CHEM 1112: Kinetics

- reaction rates

• never possible

• cant have - products forming

• - sign placed infront of rate of change of reactuants in order to provide a positive rate of reaction

Reaction rate

• the speed at which the chemical proceeds

• independent of ∆G

• amount of product formed per unit of time

• always expressed as a positive #

  • products appear (rate is positive)

  • reactants disappear (rate is negative)

Rate expression

• for the simple reaction A → P

  • rate = ∆[P] / ∆time = P_f - P_i / T_f - T_i

• for complex rxn aA + bB → cC + dD (lowercase = mole ratio)

  • rate = -(1/a)(∆[A]/∆t) = -(1/b)(∆B/∆t) = +(1/c)(∆[C]/∆t) = +(1/d)(∆[D]/∆t)

  • the rate should be the same, not matter which reactant/product you use

What affects rate

• concentration of reactants

• temperature

• presence of a catalysts

Average reaction rate

• the rate at which a reaction proceeds over a time period

• calculated using concentrations at the beginning and end of a time period

Instantaneous reaction rate

• the rate at which a reaction is proceeding at a specific time or concentration

Zero order reaction

• n = 0

• rate of reaction is completely INDEPENDENT from the concentration of a reactant

• integrated rate law:

  • [A_t] = -kt + [A_o]

• half life:

  • t_1/2= [A_o]/2k

1st order reaction

• n = 1, [A]¹

• rate of reaction is DIRECTLY proportional to concentration of one reactant

• integrated rate law:

  • ln[A_t] = -kt + ln[A_o]

• half life:

  • t_1/2= 0.693/k

2nd order reaction

• n=2, [A]²

• rate of reaction is proportional to concentration of the square root of one reactant

• integrated rate law:

  • 1/[A_t] = -kt + 1/[A_o]

• half life:

  • t_1/2= 1/k[A_o]

Overall order

• k[A]^m + [B]ⁿ

• overall order= m + n

  • gives an understanding of how all the reactants contribute to the rate of a reaction

Integrated rate law

• rate law which is integrated with respect to time to produce a concentration-time relationship

Half life

• time required for the concentration of the reactant to fall to ½ of its initial value

Carbon dating

• rate of decaying of carbon-14 after death may be tracked and used to date objects up to 50,000 years old

Collision theory

• reactants must collide in order to react with each other

• postulates:

  • rate of reaction is proportional to rate of collisions

  • molecules must be properly oriented when they collide

  • molecules must have sufficient E_a to react

Activation energy

• E_a

• minimum energy necessary to form a product during collision between reactants

• appears as a PE ‘hill’ between reactants and products

• only colliding particles that are properly oriented can deliver KE into PE at least as large as the E_a ‘hill’, so that products may be produced

Collision orientation

• molecules must be oriented properly when they collide in order for new bonds to form

• chemical reactions involve bond breaking and/or bond forming

• new bonds cannot form if the appropriate orbitals cannot overlap as they form molecular orbitals

Transition state

• activated complex

• species at point of highest energy

• exists transiently, cannot be isolated

Reaction intermediate

• a rxn may occur in more than one step

  • each step has its own activation energy barrier (E_a) and transition state (TS)

• intermediate (int) shows on energy diagram as an ‘energy pit’

Arrhenius equation

• k = Ae^{-E_a / RT}

  • k = rate constant

  • E_a = activation energy

  • R = gas constant (given)

  • T = temperature (K)

  • A = frequency factor

• used to describe temperature dependence of reaction rates

k in Arrhenius equation

• dependent on temperature

  • higher T → higher k

  • at higher temperatures, more molecules have enough KE to overcome activation energy barrier, thus increasing rate constant

• dependent on E_a

  • higher E_a → lower k

Reaction mechanism

• exact molecular pathway that starting materials follow on their way to becoming products

• reaction mechanism can not be determined simply by looking at the stoichiometry of the reaction

  • must be determined experimentally

Elementary step

• each step in a multi-step reaction

Molecularity

• number of molecules on the reactant side of the chemical equation for the elementary reaction

  • unimolecular

  • bimolecular

  • termolecular

Unimolecular

• single molecule reactant

• A → product

• (elementary) rate law:

  • k[A]

Bimolecular

• 2 molecule reactant

• A + B → product

• 2A → product

• (elementary) rate law:

  • k= [A][B]

Termolecular

• 3 molecule reactant

• A + B + C → product

• 2A + B → product

Elementary reaction

• describes the behaviour of the individual molecules

Reaction intermediate

• species only present in the elementary reactions, formed in one step and consumed in another

Rate determining step

• each elementary reaction has a characteristic rate of reaction

  • rate determining step is the slowest elementary step in a mechanism, thus governing the rate of the overall chemical reaction

• the rate law is related to the mechanism of the reaction

Linking mechanism and rate laws

• the mechanism is one or more elementary reactions describing how the chemical reaction occurs

  • a satisfactory mechanism must be comprised of ‘reasonable’ elementary steps

  • species proposed must exist (cant be half an atom)

  • stoichiometry must be reasonable

• sum of the individual steps in mechanism must give the overall balanced chemical equation

• the reaction mechanism must be consistent with the experimental rate law

RDS and rate law

• when the first step of a mechanism is RDS, the predicted rate law for the overall reaction is the rate law for that first step

Catalyst

• a substance that increases the rate of a chemical reaction by lowering the activation energy without itself being consumed by the reaction

  • catalyst is regenerated in the process

• catalysts provide an alternative reaction pathway with a lower E_a

  • sometimes the catalysed path contains multiple steps, but each individual step has an E_a that is lower than the overall E_a of the uncatalyzed reaction

• catalysts never affect the ∆G of a reaction

Homogenous catalyst

• in the same phase as reactants

• speeds up the reaction by forming a reactive intermediate

  • ex. chlorine radicals catalyse the decomp. of ozone

    . Cl_(g) + O_3(g) → ClO_(g) + O_2(g)

    . ClO_(g) + O_(g) → Cl_(g) + O_2(g)

Heterogenous catalyst

• in a different phase from that of the reactants

  • most commonly cat= solid, react= gas, liquid

• ex. catalytic converter in cars (Pt, and Rh)

  • 2CO_(g) + O_2(g) —Pt—> CO_2(g)

  • NO_(g) —Rh—> N_2(g) + O_2(g)

Haber-Bosch process

• used in the production of NH₃ , industries use high pressure and temperature as a catalyst

Enzyme catalysts

• enzymes catalyse thermodynamically favourable reactions, causing them to proceed at extraordinarily fast rates

• affect reaction rates, but do not affect equilibrium btwn. substrate and products

• selectively recognise their substrates over other molecules, resulting in high yields of their products