Reaction Mechanisms & Arrhenius Equation

1. Reaction Mechanisms & Arrhenius Equation

2. Reaction Mechanisms • Some reactions are not represented in the reaction equation; such as, • Absorbing light energy • Colliding to the walls of the container • Many reactions proceed through a sequence of steps to arrive at the products • Each step is called an elementary reaction and occurs through collision of atoms, ions and molecules.

3. Reaction Mechanisms • The slowest step in a reaction mechanism is called the Rate-determining Step • In multistep reactions, increasing the concentration of reactants at any steps other than the rate-determining step will not increase the rate of reaction • A chemical species that form and then are consumed in the reaction is calledReaction Intermediates

4. Rate Equation • mX + nY -----> products of reaction or intermediates thenr α [X]m [Y]n r = k[X]m [Y]n • When writing the reaction mechanism, there are three rules: • each step must be elementary, with no more than three reactants • The rate-determining step must be consistent with the rate equation • The elementary steps must all add up to be the overall equation

5. Elementary reactions (Molecularity) • Unimolecular; Decomposition (ex. N2O5(g) NO2(g) + NO3(g))rate = k[N2O5] • Bimolecular; Collision of 2 atoms, ions or molecules(ex. NO(g) + O3(g)  NO2(g) + O2(g))rate = k[No][O3] • Termolecular; Simultaneous collision of 3 molecules(ex. 2I(g) + Ar(g) I2(g) + Ar(g) )rate = k[I][I][Ar] = k[I]2[Ar]

6. Reaction mechanism is a detailed sequence of elementary reactions, with their rate, that are combined to yield the overall reaction. • Consider the mechanism:1) Cl2(g) 2Cl(g)2) Cl(g) + CHCl3(g)  HCl(g) + CCl3 (g)3) CCl3 (g) + Cl (g)  CCl4(g) • Some of the possible questions are…

7. a) What's the molecularity of each step?1) Unimolecular2) Bimolecular3) Bimolecular b) Write the overall equation for the reactionCl2(g) + CHCl3(g) HCl(g) + CCl4(g) c) Identify the reaction intermediate(s)Cl(g) & CCl3

8. The Arrhenius Equation • To explain the large effect of temperature and catalysis, the Arrhenius Equation is used to account for their effects k = Ae-Ea/RT Ea is the activation energy (J) A is constant related to the geometry of molecule R is the gas constant (8.314 J/(mol•K)) T is the temperature (K) • the answer k is the rate constant for the rate law equation r = k[A]n[B]m

9. By taking ln (natural log) to each side,ln k = -Ea/RT + ln A • Arrhenius equation is written for the rate constant determined at each temperature giving, ln k1 = -Ea/RT1 + ln A ln k2 = -Ea/RT2 + ln A • Subtracting second equation from the first,ln(k1/k2) = -Ea/R(1/T1 – 1/T2) • The rate and the rate constant are directly proportional to each other as long as the concentrations are held constant.

10. Examples • At 200K the rate constant for a reaction is 3.5 X 10-3s-1 , and at 250K the rate constant is 4.0X 10-3s-1 . What is the activation energy?Ea = 1.11KJ/mol • What is the rate of reaction at 450oC if the reaction rate is 6.75 X 10-6mol/(L*s) at 25oC? The activation energy was previously determined to be 35.5kJ/mol.The rate of reaction at 450oC is 3.05 X 10-2 mol/(L*s)

11. The Arrhenius Equation • To test the answer for reasonableness, two principles must be remembered:1) The larger rate constant (or rate) will always be associated with the higher temperature2) The activation energy always has a positive sign.

12. Summary • Reactions that contain more than 3 molecules colliding occurs in multi-steps • Each elementary step should only have 3 or less reactants • r = k[A]n[B]m • k = Ae-Ea/RT • Temperature and activation energy affects the value of k exponentially