山东大学：《物理化学》课程教学资源（讲义资料）9.5 Temperature-dependence of reaction rate

89.5 Temperature-dependence of reaction rate Arrhenius equation Extensive reading: Levine, pp. 554-559 Section 17.8 oals 1. Describe the effect of temperature on reaction rate 2. Activation energy: definition, measurement, estimation 3. Fundamentals for higher level scientific researches

§9.5 Temperature-dependence of reaction rate -- Arrhenius equation Extensive reading: Levine, pp. 554-559 Section 17.8 Goals: 1. Describe the effect of temperature on reaction rate; 2. Activation energy: definition, measurement, estimation; 3. Fundamentals for higher level scientific researches

89.5 Arrhenius equation 9.5.1 Types of rate-temperature curves From the middle 19 century, people began to study the effect of temperature on the reaction rate ype Type ll Ty e l k qualitative Type I\ T pe

9.5.1 Types of rate-temperature curves From the middle 19 century, people began to study the effect of temperature on the reaction rate. qualitative T k T k T k T k T k Type I Type II Type III Type IV: Type V §9.5 Arrhenius equation

89.5 Arrhenius equation 9.5.2 The first quantitative study Ludwig Ferdinand wilhelmy V. Ueber das Gesete, nach welchen die Einwir tren auf den Rohrzucker stattfindet (Dec.25,1812,-Feb.18,1864) on Ludwig ilhelmy in Heid- a german scientist who is usually er die polarisationgebene des durch seine den Lichts nach rechtsdrehende Rohrzuel Ludwig Wilhelmy, Jacobus H. van't Hoff credited with publishing the first kanntlich durch Einwirknng von Siuren in li Svante Arrhenius und die Geschichte quantitative study in chemical kinetics heit der ablppelplatte nit grouser VEpor A Raison mir hierdurch die Moglichkeit gegeben, die G 1850, Wilhelmy studied the acid Rede stehenden Vorgangs zt catalyzed conversion of a sucrose m能装 solution into a 1:1 mixture of fructose aM. and glucose with a polarimeter. He wrote a differential equation to describe the od die ausdebnung der Ko der elektrischen und magnetischen Anziehung reaction. integrated it. and used it to sung- ihrem Werth nach abhangig sey v interpret his experimental results ae Wilhelmy found that the reactions rate was proportional to the concentrations of sucrose and of acid present

Ludwig Ferdinand Wilhelmy (Dec. 25, 1812, – Feb. 18, 1864) a German scientist who is usually credited with publishing the first quantitative study in chemical kinetics 1850, Wilhelmy studied the acid￾catalyzed conversion of a sucrose solution into a 1:1 mixture of fructose and glucose with a polarimeter. He wrote a differential equation to describe the reaction, integrated it, and used it to interpret his experimental results. Wilhelmy found that the reaction's rate was proportional to the concentrations of sucrose and of acid present. 9.5.2 The first quantitative study §9.5 Arrhenius equation

89.5 Arrhenius equation 9.5.2 The first quantitative study ChOU+h,o C6H12o6+ Chloe sucrose glucose fructose In 1850, Wilhelmy determined the residual concentration of sucrose by measuring the r=k[ClH22Oul change of the rotation angle of a beam of plane-polarized light passing through the k=0.0043s hydrolysis solution with optical activity Substance sucrose glucosefructose k is quite low 25 +66.50+520 920 Does k' change with acid concentration?

C12H22O11 + H2O ⎯→ C6H12O6 + C6H12O6 sucrose glucose fructose Substance sucrose glucose fructose []D 25 +66.5 o +52 o - 92 o 12 22 11 r k = '[C H O ] k’ is quite low. In 1850, Wilhelmy determined the residual concentration of sucrose by measuring the change of the rotation angle of a beam of plane-polarized light passing through the hydrolysis solution with optical activity. 9.5.2 The first quantitative study §9.5 Arrhenius equation k = 0.0043 s-1 Does k’ change with acid concentration?

89.5 Arrhenius equation 9.5.3 Empirical rules inearization (1)vant'Hoff's Law dInk A It was found that for homogeneous reaction, an important generalization 入+ b quantitative is that reaction rate doubles or triples for every 10 degree increase in in which A and b are experimental empirical constants with their physical meaning unclear temperature T+10=2-3Semi-quantitative k 1884, vant'Hoff's equation: aIn K Difference between Experimental aT RT reports and Research paper

It was found that for homogeneous reaction, an important generalization is that reaction rate doubles or triples for every 10 degree increase in temperature. 10 2 ~ 3 T T k k + = 2 ln A B d k dT T = + in which A and B are experimental / empirical constants with their physical meaning unclear. 9.5.3 Empirical rules (1) vant’ Hoff’s Law Difference between Experimental reports and Research paper Semi-quantitative quantitative linearization 1884, vant’ Hoff’s equation: 2 ln r m p K H T RT       =    §9.5 Arrhenius equation

89.5 Arrhenius equation 9.5.3 Empirical rules (2)Arrhenius hypothesis Arrhenius postulated that only a small part of sucrose molecules with higher energy(activated In 1889, Arrhenius made theoretical molecules) can react with water and, therefore consideration on the hydrolysis of the reaction can only proceed at a low rat sucrose, in which sucrose molecules By taking enough energy, the common sucrose were surrounded by water. if all sucrose molecules can change into activated molecules molecules could react directly with The energy needed for this conversion was called water, the reaction should completed activation energy. instantly. However, this is not the case [A revolutionary concept: I Arrhenius, S.A. (1889). " Uber die Dissociationswarme und den EinflusB der Temperatur auf den Dissociationsgrad der Elektrolyte".Z. Phys. Chem. 4:96-116: 4: 226-248

In 1889, Arrhenius made theoretical consideration on the hydrolysis of sucrose, in which sucrose molecules were surrounded by water, if all sucrose molecules could react directly with water, the reaction should completed instantly. However, this is not the case. (2) Arrhenius hypothesis Arrhenius postulated that only a small part of sucrose molecules with higher energy (activated molecules) can react with water and, therefore, the reaction can only proceed at a low rate. By taking enough energy, the common sucrose molecules can change into activated molecules. The energy needed for this conversion was called activation energy. [A revolutionary concept!] 9.5.3 Empirical rules Arrhenius, S.A. (1889). "Über die Dissociationswärme und den Einflusß der Temperatur auf den Dissociationsgrad der Elektrolyte". Z. Phys. Chem. 4: 96–116; 4:226-248 §9.5 Arrhenius equation

89.5 Arrhenius equation 9.5.3 Empirical rules (2)Arrhenius hypothesis dInk E Arrhenius equation Arrhenius extended the ideas of vant 'Hoff dT RT and suggested a similar empirical equation Is the simplification reasonable? dInk A dT 72+B1 dInk E Definition of activation energy dT RT experimental activation energy e aIn K 4 aIn Ke E=RT2 dIn k OT' R72 dT aT RT

Arrhenius extended the ideas of vant’ Hoff and suggested a similar empirical equation. Is the simplification reasonable? Arrhenius equation 2 d ln d E a k T RT = 2 d ln B d k A T T = + 2 d ln d E a k T RT = 2 ln r m p K H T RT       =    2 ln r m p K U T RT       =    (2) Arrhenius hypothesis 9.5.3 Empirical rules §9.5 Arrhenius equation 2 d ln = d a k E RT T Definition of activation energy— experimental activation energy

89.5 Arrhenius equation 9.5.3 Empirical rules (2)Arrhenius hypothesis If E. is independent on temperature, integration of the equation dink e dT RT yields E In k=--a+Ina RT k=Aexp r T a is the pre-exponential factor which has the same unit as the rate constant

If Ea is independent on temperature, integration of the equation yields A is the pre-exponential factor which has the same unit as the rate constant. 2 d ln d E a k T RT = or (2) Arrhenius hypothesis 9.5.3 Empirical rules §9.5 Arrhenius equation ln = +ln E a k A RT − = exp E a k A RT     −  

89.5 Arrhenius equation 9.5.4 Experimental measurement activation energy (1)Experimental measurement: CICOOCH3+H20-C02+CH3OH+H+Cl E K 273.72278.18283.18288.14 Ink= 7+In A 104k/s10.42090.7061.2292.087 T/K 198.18308.16318.29 (1) Graphic method 104k/s1564214053265 (2)Calculation method Graphic method lnk=-85159+21.06 to plot Ink against 1/T[Arrhenius plot], for the R=0.99992 reaction of Arrhenius type, a straight line may be obtained, the slope of which equals - R 3.0x10332x10334X10336×10338x103 1/T(K

9.5.4 Experimental measurement activation energy (1) Experimental measurement: A RT E k a ln = − + ln (1) Graphic method (2) Calculation method Graphic method: to plot lnk against 1/T [Arrhenius plot], for the reaction of Arrhenius type, a straight line may be obtained, the slope of which equals –Ea /R §9.5 Arrhenius equation ClCOOCH3 + H2O → CO2 + CH3OH + H+ + Cl− T / K 273.72 278.18 283.18 288.14 104 k / s-1 0.4209 0.7016 1.229 2.087 T / K 198.18 308.16 318.29 104 k / s-1 5.642 14.05 32.65 21.06 1 ln = −8515.9 + T k R = 0.99992

89.5 Arrhenius equation 9.5.4 Experimental measurement activation energy (1)Experimental measurement (2)Calculation method In k +In a k E y=43079-19111X ConstantIn R=0.95507 k, R T In k, +In a RT 273.72278.18283.18288.14 0002250.00228000231000234000237000240000243 Rh(tmp) 104k/s0.4209070161.2292.087 198.18308.16318.29 w.r.t Rh(tmp) 104k/sh5642140532.65 T.T. Ching, S.C. Kwong and s C. Kim, JACS, 2012, 134 11388-11391

T. T. Ching, S. C. Kwong and S. C. Kim, JACS, 2012, 134: 11388-11391 9.5.4 Experimental measurement activation energy (1) Experimental measurement: §9.5 Arrhenius equation (2) Calculation method: A RT E k a ln ln 1 1 = − + A RT E k a ln ln 2 2 = − +         = − − 2 1 2 1 1 1 ln R T T E k k a T / K 273.72 278.18 283.18 288.14 104 k / s-1 0.4209 0.7016 1.229 2.087 T / K 198.18 308.16 318.29 104 k / s-1 5.642 14.05 32.65 Constant