Lecture 1 Flashcards
What does the boltzman distribution allow us to calculate?
The config that maximises W
What formula describes how particles in a system are distributed?
ni/N = (e^-Bei)/(Sum(i)e^-Bei)
Where B = 1/kT
The denominator is the partition function “q”
Where N = total no of particles
How do you convert ml/l to no of molecules?
Using avogadros constant
Na = 6.022x10^23
What makes up the “simple” model?
- The total number of particles in constant
- The total energy is constant
- Particles have access to a set of quantized energy states (e0, e1…), E is equal to the states each particle is in added up (other than 0) - 1 particle in 5e and 1 particle in 1e would be 4e total
- Particles are distinguishable and independent.
- Weakly coupled (eg collisions) - no intermolecular forces
What is a microstate configuration?
How the microstates are distributed.
These are grouped based on which config has the same number of particles in the same energy state
Fir example, if there were 4 particles and 1 was in 4e and 3 were in 3e, there is 4 ways to draw this as each particle could be in the 4e.
Whereas the ground state would only contain 1 config.
How is a configuration wrote?
Based on the population numbers {n1, n2, n3…) in each state {e1, e2, e3…}
For example if there was 4 particles, 3 in e0 and 1 in e4 it would be wrote;
{3,0,0,0,1}
Where there’s 3 in the ground state (first number), 0 in the e1 (2nd number)….
How can you work out the number of microstates in 1 config? (How much times it can be drawn differently)
Using W = (N!)/(n0!, n1!…)
Where N is the number of particles
n0 is the number of particles in the e0 energy state.
W is also called “statistical weight”
How are factorials done? and what is the factorial of 0!?
Example if it was 3! (where 3 is the 3 particles in a given energy state) it is 3! = 3 x 2 x 1 = 6
0! = 1
What is the principle of equal a priori probabilities?
Implies that the probaility of finding a particle in any of its microstates is equal (in a specific config) is ;
p(microstate) = 1/number of microstates in all config aloud.
What is the probability of finding a system in a specific config?
Finding a molecule in a specific microstate (of the same config) is equally as probable but finding it in equal config is not probable because there’s more configs than others.
p (config) = mj.p(microstates)
p(config) = no of configs for a microstate x 1/overall number of microstates
where mj is the no of particles in a specific config
What happens in a larger system? (lots of particles)
The config with the highest number of microstates will be the most probable
E = n1e + 2n2e… gives n1 = E/e - 2n2
N = n0 + n1… gives = n0 = N - (E/e) +n2
which gives a new formula for the number of microstates (W)
What happens as the number of particles is increased?
As particles increase, other states become more likely compared to others, so a small no of configs dominates.
This implies that a reaction in chemical equilibrium is most likely going to be in 1 config - one with the highest MS.
How is the config with the maximum number of microstates found?
Using the boltzman distribution which allows the calculation of the config that has the highest W.
ni/N = (e^-Bie)/Sum(i) e^-Bie)
What does each thing in the boltzman distribution stand for ?
ni = number of molecules in a given energy state
N - number of total particles
first e in an exponential
B = 1/kT
ei (ie) = the energy state
