EXAM III Chem 112

kinetics

study of rates of chemical reactions

important things to remember about rates

• reaction rates are always positive

• rate is expressed as either the appearance of a product (+) or disappearance of the reactant (-)

• rates can be expressed in several ways:

  • M/s or M*s⁻¹

  • mol/(L*s) or mol*L⁻¹s⁻¹

rate can be represented mathematically represented as…

-∆[R]/∆t

instantaneous reaction rate

• equal to slope of line drawn tangent to curve at time t

reaction rates & stoichiometry

• relative rates of disappearance of reactants or appearance of products depend on reaction stoichiometry

• EX: 2HBr → H₂ +Br₂

  • 2 moles HBr are consumed for every 1 mole H₂ and Br₂ that is formed

  • so, rate of range of [HBr] is double that of either [H₂] or [Br₂]

what is a rate law

• dependence of rate on concentration

• ex. for reaction aA + bB → products, the rate law is given by (differential rate law):

  • rate = k * [A]^x * [B]^y

differential rate law

• rate = k * [A]^x * [B]^y

• x and y are orders of the reaction in [A] and [B] respectfully

• x and y are usually small integers, but may be zero as well

• k = specific rate constant

how to find over order of reaction using differential rate law?

overall order of the reaction is x + y

relationship btwn rate & concentration in differential rate law (mathematical)

-∆[R]/∆t = k[R]^x

integrated rate law

• describes dependence of concentration on time

• [R] = f(t)

what makes zero order rate law different from the others?

reaction rate is independent of the reactant concentration [R]

zero order integrated rate law

[R] = [R]₀ - kt

zero order differential rate law

k[R]⁰

first order differential rate law

rate = k[R]

first order integrated rate law

• exponential: [R] = [R]₀e^(-kt)

• linear: ln[R] = ln[R]₀ - kt

half-life

• t½

• time required for initial concentration to dec by 1/2

first order half-life

• t = t½, then [R] = ½[R]₀

• substitute and rearrange to solve for t½: t½ = .693/k

• half-life of first order reaction is independent of concentration

what is the half-life of ¹⁴C?

t½ = 5730 years

second order differential rate law

rate = k[R]²

second order integrated rate law

1/[R] = 1/[R]₀ + kt

for integrated second order rate law, a plot of concentration vs. time yields…

a curve

for integrated second order rate law, a plot of 1/concentration vs. time yields…

a straight line

for integrated first order rate law, a plot of ln(concentration) vs. time yields…

a straight line

for integrated first order rate law, a plot of concentration vs. time yields…

a curve

how do the units of k change depending on the order?

• zero = M * s⁻¹

• first = s⁻¹

• second = M⁻¹ * s⁻¹

etc…

at higher temperatures, reactions proceed at a _____ (faster/slower) rate

• faster

• rate constant inc exponentially as temp inc

collision frequency

• Z = collision frequency, asks # of molecular collisions per second

• reaction rate is proportional to collision frequency, Z

• for reaction A + B → Products…

  • Z = Z₀[colliding species]

collision theory

not all collisions result in formation of product; this is dependent on activation energy

activation energy

• Ea

• minimum collision energy required for reaction to occur

• represents barrier to reaction proceeding

activated complex

• least-stable (highest energy) arrangement of atoms that occurs in reaction

influence of temperature on kinetic energy

• fraction of collisions w energy in excess of Ea equals e^(-Ea/RT)

• rate of reaction is proportional to collision frequency times fraction of collisions w energy in excess of Ea

steric factor

• steric factor, p, accounts for orientation of reactants

• rate = p * Z₀[colliding species] * e^(-Ea/RT)

Arrhenius Equation

• exponential form: k = A * e^(-Ea/RT)

• linear form: lnk - lnA - Ea/R * 1/T

• point-slope form: ln(k₁/k₂) = -Ea/R(1/T₁ - 1/T₂)

catalyst

• substance that inc rate of reaction but is not consumed in reaction

• provides alternate reaction path w/ lower Ea

• first appears on reactant side

homogenous catalyst

• catalyst that’s present in same phase as reactant

heterogeneous catalyst

• catalyst that’s present in diff phase from reactants

enzyme catlysis

• enzymes are large molecules are catalyze reactions they are made specifically for

• enzymes are active under mild reaction conditions

elementary step

chem equation that describes actual molecular-level collision

mechanism

sequence of elementary steps that leads from reactants to products

intermediate

• substance produced in an early step and consumed in a later step

• first appears on product side

molecularity

• # of reactant species involved in certain elementary step

• most steps are either unimolecular (involves one molecule) or bimolecular (involves two molecules)

rate laws for elementary steps

rate = k[reactant species]^(coeff of reactant in eq)

rate-limiting step

• aka slow step

• determines overall rate of multi-rate reaction

• fast steps before slow step usually affect concentrations of reactant species in rate-determining step (but the fast steps after have no effect)

typically, a fast step reaches ____. since rates at _____ are equal, then…

• equilibrium (for both blanks)

• rate₁ = rate-₁

Michaelis-Menten mechanism (enzyme catalysis)

• step 1: enzyme binds to substrate in rapid, reversible reaction to form complex; this step reaches equilibrium

  • E + S ⇌ ES

• step 2: product forms from complex, and enzyme is released; this is the rate limiting step

  • ES → E + P

the reaction rate is ___ order in substrate, S (and explain why)

• zero

• under normal conditions, [S] is much greater than [E]₀

  • nearly all enzymes are bound to substrate, so [ES] ~ [E]₀, and rate = k₂[E]₀ = constant

change in enthalpy

• aka ∆H

• represents heat absorbed or released by system at constant temp & pressure

work

• application of force thru a distance (force * distance)

• when system does work, like lifting a weight against gravity, the sign for work is negative

work done by gases

• pressure difference causing volume change is also work

• w = -P∆V

• w can be expressed in L * atm or J

  • 1 L * atm = 101.3 J

w is ____ (neg/pos) when system does work on its surroundings

negative