330 Final Exam

Question 1

Differential Rate Law

Answer 1

Tells how a rate at a particular moment depends on the concentrations at that time

Question 2

Integrated Rate Law

Answer 2

Tells us ab how a concentration changes with time

Question 3

Integrated Rate Laws -Zeroth order (rate and linearized formula)
(overall rxn A->B)

Answer 3

rate =k[A]^0, -d[A]/dt=k
integrate k =-d[A]/dt
get formula [A]=-kt+[A]o

Question 4

Integrated Rate Laws(overall rxn A->B)-1st order

Answer 4

rate= k[A]^1
Ln[A]=-kt + ln[A]o
[A]=[A]e^-kt

Question 5

Half life

Answer 5

t(1/2)= ln(2)/k

Question 6

Integrated Rate Laws-2nd order
(overall rxn A->B)

Answer 6

rate= k[A]^2
1/[A]=kt + 1/[A]o

Question 7

Elementary step

Answer 7

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

Question 8

What is the rate law for an elementary step?

Answer 8

The rate of an elementary step =k [reactants]^coeff [reactants]^coeff

Question 9

Arrhenius equation

Answer 9

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)

Question 10

Rate limiting step

Answer 10

The slowest step that determines the rate of the reaction

Question 11

Nice things i can say to myself while studying

Answer 11

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

Question 12

An intermediate

Answer 12

Something that is produced then consumed

Question 13

Rate limiting step analogy

Answer 13

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

Question 14

Hartree Fock Approximation

Answer 14

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

Question 15

2 ways to transfer energy

Answer 15

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

Question 16

If you constrain a wave, you get

Answer 16

Quantized states

Question 17

What does it mean to solve the Schrodinger equation?

Answer 17

Finding the eigenstates of the H operator and their corresponding eigenvalues

Question 18

What is a transition state according to the harmonic oscillator model

Answer 18

Highest point on the minimum energy path (saddle point) , since k (force constant) is the

Question 19

What is a normal mode in the simple harmonic oscillator?

Answer 19

Independent collective motions

Question 20

Zero point energy

Answer 20

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).

Question 21

Postulate 1 of Quantum mechanics

Answer 21

All the info ab a quantum mechanical system is contained in the wavefunction
psi is an indepterminate model (psi cannot predict the future)

Question 22

Postulate 2QM

Answer 22

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)

Question 23

Postulate 3 of Quantum mechanics

Answer 23

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

Question 24

Postulate 4

Answer 24

The average value for any observable is <a>= (integral over all space) psi (complex conj) * Ahat * psi</a>

Question 25

A typical molecule has ___ degrees of freedom

Answer 25

3N-6 internal (vibrational degrees of freedom)

Question 26

Pauli principal arrise from 2 properties of e-

Answer 26

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

Question 27

Orthogonal

Answer 27

Independent or not overlapping, can use symmetry argument

Question 28

Limitations of PIB

Answer 28

-the repulsion of other electrons in the system -ignores nuclei -finite walls (molecule can be oxidized)

Question 29

Pauli Exclusion principal

Answer 29

No 2e- within the same sys can have the same 4 QM

Question 30

Can superpostion for H atom have well defined energy?

Answer 30

Yes- in the case of degereracy- ex psi 200 and psi 211 , both have the same energy

Question 31

Only model with regularly spaced energy levels?

Answer 31

The 1D harmonic oscillator

Question 32

Microwave spectrum (rotational energy) features

Answer 32

-regularly spaced CHANGE in energy levels -gap in middle- fundemental frequency -R- branch peaks closer together than P branch (NEGATIVE delta J) peaks

Question 33

Wavefunction for the ground state RR

Answer 33

Y0,0 is a symmetrical spherical harmonic, full uncertainty about position bc molecule could be anywhere along the sphere

Question 34

order of magnitude for visible light spectrum

Answer 34

400nm-700nm

Question 35

Frequencies of visible light

Answer 35

10^-14 to 10^-15 (inverse seconds)

Question 36

Frank Condon Principal

Answer 36

Over the course of excitation, nuclei do not move

Question 37

RIGID ROTR model answers the following question...

Answer 37

what are the likely angular rotations of a diatomic molecule?

Question 38

DOF at a trans state

Answer 38

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

Question 39

A possible path is necessary but not___

Answer 39

Sufficient to happen (in terms of thermodynamics rxn coordinates

Question 40

For a rxn to happen... (3 things)

Answer 40

1. Molecules must collide 2. In the right orientation 3. With enough energy to make it over the activiation energy

Question 41

Frank Condon Principal

Answer 41

Over the course of excitation, nuclei do not move

Question 42

KINETICS is all about

Answer 42

the path!!!! (just like learning :))

Question 43

Important trade offs

Answer 43

-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

Question 44

Chemical potential

Answer 44

Chem potential of nuA = (dG/dn) just like Q>k, <, =

Question 45

Why does a CO molecule have a higher fundemental frequency than a carbonyl?

Answer 45

CO has a stiffer bond, does NOT want to stretch and has a higher force constant and so a higher frequency

Question 46

for a system must always be (greater than/less than) 2 for a system

Answer 46

GREATER

Question 47

The energy of a helium atom is *(less negative/more negative)* than the energy of two noninteracting He+ ions

Answer 47

Less negative

Question 48

Theme- KT vs energy spacing

Answer 48

Vibrational partition function: -KT<<>>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

Question 49

reaction has an inherent tendency to happen if it ______the entropy of the universe

Answer 49

increases the entropy of the universe this is equivalent to delta G of that process being less than zero

Question 50

IR inactive stretch?

Answer 50

For a molecule to have an IR inactive mode, it MUST have no net dipole and the symmetric stretch has a dipole of zero

Question 51

Average quantites

Answer 51

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)

Question 52

Dimensionality PIB

Answer 52

1D Qunatum number= n nodes: n-1= total nodes remeber nodes are intercepts of ZERO probability of finding a particle

Question 53

ALL PIB EIGENFUNCTIONS ARE

Answer 53

mutually orthogonal ODD * EVEN function OR do in terms of integral

Question 54

Types of spectra for each model

Answer 54

-PIB- UV Vis -1 D Harmonic Oscilator -IR -Rigid rotor- microwave freq -H-atom, NMR-radiowave freq

Question 55

Special feature of homonuclear diatomic molecules rotational partition function

Answer 55

alpha factor add 2 in denominator for homoduclear diatomic molecules

Question 56

The Uncertainty principal

Answer 56

We CANNOT know the momentum (thus the velocity) and the position of the particle at the same time

Question 57

Why does the transition state have an imaginary DOF?

Answer 57

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.

Question 58

When we make rate laws with the steady state approx...

Answer 58

Solve for intermediate and plug it back in since intermediate does not show up in rate law!!

Question 59

Exothermic example and analogy

Answer 59

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

Question 60

Endothermic example and analogy

Answer 60

Heat is taken into the sys melting ice be careful what we define as system or surroundings

Question 61

Commutator

Answer 61

When 2 operators commute they can be simultaneously defined for a system

Question 62

Tunneling region

Answer 62

Intersection of V(x) and the eigenstate, particle can “jump” over an energy barrier

Question 63

q Angular momentum (Lx, Ly, Lz) and L^2)

Answer 63

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)