Kinetics Flashcards
Order (wrt a reactant)
The power to which the rate of the reaction is dependent on the concentration of that reactant.
i.e. rate = k[A]^2[B]
order wrt A is 2, order wrt B is 1
Overall Order
The sum of the orders wrt each of the species the rate is dependent on
i.e. rate = k[A]^2[B]
overall order is 3 (2 + 1)
Moleculartiy
The molecularity of a reaction is defined as the number of reacting molecules which collide simultaneously to bring about a chemical reaction. In other words, the molecularity of an elementary reaction is defined as the number of reactant molecules taking part in the reaction.
What is meant by the steady-state approximation
If a reactive intermediate R is present at low and constant concentration throughout (most of) the course of the reaction, then we can set d[R]/dt = 0 in the rate equations. This is because the intermediate is used up and produced at roughly the same rate.
Why is the steady-state approximation useful?
Applying the SSA has the effect of converting a mathematically intractable (unsolvable) set of coupled differential equations into a system of simultaneous equations which can be solved (by substitution of the equations for [R] into the more general equations).
Under what conditions is the steady-state approximation valid?
The reactive intermediate, R, must be used up virtually as soon as it is formed and be present in low concentrations (and therefore roughly constant low concentration). This is true at all times apart from the very start of the reaction when [R] must build up from 0 to its low concentration, and at the end of the reaction when [R] goes to 0.
Why does the rate of most chemical reactions increase when the temperature is raised?
By considering the Arrhenius equation, it can be seen that the rate constant increases with increasing temperature. Because the rate is proportional to k, the rate will also increase with increasing temperature. This is true for all elementary reactions and is only not true for reactions which have complex mechanisms. Overall, this relationship is as a result of an increased number of successful collisions at higher temperatures which are then able to overcome the activation energy for reaction - hence the faster rate of reaction.
What is the origin of the activation energy of a reaction
The activation energy is the minimum energy required for reactants to overcome an energy barrier (in order to form the high energy transition state) and transform into products.
Half life
The half life of a substance is defined as the time it takes for the concentration of the substance to fall to half of its initial value
How do successive half lives vary for a zeroth order reaction
Decrease
How do successive half lives vary for a first order reaction
Constant
How do successive half lives vary for a second order reaction
Increase
Outline the isolation method for determining rate laws
The dependence of the reaction rate on the chosen reactant concentration is isolated by having all other reactants present in a large excess, so that their concentration reamins essentially constant throughout the course of the reaction. All the concentrations of the reactants in excess may be combined with the rate constant to yield a single effective rate constant.
Outline the differential methods for determining rate laws
When the rate law depends on only the concentration of one species (can be after using the isolation method):
v = k[A]^a
log(v) = log(k) + a log[A]
So plot log(v) against log[A] and the gradient will equal the reaction order, a, with an intercept equal to log(v)
What are the two methods in which data can be obtained for use in the differential method of determining rate law
- Measure the concentration of the reactant, A, as a function of time and use this to calculate v=-d[A]/dt
- Make a series of measurements of the initial rate of the reaction with different initial concentrations of A (initial rates method)
Outline the integral methods for determining the rate law
If the concentration(s) have been measured as a function of time, can compare their time dependence using integrated rate laws (usually after using the isolation method).
eg for zeroth order a plot of [A] vs t will be linear but for first order ln[A] vs t will be linear
Outline the half-life method for determining rate laws
Investigate the behaviour of successive half lives by measuring the concentration as a function of time.
What are the most commmon techniques for mixing the reactants and initiating reaction
- Flow techniques
- Flash photolysis and laser pump probe techniques
- Relaxation methods
- Shock tubes
- Lifetime methods
What are the most common techniques for monitoring concentrations as a function of time
For slow reactions
* Real time analysis
* Quenching
What are the most common ways of monitoring the composition of a reaction mixture
- monitoring pressure or volume
- conductivity or pH measurements
- Titration
- Colourimetry
- Absorption or emission spectroscopy
- Polarimetry
- Mass spectrometry
- Gas chromatography
- NMR/ESR
Outline flow techniques
In the simplest flow method, reactants are mixed at one end of a flow tube, and the composition of the reaction mixture is monitored at one or more
positions further along the tube. If the flow velocity along the tube is known, then measurements at different positions provide information on concentrations at different times after initiation of reaction.
In a variation, the detector may be in a fixed position, but a moveable injector may be used to inject one of the reactants into the flow tube at different positions relative to the detector.
What kind of reactions may be studied using the discharge flow method
Reactions of atomic or radical species
What is the discharge flow method
The reactive species (atomic or radical) is generated by a microwave discharge immediately prior into injection into the flow tube
What are the disadvantages of continuous flow methods and how can they be avoided
Relatively large quantities of reactants are needed, and very high flow velocities are required in order to study fast reactions. To avoid this, use the stopped flow technique where a fixed volume of reactants are rapidly flowed into a reaction chamber and mixed by the action of a syringe fitted with an end stop.
What common problem do all flow techniques share and how can this be minimised
Contributions from heterogeneous reactions at the walls of the flow tube can complicate the experiment.
This can be minimised by coating the inner surface of the flow tube with an unreactive substqance like teflon , and the relative contributions from the process under study and reactions with the walls may be quantified by varying the diameter of the flow tube (and therefore the V:SA)
Describe flash photolysis and laser pump probe techniques
In flash photolysis, reaction is initiated by a pulse of light that dissociated a suitable precursor molecule in the reaction mixture to produce a reactive species, thereby initiating reaction. The concentration of the reactive species is then monitored as a function of time. The shortest timescale over which reactions may be studied using this technique is determined by the duration of the pulse.
What are the advantages of flash photolysis
Reactants are produced from well-mixed precursors so there is no mixing time to reduce the time resolution of the technique.
Because the reactants are generated and monitored in the centre of the reaction cell, there are no wall reactions to worry about as there are in flow methods.
What is the difference between pulse-radiolysis and flash photolysis
Pulse radiolysis is a variation of flash photolysis in which a short pulse of high energy electrons is passed through the sample in order to initiate reaction.
What is the pump-probe technique and for what reactions would it be used
For very fast processes!
Pulsed lasers are employed both to initiate the reaction (the pump) and to detect the products via a pulsed spectroscopic technique (the probe)
Describe relaxation methods
A chemical system at equilibrium is then perturbed in some way - the rate of relaxation to a new equilibrium provides information about the forward and reverse rate constants for the reaction.
The rate at which the concentrations relax to their new equilibrium values is determined by the sum of the two new rate constants. The new equilibrium constant is given by the ratio of the
two rate constants, K = k2f/k2r, so together a measurement of the rate of relaxation and the equilibrium
constant allows the individual reaction rate constants for the forward and reverse reaction to be determined.
Why would relaxation methods be used over flow methods
Since a system at chemical equilibrium is already well-mixed, relaxation methods overcome the mixing problems associated with many flow methods.
Describe the use of shock tubes for initiating reactions
It provides a way of producing highly reactive atomic or radical species through rapid dissociation of a molecular precursor, without the use of a discharge or laser pulse. A rapid increase in temperature leads to rapid production of reactive species (the dissociation products) initiating the reaction of interest. A shock tube consists of two chambers separated by a diaphragm. One chamber
contains the appropriate mixture of reactants and precursor, the second an inert gas at high pressure. To
initiate reaction, the diaphragm is punctured and a shock wave propagates through the reaction mixture. The temperature rise can be controlled by varying the pressure
and composition of the inert gas. The composition of the reaction mixture after initiation is monitored in real time,
usually spectroscopically.
What kind of reactions are usually studied using the shock tube method
Combustion reactions
What are the disadvantages of shock tube methods
Rapid heating is not selective for particular molecules and is likely to lead to at least partial dissociation of all the species in the reactants chamber. This leads to a complicated mixture of reactive species and often a large number of reactions occuring in addition to the reaction under study.
Each experiment is essentially a “one off”, so no signal averaging is possible, and the signal to noise levels are often low.
Describe lifetime methods
ΔvΔt ≥ 1/4π (uncertainty principle relating energy and time (E = hv))
Excited states are short lived and there is an uncertainty in their energy. Photons corresponding to any energy within this uncertainty ΔE may be absorbed so spectral lines have a finite width known as the natural linewidth.
Kinetic processes involving excited states reduce their lifetime and cause further broadening - for first order kinetics, the rate constant is equal to the reciprocal of the lifetime and so first order rate constants may be determined from measurements of spectral linewidths.
k = 1/Δt
Describe the use of absorption spectroscopy for monitoring the composition of reaction mixtures
Absorption spectroscopy is used to track reactions in which
the reactants and products have different absorption spectra. A monochromatic light source, often a
laser beam, is passed through the reaction mixture, and the ratio of transmitted to incident light
intensity is measured as a function of time. The quantity T = I/I_0 is known as the transmittance, and may be related to the changing concentration of the absorbing species using the Beer–Lambert law.
log(T) = −εcl or ln(T) = -αcl
Describe the use of resonance fluroescence for monitoring the composition of reaction mixtures
Used for detecting atomic species. The
light source is a discharge lamp filled with a mixture of helium and a molecular precursor for the atom of interest. A microwave discharge inside the lamp dissociates the precursor and produces a mixture of ground state and excited state atoms. The lamp then emits radiation at characteristic
frequencies as the excited state atoms emit photons to return to ground state. This radiation may be used to excite
atoms of the same species present in a reaction mixture, and monitoring the intensity of radiation emitted from these atoms as they return to ground state provides a measure of their concentration in the reaction mixture.
Describe the use of laser-induced fluorescence for monitoring the composition of reaction mixtures
In laser-induced fluorescence a laser is used to excite a chosen species in a reaction mixture to an electronically excited state. The excited states then emit photons to return to the ground state, and the intensity of this fluorescent emission is measured. Because the number of excited states
produced by the laser pulse is proportional to the number of ground state molecules present in the
reaction mixture, the fluorescence intensity provides a measure of the concentration of the chosen
species.
When does an explosion occur
An explosion occurs when a reaction rate accelerates out of control. As the reaction speeds up, gaseous products are formed in larger and larger amounts, and more and more heat is generated. The rapid liberation of heat causes the gases to expand, generating extremely high pressures, and it is this sudden formation of a huge volume of expanded gas that constitutes the explosion.
What are the different mechanisms that may lead to an explosion
- If the heat generated in a reaction due to the reaction exothermicity cannot be dissipated sufficiently rapidly - thermal explosions
- Chain branching within a chain reaction - chain branching explosions or isothermal explosions
in practice, both mechanisms often occur simultaneously, as any acceleration in the rate of an exothermic reaction will eventually lead to an increase in temperature but chain branching is not a requirement
What factors affect explosion limits
- Temperature
- Surface/Volume ratio
- Overall pressure
What is the form of the rate equation proposed by simple collision theory
v = (encounter rate) (energy requirement) (steric requirement)
How is the encounter rate calculated in simple collision theory
Using properties of gases - rate of collisions of molecules using collision diameter etc
How is the energy requirement calculated in simple collision theory
Using the maxwell-boltzmann distribution of molecular speeds, the fraction of collisions for which the energy is high enough to overcome the activation barrier = exp(-E(a)/RT)
How is the steric requirement calculated in simple collision theory
Experimentally, measured rates are found to be up to an order of magnitude smaller than those calculated from just the encounter rate and energy requirement factors. We account for the disagreement by introducing a steric factor, P, into the expression for the reaction rate.
What are the disadvantages to simple collision theory
- does not account for the fact that, unless the collision is head on, not all of the kinetic energy of the two reactants is available for reaction - only the Ek corresponding to the velocity component along the relative velocity vector of the reactants actually contributes to the collision energy
- The energy stored in internal degrees of freedom is ignored - for reactions involving large molecules this leads to large discrepancies although this is partly corrected for by the inclusion of the steric factor, P
Describe the limitations of the initial rates method for determining the order of reaction
- the accuracy of measurement means that unless precise measurement is used, the uncertainty in the measured initial rate is high
- better for fast reactions as significant reaction is likely to have occurred before significant changes in concentration
- can be difficult if the mechanism is complex or there are reverse and side reactions taking place
