 0.018 0.010 ., ) f/\ ) 30 (' f\/[ Answer= 0 32 M·'s·1 [A] (,OS3 M) Answer= / ~ )eriment 3: .D1D1v\/�/.7 \.:'.. (.�1sH) [A JO / ,Dl, fv/ {,J!;()iv() Answer= 0 AUl7 M,l,;,�v ! J l Kinetics Quiz A 1. The following rate data were collected for the reaction Experiment 1 2 3 4 s Initial [NO] (M) Initial IH2l (M) ---·-- l);.60 0.60 0.60 !.20 0.30 Rate (M/hr) 0.15 J x2 J);30, 0.60 0.60 0.60 l 12 2 NO + 2 H2 ➔ N2 + 2 H2o _________.. J J 0.076 x2. 0.15 0.30 x"\ 1.21 0.076 -----·---- (a) Determine the exact rate equation for this reaction. Include the proper units fork. y-o..,�= \( [i-JDJX ro.-\-e 0° [H .1-]'1 , ()7 lc, 2 V "'2 i;: K [t,10] 7 [!-\�··1 )A) --;... ( I 5 \<:. (, (,,0 \( '.'.'- /, ,t..J 1 rvi- 2 ll)f - I ' (b) Ifthe initial concentration of NO is 0,40 Mand the initial concentration cifH1 is 0.50 M, what is the rate of reaction ? 1 rct\-e" l,Y l M·21\1· (. 4 1vf)'2:(, SM) R= .11 '3 M/hr (c) By what factor will the rate change if the [NO) is tripled and the (Ehl is doubled ? iZo-te ::: t. [NoJ � [ r\ 2.-1 0 3) 2. G) (x ·z') , 1.. :;.. '"'c.. reQS-es by o.. -tRc,:\--o-r zl \ g • Chemistry name: hour: Half�life questions I 1. The reaction Z ➔ products Is first order, with a rate of 0,0025 mol L"1!f1 when [Z] Is o.osmol L-1. What is the half life of the reaction in minutes? I("' .oss·' +•,i.-:: ,1,oq 3 r0v1t., \((.z-1 ,oozs Mfs � k (.OS �) ---:-0-s·-.r 2. The reaction A -. products is second order. When the rate is 0.01 mol L· 1s· 1, and k = 0.4 L mol"1 s·1, what Is the half life of the reaction in minutes? 2. -+--1 ;,z ro,,'le. "' \"- CA1 [AJ "' . 1 $' ti � ,Ol 1" ,4 M· s· [IIJ 1 1 i 05M·��- -t•1:2 I ::- ( .4)(.,sv) ;, /S, f)2 -sec /bo· ··· I �. -------· I :: :2. i:, YYl ' V\ 3. A certain radioactive element has two common isotopes, a stable one, and a radioactive one that decays to the stable one with a half life of 2200 Jleil�The isotopic mix is 20%.radloactive upon formation. A 2.50g sample of the element was found to be about 0.08g radioactive isotope, and the rest stable. Approximately how old Is the sample? \ _. Id 4. A certain radioactive element has two common isotopes, a stable one, and a radioactive one that decays to the stable one with a half life .Qf 15,000 t�ars. The Isotopic mix Is 3% radioactive upon formation. A �-��0_g sample "rjf the "element was found to be about �:-� radioactive • Appt'OX1mately how old Is the sample? isotope, and the rest staole. ;;i.S' 1' -0� ".01S I s.. How many grams of a 5.0g sample will remain after: a) one half-life 2.s � b) three half lives . lo ·K °' c) six half lives . ol 'I{ o � 6. What percent of a substance will remain after: a) one half-life 5 O ·t, . b) three half lives I 2., S 'I. c). six half lives 1 , 5\,,. ,. 9 'b� r;2- A c• Ao • . S (Hi-"\ � 5� --��=;�\