CHEM111 Module 6: Kinetics

how do thermodynamics and kinetics differ

thermodynamics looks at if reactions are favorable to occur (what happens)

kinetics looks at how fast reactions occur (does it actually happen)

for a reaction to be useful, it must take into consideration the thermodynamics AND the kinetics of the reaction

define reaction rate

the rate of change of concentration, with time

how do you calculate average reaction rate for a substance in a reaction?

what information must you use (equation included on formulae sheet)

what are the units of the answer

• change in concentration of the substance (d[A])

• stoichometry of the substance (a)

• change in time (dt) - what area of the graph / part of the reaction do you want the rate for

• units = mol L-1 s-1

how do rate laws differ from rates

rates tell you the change in concentration of a substance in a reaction over time, this is a quantity being measured

a rate law however is a law that defines a specific reaction, providing the parameters the reaction occurs at (an empirically found mathematical description of the reaction’s change in substance over time) allowing things to be calculated specifically for the reaction

this shows how reactant concentrations contribute to the overall rate of reaction (via partial orders), with consideration to T (reaction coefficient)

what information do you use to calculate rate laws

• partial orders of the species in a reaction (how each contribute to make the overall order of the reaction - partial orders add to give the overall order of the reaction) - unitless, usually positive integers

• k (reaction coefficient / constant) - is a proportionality constant, which varies with temperature

what are overall orders for reactions

what are the different options

these categorise the reaction into how their reactant concentrations are raised to the power of, allowing us to simplify the rate coefficient

• zero-order reactions have the reactant^0

• first order reactions have one reactant, with ^1

• second order reactions have one reactant with ², or two reactants with ^1

how do different overall orders of reaction change the equation for rate laws (/ reaction coefficient)

• 0: rate = k (A is to the power of 0)

• 1: rate = k[A] (A is to the power of 1)

• 2: rate = k[A]² (for one reactant) = k[A][B] (for two reactants)

how do units of k change depending on the reaction’s overall order

why do these change

• 0: mol L-1 s-1

• 1: s-1

• 2: L mol-1 s-1

• 3: L² mol^-2 s-1

these change as different units cancel out, due to the different arrangement of equations

what experimental evidence suggests that reaction is…

• 0th order with respect to a reactant

• 1st order with respect to a reactant

• 2nd order with respect to a reactant

• reaction rate is unchanged when intiial conc. of reactant is increases

• reaction rate is doubled when initial conc. of reactant doubles

• reaction rate is quadrupeled when initial conc. of reactant doubles

what is the initial rates method, why is this a good method

how is this helpful for finding the partial and overall orders for reactions

this method uses the concentrations and rate of the reactions initially

• beneficial because rate is highest/largest so easiest to measure

• no products present so no reverse reaction to complicate results

• can alter initial concentrations to get more measurements (could provide different reaction rates)

this helps us find partial and overall orders, as we can look at…

• if rate doubles when a reactant conc. doubles, it suggest its 1st order

• if rate quadrupels when reactant conc. doubles, it suggests 2nd order (raised ²)

• if unchanged, it suggests its 0 order for that reactant (wont contribute in the rate law)

what is the difference between differential and integrated rate laws?

• differential rate laws are in differential form, looking at change in conc. with respect to change in time (a derivative)

• this involved looking at rates of reaction, with the differential rate law

• e.g. d[A] / dt = -k (0th order)

• integrated rate laws are the integrated form of these differential rate laws

• e.g. [A] = [A]0 -kt (0th order)

what happens if you plot experimental data of reactant conc. with time, for a 0th order reaction, and why?

• it will have a linear fit, with slope = -k, and intercept = [A]0

• this is because, the integrated rate law equation, is the equation of a straight line

• therefore showing that in a 0th order reaction, there will be a constant decrease in reactant conc. with increasing time

what happens if you plot experimental data for change in reactant concentration over time for first order reactions, and why?

what is something you can do to change the appearance of this graphed data, to determine if the reaction is truly first order?

• the graph will not be linear, it will show a curve with exponential decay

• this is because the integrated rate law for first order reactions is not the equation for a straight line

• since integrated first order rate law involves e^-kt, you can take the natural log (ln) of both sides of the equation, includng reactant concentration with time, which when plotted will provide a linear relationship

• the slope of this will = -k, and the intercept = loge[A]0

how do you calculate a slope from linear data on a graph

what might this help you find

• calculate rise (change in reactant concentration between the two points) divided by run (the time in seconds this time frame goes for)

• if a 0th order reaction, -slope = k

• if a 1st order reaction, loge of concentrations plotted will have -slope = k

how does a first-order differential and integrated rate law, change for gas-phase reactions

• they simply replace concentrations of reactants (e.g. [A]) with partial pressures (e.g. pa)

• exponential decay when plotting pa with time, and linear when loge of pa plotted - same as usual first-order reactions

do the units and magnitude of k change for gas-phase reactions

no! is the same

does time units change the magnitude of k

yes! make sure to do this accurately

(e.g. 60 seconds vs 60 minutes (3600 seconds)

what is the half-life of a reaction

what equation represents this

• the time required for a reactant to reach half of its initial concentration

• (for first-order reactions) use: t1/2 = (1/k) ln(2)

• so k = ln2 / t1/2

• so t1/2 = ln2 / k

• in these equations, k and t1/2 are interchangeable, (for first order reactions only), so k can be reported as t1/2 instead

• this provides more of an intuitive view, as t1/2 is more visualisable, it must take 2 half lifes to get ¼ of intial conc, 3 half lives to get 1/8 of initial conc, and so on

how many half lifes technically gets you to completion

how many half lives gets you to 1/8 initial conc.

• 10 to completion

• 3 to 1/8 initial conc, 2 to 1/4

what is a lifetime of a reaction (first order)

what is its equation

what is its symbol

how does it relate to k

• a lifetime is the time taken for a reactant to reach 1/e of its initial value - which is the average time it takes for a reactant molecule to react

• denoted τ

• at t = τ, [A] = [A] / e

• so k = 1 / τ (gained from rearranging the first-order rate law)

compare half-life and lifetimes of a reaction

• half lives tell you the time taken for a reactant to reach ½ its initial conc.

• lifetimes tell you the time taken for a reactant to reach 1/e its initial conc., which is equal to the average time taken for a reactant molecule to react

• therefore, lifetimes tell you more useful information, as they provide a point of average reaction time, wheras half lives just go to infinite saying how long for half of initial reactant to be used, then half of that to be used, and so on

what does [A]₀ mean

• concentration at t=0, so initial conc, of a reactant

how would you determine concentrations of reactants, after some elapsed time, given the initial concentrations (for a first order reaction)?

• first consider the change in mols for the conc (denoted x), based on reaction stoichometry of the reaction

• so reactants final conc is -x multiplied by stoichometry (e.g. -2x) while for products it is x (e.g. 2x), as reactants decrease while products are formed

• then use the integrated rate law, which becomes

  [A]t = [A]0 e^-kt (for a first order reaction at time t)

• then subsitute in known information (k is often provided) to find the unknowns

what is an elementary reaction

how do these combine to form complex reactions

• an elementary reaction is a reaction that occurs as written, reactants → products directly

• complex reactions (most chemical reactions) instead involve a number of elementary steps (the reaction mechanism) that add to give the overall reaction (the reaction equation)

in complex chemical reactions, what are intermediates

• these are chemicals that appear in the reaction mechanism (in an elementary step), but not in the overall reaction

• this is due to them playing a role in the reaction, but being created and used up so are not written in the equation

what are the different molecularities of elementary steps

what are the rate laws for each

• unimolecular = 1 reactant molecule

rate = k[A]

• bimolecular = 2 reactant molecules (2 options)

rate = k[A]²

rate = k[A][B]

• termolecular = 3 reactant molecules

rate = k[A][B]²

what are rate laws for elementary reactions based on

why does this only apply to elementary steps, and not complex reactions

• just based on conc. of reactants (rate = k[A][B]², etc), as their partial orders = stoichometric coefficients

• however for complex reactions, multiple elementary steps must be considered, so their rate laws are not as simple (e.g. rate determining step)

• note - be careful assigning rate laws without knowing if a reaction is elementary / complex

what is a rate-determining step in a reaction

how may this affect a reaction’s rate law

• this is an elementary step in a complex reaction, that is much slower than the other steps, therefore it determines the overall rate of the reaction

• this causes the overall rate law to be simply determined by this rate-determining step, it becomes the rate law for this individual elementary step

how would we know a reaction is complex, based on its rate law

• if the rate law, and partial orders of the reactants, don’t correlate to the overall reaction stoichometry

• e.g. doesnt contain all reactants / partial orders

• or if there is an intermediate chemical detected while the reaction is occurring, which isn’t present in the overall reaction equation (or in its reactants / products formed)

how does collision theory explain…

• how elementary reactions occur

• how rate laws of bimolecular reactions are dependant on molecule concentrations

• how reaction rates are often greater at higher temperatures

• how termolecular reactions are rare

1. by collision of particles, resulting in reaction

2. because collision frequency, and number of collisions (contributing to reaction rate) - is influenced by concentrations of molecules (double the conc. will double the rate, etc)

3. collision frequency increases with higher temp, as molecules move faster, thus more reactions occur

4. 3-body collisions are unlikely

what relationship does the Arrhenius equation describe

what theory aids in understanding this?

• the relationship of k (Rate coefficient) with temperature, as with most chemical reactions, k increases rapidly with increasing temperature, in a non-linear fashion (a curve)

• Arrhenius equation allows this relationship to be made linear, taking the log of each side

• this can be understood using the Transition State Theory

what kinetic theory do Reaction Coordinate / Energy diagrams display?

what kinds of graphs are these

• for a collision between particles to result in a successful reaction, their kinetic energy must be sufficient to overcome the activation barrier (input energy required for a reaction occur)

• this is shown using energy as a function of reaction progress

• it shows the parameter Ea (activation energy)

• if the kinetic energy of collision (Ek) is greater than the activation barrier, it is successful and the reaction occurs (And the opposite)

similarities and differences between endothermic and exothermic (elementary) reactions in terms of Ea

• similar: they both require collisions with a certain amount of energy, to overcome the activation barrier for a reaction to occur

• different: the activation barrier is typically smaller for endothermic reactions

• different: the products have lower energy than reactants in exothermic, and higher enery in endothermic

describe the Transition State Theory

• the tip of the activation barrier (the middle between products/reactants), is transition state (between products and reactants)

• Ea is the energy required to break the bonds in the reactant, in order for bonds to be formed between reactants to create the products

• we must get through the transition state (pass Ea barrier) to get to the end

• all reactions have these, often more complex with more bonds breaking / forming (but always requires energy)

how does k correlate to P (Ek>Ea), for a collision

how does this link to temperature

• k and rate of reaction, depends on the probability that a collision will be successful (have sufficient energy Ek to overcome Ea barrier)

• as temperature increases, the distribution (Maxwell Boltzmann dist.) of Ek of molecules in a reaction, flattens out (so a higher area of the distribution, has Ek > Ea)

along with Ea of collisions, what else must be considered to use the Arrhenius equation (and relate k to collision theory)

• orientation effects and the steric factor

• successful collisions also require reactants to have the correct orientations relative to each other, particles must hit the right particle they specifically react with (in a certain cone of area)

• steric factor refers to the probability of correct orientation

how do kinetic theories transform the Arrhenius equation, for usability (form a theoretical relationship form this empirical one)

what functions make this up

• these reveal the Arrhenius constants (A&B) to be

  • collision frequency x steric factor = zp = A (frequency factor)

  • p(Ek>Ea) = exp(-Ea / RT) = B (activation energy)

• using collision theory, Ea and orientation of particles, for reactions to occur

how do the collision theory and Arrhenius equation apply for complex reactions

• use the z/p/Ea for the rate-determining step (an elementary reaction), to find k

after putting theoretical ideas into the Arrhenius equation, how does it reveal how k is temperature dependent

what final equation does it provide

• the things that make up the Arrhenius equation (-Ea/RT & A) are temperature dependent, therefore the k they equal, also must be temperature dependent

• this creates the curved relationship we see of rate coefficient (k) with increasing temperature

• this also makes sense considering collision theory

• treating A as a constant provides us with the final Arrhenius equation in the formulae sheet

what can you calculate using the Arrhenius equation

what approach should you use

what units should be used

• Ea (provided k1, k2, T1, T2)

• k(x) at T(x) (provided Ea, and other k & T)

• corresponding T for given k (also provided Ea and other k & T)

• to calculate, input the known data, and rearrange the equation

• units combine for J mol-1, temperature in K, time in s

describe how a reaction coordinate diagram changes for complex reactions

• transition states

• intermediate troughs

• rate determining step

• these just become a combination of multiple diagrams for elementary steps, for the ones that make up the reaction mechanism

• the peaks of the graphs are each transition state, and the Ea required to overcome the specific bond forming / breaking to transition from reactants → products

• the troughs after these peaks, are the intermediates formed (products of the previous step, reactants for the next, used up so not in reaction mechanism)

• the step with the higher Ea, is the rate determining step (Elementary reaction)

what is a catalyst

how do these differ from intermediates

• species that increase the rate of reaction, by providing an alternate complex mechanism reaction pathway, with lower Ea

• but aren’t used up (must partake, so are consumed and regenerated), therefore distinct from intermediates (formed then consumed)

how does the presence of a catalyst change the reaction coordinate diagram

what functions does it change, what functions remain the same

• it creates more steps on the coordinate diagram (together with less Ea in total), in order to consume and regenerate the catalyst (AND do the original reaction) - therefore reaction is definitely complex

• reactants / products keep the same deltaH (change in reaction energy) as before, the catalyst only reduces the Ea part of the coordinate diagram (lowers this energy)

• therefore only kinetics change (rate coefficients) NOT thermodynamics (state functions / heat / deltaH, etc)

how does a catalyst affect equilibrium

• a catalyst does not affect equilibrium!

• this is because thermodynamic state functions aren’t changed, only kinetics are

• therefore rate increases and equilibrium is reached faster, but equilibrium’s position (favoring forwards/reverse) is unchanged, as this rate increase will equally increase the reverse reaction

name the 3 types of catalysis

• homogenous catalysis

• heterogenous catalysis

• enzyme catalysis

distinguish between homogenous and heterogenous catalysis

homogenous

• reactants and catalysts are in the same phase (either everything is gas, or everything in solution)

heterogenous

• reactants and catalysts in the same phase (reactants usually gas / solution, catalysts usually solids)

• this provides a solid surface to catalyse the reaction (catalyic surface)

• adsorbates are the intermediates, which are the molecules + the solid surface, at each step

• can break bonds =

  • the reactant molecule weakly binds to solid (absorption)

  • the bonds between reactant are broken, while still bound to the solid (requiring less energy)

  • it then can easily seperats from the surface

• can form bonds =

  • reactant weakly binds to solid

  • they dissociate from their original form and become atoms

  • these atoms then rearrange to form new bonds, and unbind as the product

what is the Haber-Bosch process

how is it done efficiently

• the industrial process for ammonia synthesis

• is thermodynamically favored (spontaneous) but kinetically slow

• therefore a catalyst is used (heterogenous), originally Os, now Fe, along with high T & P

describe enzyme catalysis

• occurs in biological systems

• the catalysts are enzymes (large protein molecules), with one or more active sites, which catalyse the reaction (reactants = substrates)

• this process is somewhat homologous to heterogenous catalysis, the active site providing this solid surface (specifically designed for the molecule to favor reaction)

  • E + S → ES → EP → E + P (adds elementary steps)

• the intermediates are the enzyme-substrate & enzyme-product complexes

• e.g. biological N fixation, using nitrogenous enzyme, with N2(g) + H2(g) (and ATP), to form NH2

name a common example of catalysis…

• in nature

• in modern day life

• ozone hole formation at the poles is driven by catalytic reaction cycles of stratospheric Cl (resulting in O3 depletion)

• car exhaust pipes contain catalytic converts, catalysing the conversion of undesirable gases (CO, NOx, unburnt hydrocarbons) → more environmentally friendly ones (which are pumped out

for taking measurements on kinetics of a reaction…

• what do you measure

• what do you change

• what do you keep the same

• concentration of reactants (or products?) as a function of time

• ensure fixed T between trials (to not complicate measurement - influences k)

• only change concentration between trials (Gather a variety of data)

• this provides a graph of reaction rate

what kinetics measurement method would you use for slow reactions (lower reaction rate)

• measurements of timescales of minutes (or longer) apart

• solution-phase = may involve titrations (take out titration → work out conc. → plot point on graph → determine rate)

• gas-phase = may involve mass spectrometer (open the gas to spectrometer → provides gas concentrations → plot point on graph → determine rate)

what kinetics measurement method would you use for fast reactions

• make measurements on a timescale of seconds (or less) apart

• solutions =

  • electromagnetic radiation (e.g. light) passed through reaction mixture → absorbtion detected and recorded (often by a computer, done quick) → Beer-Lambert law done to determine conc. → plotted on graph

• electrochemical reactions (redox solutions & battery) =

  • electrodes in solution attached to voltmeter → voltage measured at intervals to computer → computer finds conc. → data plotted

• gases =

  • reaction mixture open to pressure transducer → constantly measures pressure to computer → computer finds conc. from pressure (ideal gas law) → data plotted