330 Final Exam Flashcards
Differential Rate Law
Tells how a rate at a particular moment depends on the concentrations at that time
Integrated Rate Law
Tells us ab how a concentration changes with time
Integrated Rate Laws -Zeroth order (rate and linearized formula)
(overall rxn A->B)
rate =k[A]^0, -d[A]/dt=k
integrate k =-d[A]/dt
get formula [A]=-kt+[A]o
Integrated Rate Laws(overall rxn A->B)-1st order
rate= k[A]^1
Ln[A]=-kt + ln[A]o
[A]=[A]e^-kt
Half life
t(1/2)= ln(2)/k
Integrated Rate Laws-2nd order
(overall rxn A->B)
rate= k[A]^2
1/[A]=kt + 1/[A]o
Elementary step
We CANNOT know the rate law of an overall rxn just by looking at the reaction
We CAN know rate law for an elementary step bc it describes physical collisions
What is the rate law for an elementary step?
The rate of an elementary step =k [reactants]^coeff [reactants]^coeff
Arrhenius equation
allows us to see the effect of temperature on rate
A (orientational collisions)
e^(-Ea/RT) (fraction of molecules that can overcome the activation energy)
Rate limiting step
The slowest step that determines the rate of the reaction
Nice things i can say to myself while studying
I am learning so much!
I am making progress towards my goals little by little <3
I am a competent chemisty student and chemistry major
I am very grateful for my education and work hard every day
An intermediate
Something that is produced then consumed
Rate limiting step analogy
Stupid boys that don’t text you back he waits for your messages to acculumate and limits the rate of the chemical reaction in a relationship </3 but its ok bc you are a baddie and are too good for him
Hartree Fock Approximation
Consider each e- as an individual psi that forms a seperable product of a total wavefunction
Thus e- depend on eachother in an average way
IN REALITY… e- respulsion happens and e- instantaneously adjust to eachother
Remeber this means that Hartree Fock approximation is ALWAYS an overapprox. The V(x)s and wavefunctions depend on eachother so must be solved in an iterative process (self consistent field approach ) using basis functions
2 ways to transfer energy
1) HEAT: transfer of energy of energy due to random thermal motion -> occurs only when system and surroundings are @ different temps
2)WORK: the action of F over a distance (mechanical, gravitational, echemical, pressure
If you constrain a wave, you get
Quantized states
What does it mean to solve the Schrodinger equation?
Finding the eigenstates of the H operator and their corresponding eigenvalues
What is a transition state according to the harmonic oscillator model
Highest point on the minimum energy path (saddle point) , since k (force constant) is the
What is a normal mode in the simple harmonic oscillator?
Independent collective motions
Zero point energy
he zero point energy is the ground state energy for the harmonic oscillator E=h(nu). Given the uncertainty principal , if E=0 here, then there would be certain position and certain momentum (since velocity=0).
Postulate 1 of Quantum mechanics
All the info ab a quantum mechanical system is contained in the wavefunction
psi is an indepterminate model (psi cannot predict the future)
Postulate 2QM
Every observable in classical mechanics corresponds with a linear operator
a linear operator is distributive
psi must be single valued,continuous, finite,
(end behavior that goes to zero)
Postulate 3 of Quantum mechanics
Any measurement associated with an observable associated with the operator A, only values that can ever be observed are the eigenvalues from A psi =a psi
Postulate 4
The average value for any observable is <a>= (integral over all space) psi (complex conj) * Ahat * psi</a>
A typical molecule has ___ degrees of freedom
3N-6 internal (vibrational degrees of freedom)
Pauli principal arrise from 2 properties of e-
1) electrons are indistinguisable (we can’t tag them to know their location)
2) Wavefunctions of e- MUST be asymmetric with respect to exchange bc e- are fermions
Orthogonal
Independent or not overlapping,
can use symmetry argument
Limitations of PIB
-the repulsion of other electrons in the system
-ignores nuclei
-finite walls (molecule can be oxidized)
Pauli Exclusion principal
No 2e- within the same sys can have the same 4 QM
Can superpostion for H atom have well defined energy?
Yes- in the case of degereracy- ex psi 200 and psi 211 , both have the same energy
Only model with regularly spaced energy levels?
The 1D harmonic oscillator
Microwave spectrum (rotational energy) features
-regularly spaced CHANGE in energy levels
-gap in middle- fundemental frequency
-R- branch peaks closer together than P branch (NEGATIVE delta J) peaks
Wavefunction for the ground state RR
Y0,0 is a symmetrical spherical harmonic, full uncertainty about position bc molecule could be anywhere along the sphere
order of magnitude for visible light spectrum
400nm-700nm
Frequencies of visible light
10^-14 to 10^-15 (inverse seconds)
Frank Condon Principal
Over the course of excitation, nuclei do not move
RIGID ROTR model answers the following question…
what are the likely angular rotations of a diatomic molecule?
DOF at a trans state
Most unstable, 3N-7 degees of freedom
force constant is negative, and so there is an imaginary frequency meaning that the molecule cannot oscillate, so that it cannot feel a restoring force and so a slight distruption to the bond pushes the molecule to fall to stable product
A possible path is necessary but not___
Sufficient to happen (in terms of thermodynamics rxn coordinates
For a rxn to happen… (3 things)
- Molecules must collide
- In the right orientation
- With enough energy to make it over the activiation energy
Frank Condon Principal
Over the course of excitation, nuclei do not move
KINETICS is all about
the path!!!! (just like learning :))
Important trade offs
-Speed of molecules trade off btwn energy and degeneracy: higher av speed good bc more ways to go faster than slower BUT higher probabilty over being at lower energy (closer to zero) since lower energy levels can be more favored acc to e^(‐E/kT)
SO temp governs the most probable speed
-Trade off between degeneracy and stability with J levels- RR model (stability favors ground state J value but degeneracy favors higher level but only with higher energy)
-Trade off with most probable distance from the nucleus (most attracted to the nucleus and so wants to be there but then more ways to be futher from the nucleus given the surface areas
Chemical potential
Chem potential of nuA = (dG/dn)
just like Q>k, <, =
Why does a CO molecule have a higher fundemental frequency than a carbonyl?
CO has a stiffer bond, does NOT want to stretch and has a higher force constant and so a higher frequency
<x2> for a system must always be (greater than/less than) <x>2 for a system
</x></x2>
GREATER
The energy of a helium atom is (less negative/more negative) than the energy of two noninteracting He+ ions
Less negative
Theme- KT vs energy spacing
Vibrational partition function:
-KT«<E , q goes to infinity
-E»>KT, q goes to 1 as spacings are higher than thermal energy
Rotational partition functions
KT»E spacing (@ room T for most molecules) this allows us to assume energy levels are continuous and use KT/B
reaction has an inherent tendency to happen if it ______the entropy of the universe
increases the entropy of the universe
this is equivalent to delta G of that process being less than zero
IR inactive stretch?
For a molecule to have an IR inactive mode, it MUST have no net dipole and the symmetric stretch has a dipole of zero
Average quantites
Take the integral psi* operator * psi
for instance integral (psi * p hat* psi) to find average momentum (p)
Or average position= integral psi * x* psi
I can also do this visually- draw out if psi is odd/even and if we take derivative we get oppisite of original even/odd so that id we have the integral of even and odd psi, which means that they are orthogonal so integral is zero (no overlap)
Dimensionality PIB
1D
Qunatum number= n
nodes: n-1= total nodes
remeber nodes are intercepts of ZERO probability of finding a particle
ALL PIB EIGENFUNCTIONS ARE
mutually orthogonal
ODD * EVEN function OR do in terms of integral
Types of spectra for each model
-PIB- UV Vis
-1 D Harmonic Oscilator -IR
-Rigid rotor- microwave freq
-H-atom, NMR-radiowave freq
Special feature of homonuclear diatomic molecules rotational partition function
alpha factor
add 2 in denominator for homoduclear diatomic molecules
The Uncertainty principal
We CANNOT know the momentum (thus the velocity) and the position of the particle at the same time
Why does the transition state have an imaginary DOF?
transition state is the max point along the
minimum energy pathway. In other words, it’s a local minimum along all but one
vibrational DOF, along which it is a maximum. As such, its
second derivative in one direction will be negative (i.e. it’s a max). Since k, the force
constant, is the second derivative of the potential, and frequency =
sqrt(k/mu), the frequency becomes the square root of a negative number, so it becomes imaginary.
When we make rate laws with the steady state approx…
Solve for intermediate and plug it back in since intermediate does not show up in rate law!!
Exothermic example and analogy
Heat is released (burning his stuff on fire after u break up),
Ex lighting a match, a rxn in a heat pack
be careful what we define as system or surroundings
Endothermic example and analogy
Heat is taken into the sys
melting ice
be careful what we define as system or surroundings
Commutator
When 2 operators commute they can be simultaneously defined for a system
Tunneling region
Intersection of V(x) and the eigenstate, particle can “jump” over an energy barrier
q
Angular momentum (Lx, Ly, Lz) and L^2)
Can only define one component at a time(carves out curve of uncertainty)
ONE exception to this is when L^2 is zero- then each component is zero but for the uncertainty prinicpal to be met ther must be uncertainty in postion (spherical so know r but could be anywher on the surface)
