Kinetics Flashcards
Define the average rate of reaction
Avr. Rate = Change in conc/change in time = deltaC/deltaT
what is the instantaneous rate of reaction
Rate = d(conc.)/dt = derivative of concentration wrt time
i.e. derivative of the line of a conc-time graph
What does a +ve and what does a -ve ROR represent
+ve ROR means the conc. of the species is increasing with time
-ve ROR means the conc. of the species is reducing with time
what are the units for ROR and what is the shorthand for concs
ROR has units of moldm^-3s^-1 usually
[A] is the shorthand for conc. of whatever is inside the square brackets
what is the equation for rate of reaction in terms of the stoichiometric coeffs.
how are these different for products / reactants
use formation of H2O as example
2H2 + O2 —> 2H2O
ROR = r = (1/va) (d[A] / dt)
where va is the stoichiometric coeff
va has -ve sign for reagents, +ve sign for products
e.g. using example
ROR = r = -1/2 d[H2]/dt
d[H2O]/dt = -2 d[O2]/dt
what is the general form of the rate equation (for our purposes), what is k, what do we call the dependence on different species
Rate = k[A]^a [B]^b
k = Rate constant or coefficient
a, b are constants, these are powers which give the ‘orders’ wrt different species
what is a first order rate equation, what is a second order rate equation, give the units of K in each case
r = k[A]
is a first order rate equation, in this case k has units of s^-1
r = k[A]^2
or
r = k[A][B]
are examples of second order rate equations, the units of k are dm^3mol^-1s^-1
give the main three reasons for the importance of rate laws
1) If we know the rate law and the constants in it then we can use it to predict the rate for any set of conditions
2) the form of the rate law can tell us something about the mechanism of the reaction
3) knowing the rate law enables us to sperate the conc. dependence from underlying fundamental effect which is size of rate const.
are rate constants temperature dependent, what is usually the trend
Rate constants (and so rates overall) are heavily temperature dependent so ALWAYS state temperature
generally size of rate coefficient increases with temp
what is the most common relationship between rate coefficient and temp, give the equation and explain what each of the parts give
- Many rate constants will follow the Arrhenius equation
k = A exp(-Ea / RT)
k = rate constant (variable units)
A = pre-expo factor (same units as k)
Ea = activation energy (Jmol^-1)
T = temp (T)
R = ideal gas const. (J K^-1 mol^-1)
what does a graph of ln(k) against 1/T give, what are its key features
ln(k) against 1/T will give a straight line graph of
gradient = -Ea/R
Y-int = ln(A)
derive the expression for the equilibrium constants in terms of rate constants for the reaction
Assume we have some equil. of
A+B —REV.—> C+D
assume the forwards direction follows rate law
rate(f) = kf [A] [B]
and the reverse follows
rate(r) = kr[A][B]
At equil. these have the same value as the forwards and backwards reactions have the same rate so
kf [A(eq)] [B(eq)] = kr [B(eq)] [C(eq)]
K = [C(eq)] [D(eq)] / [A(eq)] [B(eq)] = kf / kr
so
K = kf / kr
What is the main thing that occurs in all reactions that we must understand to analyse RORs
MOs need to interact:
- this is usually HOMO-LUMO interactions
- Bonds are broken, Bonds are formed
What is a potential energy surface, why are they difficult in practice
- a potential energy surface uses the fact that in theory, using MOs, we can calculate the energy of any arbitrary arrangement of molecules
- in principle we can calculate the energy of any given arrangement of A and B as they interact
- we end up with a potential energy surface (PES) which gives the PE of the system as a function of the positions of all the atoms in the system
- in reality this is monumentally difficult to form and usually requires multi-dimensional plots
What are some key features of PESs, what can we use them to imagine
we can use the PE surface to imagine the atoms ‘moving’ over it, they start out in a position which corresponds to reactants then move along some path over the surface as they rearrange themselves and end up in a position corresponding to products
the stable molecules, products/reactants exist in potential energy minima
which path over the PES is most favoured and why
- when going from reactants to products over the PES, some energy will always have to be put in because the reactants and products exist in potential energy minima
- the route which involves the least expenditure of energy is the most favoured route
- it’s the most favoured route because the energy E which has to be put in in order to reach the energy of the transition state is only present in some cases, the lower this energy is, the more reactions can occur
- we can safely assume as very few molecules have sufficient energy to react, that they all go via the favoured route
what is the transition state of a reaction, what are the key points about it
- The transition state is the state of the molecule(s) at the highest energy point on the PES on the route between the reactants and products
- it is not a molecule in the conventional sense because it is very unstable as molecules exist in potential energy minima and intermediates exist on potential energy maxima (unstable equil.) so any slight change and there’s a driving force to remove the intermediate
- they exist for a very small amount of time, in the order of a single molecular vibration
what is an intermediate, how is this different to a transition state
an intermediate is a standard molecule but one which exists in a metastable equilibrium between the reactants and products
a transition state is not stable
what is the minimum energy pathway from reactants to products called, what can we plot with it, what is the key feature of this plot
- the minimum energy pathway from reactants to products is called the reaction coordinate
- it can be plotted (on X) against potential energy
- this means we have
Reactants (low energy)
rising up to maxima (transition state)
lowering in energy again to products - the activation energy is the key feature of this plot, Ea is the energy difference between the maxima and the reactants
what is collision theory, what are the key concepts we’ll work with, is it accurate?
- Collision theory is a theory about the motions and energies of the particles of gases, its entirely classical
- the theory treats particles as objects where size «distance between them
- the particles have kinetic energy which causes them to move in random directions
- they collide elastically with each other and the walls of the container
what is the mean speed of gas particles in collision theory given by
- the energies and speeds of the particles can be given by the Maxwell Distribution
- the mean relative speed (cbar(rel))
cbar(rel) = (8kbT / pi*mu)^1/2
kb = Boltzmann constant
T = temp
mu = reduced mass of system
what is mu, the reduced mass of a system of two molecules A and B
mu = (mA*mB) / (mA + mB)
what is the mean relative speed of two molecules A and B in collision theory
cbar(rel) = (8kbT / pi*μ)^1/2
Assuming the molecules are structureless spheres, state the expressions for collision rate between A and B (according to collision theory), explain each of the variables
Collision rate = Z(AB), collisions m^-3 s^-1
Z(AB) = cAcBpi(rA + rB)^2 * cbar(rel)
= cAcBpi(rA+rB)^2 * (8kbT / pi*mu)^1/2
cA = conc. of A in molecules per m^3
cB = conc. of B in molecules per m^3
rA = radius of A
rB = radius of B
cbar(rel) = mean relative speed
this expression can be simplified by defining the collision cross-section, σ, as
pi*(rA+rB)^2, giving
Z(AB) = cAcBσ(8kbT / pimu)^1/2