The Reaction Toolkit Flashcards
(256 cards)
1
Q
What is the difference between thermodynamics and kinetics?
A
Thermodynamics - tells us whether a reaction is feasible and the energetic changes involved
Kinetics - tells us how fast reactions happen
T - energy changes
K - rates of reaction
2
Q
What do both thermodynamics and kinetics give understanding of?
A
Can give understanding of mechanism
3
Q
What is a reaction energy profile?
A
Profile that shows us the energy of the atoms and molecules over the course of a reaction
Reaction coordinate shows progress
Energy shows total relative energy of reacting molecules as they change their arrangement
4
Q
What are the two values we can get from reaction energy profiles?
A
Ea - Activation energy (distance from reactants to top)
ΔrG - Free energy change (distance from reactants to products)
5
Q
What do activation energy and the reaction free energy change determine?
A
Ea - impacts rate of reaction
ΔrG - determines if reaction is spontaneous
6
Q
What is internal energy?
A
The internal energy of a molecule is the total contribution from all the energies
(kinetic/intermolecular/intramolecular/nuclear)
7
Q
What is true about internal energy?
A
Impossible to measure exactly
Need to look at changes in internal energy
8
Q
What are the assumptions for the kinetic theory of gases?
A
- Gas consists of molecules with mass (m) and diameter (d) in constant random motion
- Size of the molecules are negligible (compared to distance travelled between collisions)
- No interactions between particles, except through perfectly elastic collisions
9
Q
What is a perfectly elastic collision?
A
One in which the total translational kinetic energy of the molecules is conserved
10
Q
What is temperature a measure of?
A
Measure of the amount of kinetic energy that the particles in a material have
11
Q
What are the different contributions to the energy in different states?
A
In a gas - main contribution is from translational motion
In a solid - from vibrational motion
12
Q
What is true about velocities in particle collisions?
A
Velocity will change in a single collision
Velocity distribution is conserved at a given temp
13
Q
What is the difference between heat and temperature?
A
Related but different
Heat is a form of energy
Heat can flow between two objects with different temps
- Heat will flow from object with higher temp to object with lower temp
14
Q
What is true about heat?
A
An object doesn’t have heat and heat causes a temp change
15
Q
What can heat be conducted between?
A
Between two objects between the molecules at an interface between the two objects of different temps
16
Q
What is true about molecules in an object with higher temp?
A
They have higher kinetic energy
17
Q
What is Maxwell-Boltzmann distribution of speeds?
A
The distribution of speeds in an ideal gas at thermal equilibrium
In a gas, speeds of molecules vary and are always changing
18
Q
What is work?
A
Work is a form of energy
Mechanical work is done when a force moves through a distance
Work = Force x Distance (w = Fd)
19
Q
How can you send energy from one thing to another?
A
Using work (regular motion in a direction) or heat (random thermal motion)
20
Q
What is the formula for work with respect to a gas being compressed in a cylinder?
A
w = -PΔV
21
Q
How do reactions take place?
A
Through a series of elementary steps (the mechanism)
22
Q
What are the different types of elementary steps
A
These are usually either:
- Bimolecular - single collision between two molecules
- Unimolecular - dissociation or isomerisation of a single molecule
Or on rare occasions can be:
- Termolecular - simultaneous collision of three molecules
23
Q
How do we find the mechanism for a chemical reaction?
A
Propose a mechanism and then see whether the proposal agrees with:
- rate law
- intermediates
- stereochemistry
- temp dependence
- product distribution
Cannot prove a mechanism is correct
24
Q
How can we consider a situation?
A
As two parts:
- The system - what we are studying
- The surroundings - everything else (rest of the universe)
25
How can you classify a system?
What are the three types of system?
Can classify based on what it can exchange with the environment
1. Isolated - no exchange of energy or mass (material)
2. Closed - exchange of energy (heat or work) but no exchange of mass
3. Open - exchange of energy and mass
26
What is the complexity of each type of system?
Isolated - easy to study but no interesting
Closed - often applicable and relatively straightforward to deal with
Open - too complex for this course
27
What are the types of closed system?
Isobaric - constant pressure
Isothermal - constant temperature
Isochoric - constant volume
Adiabatic - no heat flow between system and surroundings
28
What is the relationship between adiabatic systems and isothermal systems?
If a system is adiabatic it will often involve a change in temperature - therefore not being isothermal
29
What is the total energy of a system called?
Its internal energy (U)
30
When a system changes its energy what can we say?
It changes from one state to another
31
What happens to ΔU, q and w when U, q and w change?
If internal energy of a system (U) increases, the internal energy change (ΔU) is positive
If system gains heat energy (q) from surroundings, the heat energy exchange (q) is positive
If work (w) is done on the system by the surroundings, the work energy exchange (w) is positive
32
What is the first law of thermodynamics?
The internal energy of an isolated system is constant (energy cannot be created or destroyed)
33
What can changes in the internal energy of a closed system be due to?
Heat or work energy (or both) being exchanged between the system and surroundings
But the combined energy of the system and surroundings must stay constant
34
What is true according to the first law of thermodynamics if there is only heat flow or only work?
ΔU = q
or
ΔU = w
35
What is the mathematical expression of the first law of thermodynamics?
ΔU = q + w
A closed system where heat flows and work can be done
36
How can you change the direction of a reversible process?
By making an infinitesimal change to a variable
37
What is true about a process that occurs irreversibly or non-reversibly?
Doesn't mean that you can never undo it but it just means that it will require a large change in conditions to reverse the process
38
What is the notation for small changes?
Δ indicates a change in quantity
d indicates very small changes to a state function
đ indicates very small changes to a path function
39
What is a state function?
A property of a system that only depends on the systems state, not on how it got there
e.g. Internal energy (U) or temperature (T)
40
What is a path function?
A parameter that does depend on the way a system changed from one state to another
e.g. heat energy transferred (q) or work done (w)
41
What is important to remember to equations in thermodynamics?
If a system loses something it will be negative in the equation
42
How do you explain the difference between a state and a path function?
A state function will remain the same no matter what path is taken whereas the path function value depends on the path taken
43
Why is enthalpy change very useful?
ΔH is very useful as it can be related to the heat change in a system and is relatively easy to measure
44
What does a subscript P, V or T indicate?
Constant variables
e.g. qᵥ means amount of heat at constant volume
45
How is enthalpy defined?
H = U + PV
As addition of state functions, H is also a state function
Enthalpy = energy in our system + work needed to make space for our system
46
How can we write enthalpy change? (small changes)
dH = dU + d(PV) = dU + PdV + VdP
At constant pressure: dH = dU + PdV
47
For large changes in enthalpy (ΔH), how can we write that?
ΔH = ΔU + PΔV + VΔP
48
How do we calculate enthalpy change (ΔH) for constant pressure and volume?
ΔH ≈ ΔU
If there is no other work done:
ΔH ≈ ΔU = q(v,p) (heat at constant volume and pressure)
49
How do we calculate enthalpy change for constant pressure?
ΔH = Δqp (heat at constant pressure)
50
What is the equation for enthalpy change using PV = nRT? (at constant temperature)
ΔH = ΔU + ΔnRT where Δn is change in number of moles of gas
51
How do we calculate enthalpy change (ΔH) at constant volume?
ΔH = Δqᵥ + ΔnRT
52
What are the set of standard conditions?
Pressure = 1x10⁵ Pa (1 bar ≈ 1 atmosphere)
Temperature = 298.15K (exactly 25°C)
53
What is heat capacity?
Helps us relate heat energy to temperature changes and can be written in two ways:
C = Δq/ΔT or C = dq/dT
Generally specified for constant pressure or constant volumes
54
What does heat capacity need to be specified for?
A certain quantity of material
55
What are the different kinds of heat capacity?
Specific heat capacity (c)
- Units: Jkg-1K-1
- Heat energy (q) to raise 1 kg of a substance by 1 K
Molar heat capacity (Cm)
- Units Jmol-1K-1
- Heat energy (q) to raise 1 mole of a substance by 1 K
Heat capacity (C)
- Units: J K-1
- Heat energy (q) to raise the whole system by 1 K
56
How do you convert between types of heat capacity?
First convert to heat capacity (C) and then to the one you want
57
What is the heat capacity of mixtures?
Heat capacities can be summed so:
C = n1Cm1 + n2Cm2 ...
C = m1c1 + m2c2
where there is nx moles of each component with molar heat capacity Cmx and mx kg of each component with specific heat cx
58
What is Hess's law?
The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reaction into which it can be divided
ΔrH = ΔrH(A) + ΔrH(B) ...
Must sum reactions in the correct direction
59
How can you use enthalpy of formation and Hess's law?
Values of ΔfH can be used to find ΔrH
A reaction can be divided into:
1. reactants decomposing to form elements
2. products forming from those elements
Arrows go from elements to reactants and products
60
How can you use enthalpy of combustion and Hess's law?
Values of ΔcH can be used to find ΔrH
A reaction can be divided into:
1. reactants combusting to form combustion products
2. products forming from those combustion products
Arrows go from reactants and products to combustion products
61
What is important to remember about ΔfH?
Enthalpy change of formation of an element is zero
62
What are intra-molecular bonds?
Chemical bonds within a molecule and has bond energy
63
What are the different interactions between molecules?
Ion-Ion
Dipole-dipole (stationary)
Dipole-dipole (rotating)
Dispersion
Distance dependence:
1/r, 1/r³,1/r⁶,1/r⁶
64
What are ion-ion interactions?
Interactions between charges that either repel or attract each other
65
What is the potential energy (u) associated with ion-ion interactions?
u(r) = (Kq1q2)/r
where K is coulombs constant, q are the charges of the two particles that are r distance apart
(Given in formula sheet)
66
What does negative potential show?
An attractive interaction
67
What is a dipole?
A separation of charge
A molecule can have a dipole but still be overall neutral
68
How do we quantify overall charge separation?
Using dipole moment μ
μ = Qr
where Q is two equal magnitude but opposite sign charges are separated by distance r
69
What is good to know about dipole moments?
They are vectors and can be summed up
If a molecule has symmetry, dipole moments may cancel out along certain directions
70
What is the difference between dipole-dipole interactions in fixed molecules or tumbling molecules?
For fixed molecules interaction varies with angle between parallel dipoles
For tumbling molecules interaction gets averaged
71
What is true about interactions between dipoles of tumbling molecules?
always an attractive interaction as the molecules will try to orientate in a low energy configuration which is more negative
means the average interaction energy over all the molecules
72
How do dispersion interactions arise?
On average there is a uniform distribution of electrons within each molecule
Temporary fluctuations in the electronic distribution within one molecule causes a transient dipole moment
The dipole moment can induce an opposite dipole in a nearby molecule
73
What are I and ɑ in the formula for dispersion interactions?
I is ionisation energy of each molecule
ɑ is polarisability of each molecule
74
What is true about the distance dependence 1/r⁶?
They relate to tumbling dipole-dipole, dispersion and dipole-induced dipole
Always attractive
Often described together as van der Walls attraction
75
What is the formula for van der Waals interaction?
u(r) = C/r⁶
76
If vdW interactions are always attractive how do molecules repel?
If you bring two molecules very close together they will repel due to electron clouds starting to strongly repel each other
- short range and depends on 1/r¹²
77
What do you get if you combine repulsion and vdW attraction?
Leonard Jones Potential
Widely used model for interaction between molecules
ε represents interaction strength and σ is distance where interaction is zero
78
What is the difference between exothermic and endothermic processes?
Exothermic - energy is released as heat
At constant pressure ΔH < 0
At constant volume ΔU > 0
Endothermic - energy is taken in by the system as heat
At constant pressure ΔH > 0
At constant volume ΔU > 0
79
What is a spontaneous process?
Occurs without being driven but some may occur very slowly
Can be exothermic or endothermic
Not all exothermic changes are spontaneous
80
What do all spontaneous processes involve?
They all involve an increase in total disorder
The disorder of a system is called entropy
81
What is the second law of thermodynamics?
'The entropy of an isolated system tends to increase to the maximum'
Means that in an isolated system, any spontaneous process involves an increase in entropy
82
What is there to know about entropy?
Given the symbol S
Entropy change is written ΔS
A state function
You can write entropy of one mole of a substance (molar entropy) Sm
83
How does entropy relate to heat? What about work?
Heat can be thought of as 'disordered energy', heat flowing into a system increases random thermal motion
Converely work can be considered as ordered energy, doing work on a system causes ordered motion
84
What happens to entropy when temperature increases and why?
Entropy increases as temperature increases due to increased random thermal motion
85
How else does entropy increase, not including change in temp?
Increases if goes from solid to liquid to gas as more disorder
86
What are the entropy changes from a solid to a liquid to a gas called?
Entropy change of fusion and entropy change of vaporisation
87
How do you explain the difference between entropy and enthalpy using one word?
Entropy - structure
Enthalpy - interactions
88
What is the statistical view of entropy?
As a system becomes disordered, there are more ways that the system can be arranged
S = kʙ*lnΩ
where kʙ is Boltzmanns constant and Ω is number of ways a system can be arranged
89
What is true about mixtures and entropy?
Mixtures can be arranged in more ways than a pure substance and so have higher entropy
90
What is the third law of thermodynamics?
'The entropy of all perfect crystalline substances is zero at zero temperature (0K)'
Only one way to achieve this
91
How can you justify the third law of thermodynamics?
Using the statistical view of entropy
S = kʙ*ln1 = 0
Meaning we can define standard entropies relative to zero
92
What is true about entropy that is not true for enthalpy?
Entropy doesn't always have to be stated as a change
93
Why do some substances have residual entropy at 0K?
If there is more than one energetically equivalent arrangement
e.g. H bonding in water
94
What happens if ΔS < 0 for a reaction?
The system becomes more ordered
95
What do we need to do to predict spontaneous processes?
Consider an isolated system
96
What can small entropy changes be defined as?
dS = đqrev/T
where đqrev is a small amount of heat supplied reversibly to the system and T is temp
97
What is true about heat that flows to and from the system?
Heat that flows to the system must have come from the surroundings
Heat that flows from the system must go to the surroundings
98
What is the most important equation in thermodynamics?
ΔG = ΔH - TΔS
99
What is true about expanding gases?
A gas expands to fill its container in a spontaneous process
If we have n molecules there are 2ⁿ ways to organise them between two containers
Only one arrangement has all molecules in one container
100
For any number (N) of distinguishable molecules, how many ways are there to arrange them?
N!
101
What is the total number of unique arrangements or multiplicity Ω if we have a mixture of N molecules that fit into t different categories with nt molecules in each category?
Ω = N!/(n1!n2!....nt!)
102
What is the lattice model when considering arrangements?
To look at arrangements of molecules it is useful to divide space into molecule size boxes
Each box is a lattice site and can contain 1 or 0 molecules
103
What is the difference between a macrostate and a microstate?
A macrostate is an observable state where we can make measurements of its properties
A microstate is an individual snapshot of the specific organism of a system
A macrostate is made up of one or more microstates
104
What is the probability of observing a particular macrostate?
Proportional to the number of microstates that make it up
105
Using the lattice model, why does a gas exert pressure and fill its container?
It maximises multiplicity as the macrostate with maximum microstates will always be the most likely
Also maximises entropy
106
Why do molecules diffuse and mix?
Multiplicity increases with increased mixing
Entropy always wants mixing but other factors balance this out
107
What is the standard chemical potential?
Standard chemical potential of a substance is the Gibbs free energy of 1 mole of that substance at a conc of 1 moldm-3 and at standard conditions
108
What is chemical potential μ?
Chemical potential of a substance is the Gibbs free energy of one mole of the substance at a specified conc
109
What is the equation for calculating chem potential?
μA = μ°A + RTln[A]
Assumes the solution behaves ideally
110
What happens to chem potential if [A] is > or < 1 moldm-3?
If [A] < 1 moldm-3 -> μA is lower than μ°
If [A] > 1 moldm-3 -> μA is higher than μ°
Can be justified because if A is more dilute it is more disordered so using equation for ΔG the Gibbs free energy must be lower
111
For gases what can you use to calculate chemical potential?
Partial pressures in bar
μA = μ°I + RTlnPi
112
How to calculate the contribution of each component in a mixture to the total Gibbs free energy of the mixture?
Multiply the chemical potential of each component by the number of moles of that component present
Gi = niμi
113
How to calculate Gibbs free energy of a mixture?
G = ∑niμi
114
How to calculate chemical potential of a component with respect to partial derivatives?
μi = ∂G/∂ni
if n is changed by a small amount
115
Where can we find the Gibbs energy of the mixture?
At any point along the reaction so long as we quantify extent of reaction between 0 (all reactants) and 1 (all products)
116
What is the equation for ΔG that involves reaction quotient?
What is true if the reaction is at equilibrium?
ΔG = ΔrG° + RTlnQ
ΔG = 0 and Q=K
So ΔrG° = -RTlnK
117
What does the equation ΔrG° = -RTlnK tell us?
If ΔrG° is negative K > 1 and equilibrium lies towards the products
if ΔrG° is positive K < 1 and equilibrium lies towards the reactants
118
What is the equation for lnK?
lnK = -ΔrG°/RT + ΔrS°/R
which is a straight line of lnK against 1/T
Assumes that ΔrG° and ΔrS° do not vary with temp
119
What is the link between equilibrium constant and rate constants?
K = k1/k-1
where k1 is rate constant for forwards reaction and k-1 is rate constant for backwards reaction
At equilibrium no net change in composition so reactions take place at the same rate
120
What is true about equilibrium for different values of k1 and k-1?
If k1 and k-1 are large, equilibrium will be reached quickly
If k1 and k-1 are small, equilibrium will be reached slowly
Position of equilibrium only depends on the ratio of the two and not the specific values
121
What happens if we plot G against the progress of a reaction?
G will reach a minimum at equilibrium
ΔG tells us the gradient of this line
122
What is ΔrG°?
ΔrG° is Gibbs free energy change when 1 mole of reactants changes to 1 mole of products in their standard states (For 1 mole of the reaction as written)
Difference in molar gibbs energies of the reactions and products in the standard states at a specified temperature
123
What is ΔG and G?
ΔG is Gibbs free energy change which relates to the specific conditions and concs that you have at a particular point in the reaction
Changes as the reaction proceeds and reaches zero at equilibrium
G is the total gibbs energy of the reaction mixture
124
What is the equation for dG with respect to V,P,S and T?
dG = VdP - SdT
125
At constant pressure condition what does entropy tell us?
Entropy tells us rate of change of G with temperature
dG/dT = -S
126
At constant temperature condition what does volume tell us?
Volume tells us rate of change of G with pressure
dG/dP = V
127
How can formation of solids be understood?
G = H - TS
Solids have lots of strong intermolecular interactions so large negative H, but low S due to restricted motion
So solids form at low temps when magnitude of -TS is small
128
How can formation of gases be understood?
G = H - TS
Gases have very few intermolecular interactions so near zero enthalpy, but high entropy due to rapid molecular motion
So gases form at high temps when magnitude of -TS is large
129
How can formation of liquids be understood?
Liquids are intermediates in both H and S so form at intermediate temperatures
130
How do we know what phase will form spontaneously?
Phase with the lowest free energy
131
What happens when we plot G against temperature for each phase for a material?
It will change fastest for gas and slowest for solid and give us the temperature for fusion and vaporisation
The lowest G is the phase that will form
132
What are phase diagrams?
They show stable phases and are usually as a function of of pressure and temperature
133
What is true for two phase at equilibrium (at a phase boundary)?
Their Gibbs free energies are equal
134
If we change temp and pressure slightly and phases are still in equilibrium what must be happening?
Must be moving along the phase boundary and:
dG(l) = dG(g)
135
What is the relationship between pressure and temperature at any phase boundary?
What can we predict using it?
dP/dT = ΔH/TΔV
This is the Clapeyron that lets us predict the gradient of phase boundaries from the phase transition enthalpy and volume change
136
How do you calculate the volume/enthalpy change of vaporisation?
V(g) - V(l)
S(g) - S(l)
137
What is the definition of rate?
The rate of change of concentration of specified reactant
A measure of the rate is given by the formation or consumption of a specified species
138
What is the rate of consumption of reactant A?
vA = -d[A]/dt
It is negative so rate can be recorded as positive
139
What is the rate of formation of product C?
vC = d[C]/dt
140
What are rate graphs?
What does the tangent give you?
Graphs of concentration against time with the tangent of the graph being either the rate or -rate
141
What is the instantaneous rate of reaction?
Slope of the tangent to the graph of concentration against time
142
What is the general equation for rate of reaction, v?
vR = 1/vJ*d[J]/dt
where vJ is the stoichiometric coefficient of substance J (with vJ being negative for reactants and positive for products)
143
What are the units of concentration and rate of reaction?
molL-1 or moldm-3
molL-1s-1 or moldm-3s-1
144
What is the rate law?
Expresses the rate in terms of concs of reactants, products and catalysts (not intermediates)
v = k[A]ⁱ[B]ⁿ
where i and n are orders of reaction with respect to [A] and [B]
and k is the rate constant
145
What is the overall order of reaction?
The sum of the individual order
146
How is the rate law determined and what can it be used for?
It is experimentally determined
Can predict the rate of reaction from composition of mixture
Can be used as a guide to the mechanism
147
What is true about any proposed mechanism?
It needs to be consistent with the rate law
148
What might you not know about the rate law?
Can have more than one rate constant
Orders do not need to be integers
149
What are the units of the rate constant?
They depend on the overall order of the reaction
1st order: s-1
2nd order: moldm-3s-1
etc
150
How do we determine the rate law? (Experimentally)
Need experimental methods of monitoring the progress (any physical change can be monitored)
1. Real time analysis - in situ process where composition of the system is analysed while the reaction is in progress
2. Quenching methods - involves ex situ analysis. The reaction is quenched after it has proceeded for a certain length of time, it can then be examined by different techniques
151
What is real time analysis limited by?
The response time of the detector
152
How do you monitor reaction progress using pressure changes?
Recording pressure against time
e.g. if one mole of reactants forms 2.5 moles of products then pressure has increased
153
How do you monitor reaction progress using spectroscopic analysis?
Measurement of the absorption of light by a particular species can be used to monitor its concentration, when reactants and products have different absorption spectra
Use Beer-Lambert Law
A = εcl
154
What is the Beer-Lambert law?
A = εcl = -logT = -logI/I₀
ε is absorption/extinction coefficient (dm3mol-1cm-1)
Measure intensity of light before and after
155
What is the isolation method? What does it form?
Set up a reaction so all reagents, except one, are in such great excess that their concs are effectively constant
Forms a pseudo rate law with a new rate constant k'
156
How do you find dependence of the rate on all the reactants using the isolation method?
Isolate them all one by one and find order of each one
157
What is the method of initial rates?
Often used with isolation method
The initial rate is the rate at t=0
So rate is measured at the beginning of the reaction for several different initial concs of reactants
158
What is the differential method?
By varying values of [A]₀ and holding [B]₀ constant and measuring the initial rates, v₀, the value of the order of A can be obtained from a log-log plot of logv₀ against log[B]₀
Should be repeated for all reactants
159
What are integrated rate laws?
The integrated versions of regular rate laws
- As rate laws are differential equations you must integrate them
- All equations can be solved numerically and some can be solved analytically
160
What is half life?
The time taken for a concentration of a reactant to fall to half its initial values
Good initial guide to rate law
161
What is the reaction time constant?
Time constant τ is the time required for the concentration of a reactant to fall to 1/e of its initial value
162
What could you compare with integrated rate laws?
Could measure concs as a function of time and compare results to integrated rate laws
By plotting graphs until a linear fit is obtained
163
What graphs of concentration against time do you need for zero, first and second order reactions to find a straight line?
Zero order: [A] against time
- Gradient = -k
First order: ln[A] against time
- Gradient = -k
Second order: 1/[A] against time
- Gradient = k
164
What is the half life method?
Orders can be determined by following a reaction over several half-lives and determining dependence of the half life on concentration
e.g. constant half life = first order
165
What relationship do the rate constants for the vast majority of reactions follow?
k = Ae^-Ea/RT
where A and Ea are the Arrhenius parameters
166
What kind of observation is the Arrhenius equation?
Experimental observation that is only followed approximately over a finite temp range
167
What is A and Ea in the Arrhenius equation?
What are the two components to the equation?
A is pre exponential factor that is a measure of the total number of collisions (irrespective of success)
Ea is the activation energy
Second component concerns fraction of molecules that have an energy equal to or greater than Ea
168
What does multiplying the two components of the Arrhenius equation get?
Multiplying them together gets total number of successful collisions per unit time
169
How can the Arrhenius parameters be determined?
From a plot of ink against 1/T
Intercept = lnA
Gradient = -Ea/R
170
What is the physical meaning of Ea?
For an elementary reaction, Ea is the energy difference between the reactants and the TS involved
When the Arrhenius is applied to the overall kinetics, Ea is just an experimental parameter describing the temp dependence of overall reaction rate
171
What is there to know about activation energy?
Higher the activation energy, the stronger the temp dependence of the rate constant - if no temp dependence Ea=0
A negative Ea implies rate decreases as temp increases
172
What does a catalyst do? (mathematical explanation)
Decreases the value of Ea
173
What can you say about an elementary step that you cannot say about the overall reaction?
If the equation is A + B -> C then if its elementary step A hits B and it forms C however if overall reaction you cannot say that
174
What do the simple rate laws for each elementary step tell us?
The order with respect to each reactant is no of molecules of that reactant in the elementary step
Molecularity of a step is total no of molecules of reactants taking part in that step
175
What is the simplest mechanism that involves more than one elementary step?
Single reactant decaying irreversibly to a single intermediate, which subsequently decays irreversibly to a single product
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What happens if the first step of the simplest mechanism reaction is rate determining?
What about the second step?
ka << kb and there is little formation of the intermediate
ka >> kb and there is much more intermediate formed
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What is true about the energy profile diagram for the simplest mechanism if the first or second step is rate determining?
If first step is RDS, first TS is higher than second TS so forms second TS much faster
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What is 'pre equilibrium'?
Where an intermediate is in equilibrium with the reactants
Occurs when the decay of the intermediate into A and B is much faster than the rate at which the intermediate forms product
i.e. k'a >> kb
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In 'pre equilibrium' reactions what is the equation for K?
K = [I]/[A][B]
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How do you find the rate equation for 'pre equilibrium'?
Use expression for K and rate of d[P]/dt
Substitute one into 2
Also know rates of forwards and backwards reactions at equilibrium are equal
rearrange at substitute
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In general can you solve rate equations analytically?
No you generally cannot solve rate equations for complex multi-step mechanisms analytically
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What is the steady state approximation?
SSA d[I]/dt ≈ 0
If a reactive intermediate is present at low and constant concentration throughout (most of) the course of the reaction we can set d[I]/dt = 0 in rate equations
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What is generally the case for reactive intermediates?
The intermediate is consumed as fast as it is produced
- if ka << kb
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What does the steady state approximation allow you to do?
Generate a rate law that does not include intermediates
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How do you use the steady state approximation?
1. Propose a mechanism and identify the intermediates
2. Write equation for rate - look at which intermediates this equation involves
3. Write an equation for d[I]/dt for all intermediates
4. Apply SSA for all intermediates
5. Substitute for [I] in equation for rate so it no longer contains intermediates
6. Combine constants into a single constant
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What is important to remember when writing equations for d[I]/dt?
Positive terms for forming intermediates and negative terms for removing intermediates
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What are unimolecular reactions?
Gas phase reactions that exhibit first order kinetics and apparently involve only one chemical species
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What is the Lindemann-Hinshelwood mechanism?
Explains unimolecular reactions
1. Bimolecular activation step: A + A ⇌ A* + A
where A* is an energised molecule
2. Unimolecular decay: A* → P
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How can the rate law for the Lindemann-Hinshelwood mechanism be determined?
By putting A* in the steady state
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What happens at high pressures in the Lindemann-Hinshelwood mechanism?
At high pressures, k-1[A] >> k2 so rate simplifies to first order
- Collisional deactivation is much faster than the unimolecular reaction of A*
- The RDS is first order reaction of A*
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What happens at low pressures in the Lindemann-Hinshelwood mechanism?
At low pressures, k-1[A] << k2 so rate simplifies to second order
- Once activated molecule is formed, it is more likely to react than be deactivated
- The RDS is bimolecular excitation
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What is an effective rate constant?
A modified rate constant that accounts for factors influencing a reaction beyond the intrinsic rate constant
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Why does Lindemann-Hinshelwood mechanism not always align with experimental data?
It fails at high pressure. One failure is that its doesn't recognise a specific excitation of a molecule may be required before reaction occurs i.e. any excited A* can product products
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What does the Lindemann-Hinshelwood mechanism predict?
Predicts that a plot of 1/keff against 1/[A] should be linear
Normally a good fit at low pressures
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What is a catalyst?
How do they work?
A substance that accelerates a reaction yet undergoes no net chemical change
Provide an alternative path that avoids the RDS of the uncatalysed reaction
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What is the difference between homogeneous catalysts and heterogenous catalysts?
Homogeneous - same phase as the reaction mixture
Heterogeneous - different phase
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What is there to know about what a catalyst changes?
Accelerates the attainment of equilibria
Doesn't shift equilibrium position
Activation energy lowers
ΔE doesn't change
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What do catalysts change about the transition state?
They create a new reaction pathway whose transition state pathway is lower
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What is an enzyme?
A protein that catalyses a reaction by lowering Ea
- Millions of times faster than uncatalysed
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What combination creates a new reaction pathway in enzyme catalysis?
Combination of substrate and enzyme
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What is true about each enzyme?
It is specific to a particular reaction
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How do enzymes work?
Generally work by having an active site that binds a particular reactant molecule (known as the substrate)
Substrates are bound to enzymes via weak attractions
Ea for the reaction of the enzyme-bound substrate is lower than the free substrate
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What is an active site?
A cleft/crevice that takes up a small part of the molecule
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Why is the Ea of the enzyme bound substrate lower than the free substrate?
Often because interactions involved in binding short the substrate geometry closer to that of the transition state
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What can happen to the substrate when it is in the enzyme?
Can either react or just fall out
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What do the enzyme and substrate bind to form?
Enzyme-substrate complex
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What is the lock and key model?
Active site and substrate have complimentary 3D structures
Dock without the need for major structural change
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What is the induced fit model?
Binding of the substrates induces a conformational change in the active binding site
After this change it fits well in the active site
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What features do enzyme catalysed reaction tend to show?
- Rate varies with conc of substrate
- At a fixed conc of enzyme, rate is almost linearly proportional to [S] when [S] is small
- At high [S] rate is nearly independent of [S]
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What happens at high [S] in enzyme catalysed reactions?
Rate approaches a maximum value known as maximum velocity
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What is the Michaelis Menten mechanism?
Models the enzyme with one active site that weakly and reversibly binds a substrate in homogeneous solution
Three steps
E + S ⇌ ES
ES → P + E
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When can the SSA be applied to conc of ES?
If [ES] is much less than concentration of the reactants
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What is important to note about [E]?
It is the conc of free enzyme so often hard to measure directly
Often expressed in terms of conc of total enzyme
[E]₀ = [E] + [ES]
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What is the rate law for Michaelis Menten mechanism usually written as? (Michaelis-Menten equation)
v = vmax[S]/(KM + [S])
where vmax = k2[E]₀ and KM = (k-1 + k2)/k1
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What is true at high substrate concs and low substrate concs in the Michaelis Menten equation?
v = vmax at high substrate concs ([S] >> KM)
- A max rate occurs because enzyme is saturated, meaning all available enzyme molecules are bound to substrate
v = vmax[S]/KM at low substrate conc ([S] << KM)
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What is KM?
Substrate conc at which the rate is half its maximum value
Also a measure of an enzymes affinity for its substrate
Lower Km corresponds to a higher affinity
Km is a characteristic of a particular enzyme
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What is the turnover number in Michaelis Menten mechanism?
k2 is called the turnover number since it is the max number of molecules of substrate that each molecule of enzyme can 'turn over' per second
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What is the Lineweaver-Burk plot?
Linear form of the Michaelis Menten equation of 1/v against 1/[S]
1/v = 1/vmax + KM/vmax[S]
Intercept = 1/vmax
Slope = KM/vmax
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What is inhibition?
The action of an enzyme may be partially suppressed by the presence of a foreign substance called an inhibitor
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What is competitive inhibition?
Inhibitor has a similar structure to the substrate
So competes for the active site and reduces ability of enzyme to bind to substrate
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What is non-competitive inhibition?
The inhibitor and substrate can both be bound to enzyme at any given time
Inhibitor binds at a site other than the active site
Influences the activity of the enzyme meaning the enzyme-substrate complex cannot form product
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What are sites that inhibitors bind to in non-competitive inhibition called?
Allosteric sites
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How does inhibition affect the Lineweaver-Burk plot?
Competitive inhibition - vmax stays constant
Km increases
- Same intercept and higher gradient
Non-competitive inhibition -
vmax decreases
Km stays constant
- Higher intercept and higher gradient
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What is one of the simplest ways of rationalising the Arrhenius equation?
Collision theory
- This assumes molecules are hard spheres
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According to collision theory, when does a bimolecular gas-phase reaction take place?
When reactants collide, providing their relative KE exceeds a threshold value and certain steric requirements are fulfilled
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What can we predict the expression for the rate of a bimolecular reaction will look like?
v = (collision rate)(energy requirement)(steric requirement)
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What can we assume to start thinking about collision rate?
We can assume molecules collide with each other whenever the centres come within a distance d of each other
d is the collision diameter
Becomes easier all but one of the molecules to be frozen - the mobile molecules travels though the gas with a mean relative speed ⟨vrel⟩
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What is the collision cross section?
σ is the collision cross section in σ = πd² (cross sectional area of the collision tube)
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When, using σ, do molecules collide?
It collides with any other molecules whose centres lie within an area σ about the trajectory of the moving molecule
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What is the volume of the collision tube?
σ⟨vrel⟩Δt
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How do you calculate the number density?
The total number of molecules divided by the total volume
𝒩 = N/V
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How do you calculate collision frequency, z?
z =σ⟨vrel⟩N/V
Number of stationary molecules with centres inside the collision tube per unit time
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Considering a bimolecular reaction between A and B, then the collision frequency of one A molecule with B molecules which are present at number density 𝒩B is given by what?
z = σ⟨vrel⟩𝒩B
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What is the collision density and what is the formula involving a bimolecular reaction of A and B?
Collision density ZAB is total number of (A,B) collisions per unit volume per unit time
Therefore it is given by:
ZAB = σ⟨vrel⟩𝒩B𝒩A
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As A and B are different molecules how do you calculate collision cross section?
Use d = 1/2(dA+dB)
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What is our expression for collision rate without expressing mean relative speed in terms of temperature?
ZAB = σ⟨vrel⟩N²[A][B]
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What is the mean free path length?
Mean free path length, λ, is the average distance a molecule travels between collisions
Time spent before colliding with another molecule is 1/z
Distance = speed x time
λ = ⟨vrel⟩ x 1/z
λ = kT/σP
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In an ideal gas, what is the distribution of molecular speeds given by?
Distribution of molecular speeds, f(v), is given by the Maxwell-Boltzmann distribution
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What is true about speeds of molecules in a gas?
Speeds of individual molecules span a wide range, and the collisions ensure that their speeds are ceaselessly changing
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What happens to the Boltzmann distribution with heavier particles and temperature change?
Heavier particles have a slower, narrower distribution of speeds than lighter particles at the same temp
Increasing the temperature broadens the distribution and shifts the peak to the right
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How can we use the Maxwell-boltzmann distribution to calculate the mean speed?
⟨x⟩ = ∫xp(x) dx
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How does the mean relative speed vary with temperature?
⟨vrel⟩ = (8RT/πμ)^1/2 where μ is reduced mass
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How do you find the most probable speed from Boltzmann?
Most probable speed: Peak of the distribution, so differentiate f(v) and set to zero
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What must be true for a collision to be successful relating to energy?
Colliding pairs must have enough energy to overcome the activation barrier
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For a maxwell-boltzmann distribution of molecular speeds, what is the fraction of collisions for which the energy is high enough to overcome Ea?
e^-Ea/RT
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What is the steric requirement for rate?
Need a steric factor, P, in the expression
Rates determined from experiment can often be significantly smaller than those predicted by simple collision theory
So disagreement needs to be accounted for
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What values can P (steric factor) take?
All values between 1 (all orientations lead to reaction) and 0 (no orientations lead to reaction)
P is usually several orders of magnitude smaller than one
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What is a different way of viewing steric requirement?
Can replace σ with σ star. Effectively, the cross section for reaction has been reduced due to steric requirements
σ * = Pσ
where σ* is relative cross section
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What is the Harpoon mechanism?
When two molecules are close enough an electron (the harpoon) is transferred which forms two ions. Meaning coulomb attraction moves them closer together
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What has the harpoon done in the harpoon mechanism?
It has extended the cross-section for reactive encounter
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What does collision theory allow us to rationalise?
The Arrhenius temperature dependence seen for many reaction rate constants
Collision theory equation will show the same temp dependence as the Arrhenius equation
- As long as the exponential temp dependence dominates the square root temp dependence
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What are the limitations of collision theory?
Assumes all kinetic energy is available for reaction
- However due to conservation of angular momentum - only true if particles collide head on
Also ignored energy stored in internal degrees of freedom, such as vibrational or rotational energy
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How do you do the differential method?
Run multiple experiments varying initial conc of one reactant each time
Measure initial rates in each case
Compare the rates to see how they depend on conc
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How do you use the integration method
Measure conc at various times
Plot different graphs
- [A] against t
- ln[A] against t
- 1/[A] against t
Whichever plot is a straight line tells you the order of the reaction
Slope gives you rate constant k
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How do you do the half life method?
Get concentration vs time data
Find multiple half lives
Compare how the half lives change as conc changes
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When you have complex initial rates, how do you find orders?
Use equation: Runx/Runy = k[A]^a[B]^b.../k[A]^a[B]^b...
