Lecture 2 Flashcards
What is the molecular partition function (q)? (hint; bottom of the boltzman)
q = Sum(i)e^-Bie
What does the Boltzmann distribution look like/represent (hint; harmonic oscillator)
Harmonic oscillator is a system with evenly spaced energy levels that just keep increasing to infinity, each gap represents delta e = 0.5kT(298K) with units J.
k = 1.381E-23[J K-1]
T = K
How is the energy between spaces in a harmonic oscillator converted to molar units?
Using Na = 6.02223
delta e = 0.5kNaT
delta e = 0.5RT
In this R = 8.314E-3 as the units are kJ mol-1 K-1
When given in molar units, final unit is kJ mol-1
k x Na GIVES THE GAS CONSTANT!
What is the difference in units for the harmonic oscillator approach?
When delta e is 0.5kT the units are J
When delta is in molar units, 0.5kNaT = 0.5RT the unit is kJ mol-1
MAKE SURE R IS E-3
What 2 different ways can the Boltzmann distribution be wrote?
Using 1/kT (where energy is in J) or using 1/RT if in molar units (where energy is in kJ mol-1).
What is the Boltzmann factor? and what is it proportional too?
The Boltzmann factor is on the top of the equation and is the exponential factor, e^-Bie and is proportional too the probability of give energy state being occupied at a given temperature.
How does increasing the temperature effect the exponential factor?
As the temp increases, the energy is populated at higher energy states. At 0K no particles are going to be in a higher energy level.
What is the bottom part of the formula?
The molecular partition function, q, which is a sum of all Boltzmann factors (top part) over all the energy levels.
How does the molecular partition function change with temperature?
It increases.
How is the fractional occupanyc of each state (ni/N) found using the boltzman equation?
The Boltzmann function and the molecular partition function make up the formula. This is done at a given temperature.
What does the fractional occupancy (how particles are distributed over all states) change with temperature?
When the temp is at 0K, all particles are in the ground state. As temp is increased more particles move to higher energy levels but the ground state stays the most occupied. (THIS WONT ALWAYS BE TRUE FOR OTHER SYSTEMS)
What happens if the energy gap is increased? (doubled in this exmaple)
delta e = kT (as 0.5 x 2 is 1)
This means that there’s less likely off a chance for particles to occupy higher energy levels re more are in the GS. This is because less particles have sufficient thermal energy to reach these higher states.
What happens when theres degeneracy in the system? (more than 1 state in a energy level)
i in the Boltzman distribution changes to j, and j is the number of different energy states in all of the energy levels.
What is degeneracy given by?
The symbol g
If the e1 energy state has 3 levels then g1=3)
What formula can be used to find the population of 2 energy levels relative to each other?
ni/nj = (gi/gj)e^-Bie
ni = the number of particles in level i
nj = the number of particles in state i
Answer wrote as ni = ansnj
