Lecture 4 - Temperature Dependence Of Reaction Rates Flashcards
What is Arrhenius’ equation
k = Ae^-(Ea/RT)
A small increase in temperature will produce a
significant increase in the magnitude of the rate
coefficient for the reaction.
k - rate constant - units depend on order of reaction
A - frequency factor - same units as k
Ea - activation energy J/mol
R - gas constant J mol-1 K-1
T - temperature K
What needs to happen for a bimolecular, gas-phase reaction? How does this relate to Arrhenius eq?
Need to have a collision
Need a specific orientation
Need enough energy to react
A - related to probability molecules meet in the correct orientation to react
e^-(Ea/RT) - probability molecules have enough energy to react (get over activation energy)
What needs to happen for a unimolecular, gas-phase reaction? How does this relate to Arrhenius eq?
Eg for the diatomic molecule A2 to form 2A
Needs to vibrate and to get to 2A you must break the bond
Therefore there is no orientation problem anymore but there is the idea that you need to have the correct frequency of vibration to break the bond
A - relates to frequency of vibration
e^-(Ea/RT) - probability molecules have enough energy to BB
(Also can ve from going trans to cis etc for isomers)
How are k and T related graphically using Arrhenius’ equation
T increases exponentially with k
However…
k = Ae^-(Ea/RT)
Lnk = lnA - Ea/RT
Lnk = lnA - Ea/R(1/T)
Y C M X
Straight -ve line when plot lnk vs 1/T
What is Ea
• Ea is called the activation energy. It is experimentally determined.
• It can be interpreted as the minimum energy the reacting molecules must have to overcome an energy barrier to reaction. (Think energy vs reaction coord graphs)
• A is called the pre-exponential factor. It has the same units as k.
A common mistake seen in exams is that bond energies are given in KJ per mol. You must must convert KJ to J to plug into eq so units are all homogenous.
A common mistake seen in exams is that bond energies are given in KJ per mol./ you must must convert KJ to J to plug into eq so units are all homogenous.
Comparing Ea to RT (also known as thermal energy)
Nature of reaction effecting Ea:
if you are just BB you will have a higher Ea but if you are both BB and BM it will be lower because you are doing some concerted reactions. Ea is 10s to 100s of KJ mol-1
Compared to RT, thermal energy (at 298K) = 2.5 KJ mol-1
the exponential term provides the probability that a
given molecule has energy Ea
Calculation made from graphs of lnk vs 1/T
- make sure to use a large ‘triangle’ to get gradient
To find A, instead of using the intercept, use Arrhenius equation to find lnA for each data point, then find A and take a mean
What happens when Arrhenius equation is not straight:
- why does this happen?
- how can you work out Ea
Occurs due to electron tunnelling, where the electron
tunnels through, rather than over, the energy barrier (effects anything that is super light)
we can still define an Activation energy,
Ea, based on the gradient of the ln k vs. T curve at that
temperature, i.e. from:
Lnk = lnA - Ea/RT so dlnk/dT = Ea/RT
Don’t think its needed this year tho
Catalysis
• A catalyst gives an alternative reaction pathway with
lower activation energy
From eg qu, by halving the Ea you get 10^13 more molecules that have enough energy to be over the barrier. Rate of reaction goes up a lot with catalysts at the same temperature therefore less energy input required etc
SUMMARY
• Reaction rates (and so rate coefficients) usually increase exponentially with temperature —> Arrhenius equation.
• The activation energy is interpreted as the energy barrier that needs to be crossed to get from reactants to products.
• A linear plot of ln k against 1/T allows the determination of Ea and the pre-exponential factor, A.
• Catalysts act by providing a lower activation pathway from reactants to products.
