Chem1301 Physical Chemistry

Front 1

Ideal gas law

Back 1

pV=nRT

Front 2

Compression Factor

Back 2

Z = Vm / Vm ideal

Ideal gas when Z = 1 so Z = pVm/RT

Front 3

Van der Waal's Equation

Back 3

p = RT/Vm-nb - a/Vm^2

Ideal gas: a & b = 0

Front 4

The van der Waals coefficient a depends on

Back 4

strength of interactions

units -> Pa/mol^2/m^6

Front 5

The van der Waals coefficient b depends on

Back 5

size of molecules

units -> m^3/mol

Front 6

Virial Equation of State

Back 6

p = RT/Vm ( 1 + B/Vm + C/Vm^2 + ...)

Ideal gas: B & C = 0

Front 7

Define Boyle Temperature

Back 7

When attractive and repulsive forces compensate each other --> ideal gas

Front 8

State the 1st law of Thermodynamics

Back 8

energy cannot be created or destroyed. Energy is transferred.

Front 9

Internal energy formula

Back 9

delta U = q + w

= heat transfer + work
= surroundings + system

Front 10

Define "diathermic"

Back 10

allows heat transfer across a boundary between the system and surroundings

Front 11

Define "adiabatic"

Back 11

isolated system, q = 0

work done, but no heat transfer

Front 12

Expansion formula

Back 12

w = -p. delta V

Front 13

When a gas expands into a vacuum, w =

Back 13

w = 0

Front 14

When expansion is reversible, w =

Back 14

w = -nRT ln(Vfinal/Vinitial)

Front 15

Define "isothermic"

Back 15

constant temperature

Front 16

Define "isobaric"

Back 16

constant pressure

Front 17

Define "isochoric"

Back 17

constant volume

Front 18

Define "isopleth"

Back 18

constant composition

Front 19

Define "state function"

Back 19

depends only on current state of the system, independent of route taken

Front 20

Define "heat capacity"

Back 20

amount of heat required to raise 1 mole of a substance by 1 K

C = dq/dT

Front 21

Heat Capacity identities

Back 21

At constant volume, dq = dU
At constant pressure, dq = dH

Cp = Cv + nR

Front 22

Define "standard enthalpy of formation"

Back 22

formation of 1 mole of a compound from its constituent elements

Front 23

Define "standard enthalpy of combustion"

Back 23

complete oxidation of organic compounds to CO2 + H2O

Front 24

Define "fusion"

Back 24

solid --> liquid

Front 25

Define "sublimation"

Back 25

solid --> gas

Front 26

Define "vaporisation"

Back 26

liquid --> gas

Front 27

State the 2nd law of Thermodynamics

Back 27

total entropy increases in the course of a spontaneous change

Front 28

Standard entropy of gases is approximately equal to

Back 28

85J/K

except water

Front 29

State Le Chatelier's Principle

Back 29

a system at equilibrium when subjected to a disturbance responds in a way that tends to minimise the effect of the disturbance

Front 30

Define "constituent"

Back 30

a chemical species present in the system

Front 31

Define "component"

Back 31

chemically independent constituent

Front 32

Axis of a phase diagram

Back 32

x axis --> temperature, T
y axis --> pressure, p

Front 33

Graph to show temperature dependence on Gibb's free energy

Back 33

x axis --> temperature, T
y axis --> molar Gibb's free energy, Gm

dGm/dT = -Sm

Phase with lowest Gm, is most stable

Front 34

Graph to show pressure dependence on Gibb's free energy

Back 34

x axis --> pressure, p
y axis --> molar Gibb's free energy, Gm

dGm/dp = Vm

Gases have large volume --> stable at high pressure

Front 35

On a phase diagram, phase boundaries have which same property at any point (p,T)?

Back 35

Gm, molar Gibb's free energy

Front 36

Define "polymorphism"

Back 36

occurence of different solid phases

Front 37

Steps to measure enthalpy of vaporisation

Back 37

Freeze liquid in flask
Evacuate air
Warm up solid and measure pressure of gas evolved
Varying T produces a data set of p
Plot ln(p) against 1/T to obtain enthalpy of vaporisation

Front 38

Equation linking pressure, temperature and enthalpy of vaporisation

Back 38

p = exp( -Hvap/R . 1/T + constant)

Front 39

Composition Diagrams

Back 39

x axis --> proportion in moles of substance a
y axis --> temperature, T

Phase region shows no sharp boiling point

Front 40

When is there azeotropic behaviour?

Back 40

when A-B interactions are very different from A-A and B-B behaviour

Front 41

Boyle's law

Back 41

p is proportional to 1/V

Front 42

pressure =

Back 42

Force/Area

Front 43

Charles' Law

Back 43

V = kT

extrapolation shows zero volume at zero Kelvin

Front 44

Approximate volume of 1 mole of any ideal gas

Back 44

22.414 dm^3

slight discrepancies are due to interactions of polar molecules

Front 45

Assumptions of ideal gas

Back 45

Gas particles are in ceaseless random motion
Volume occupied by gas molecules is negligible compared to volume of the gas
Molecules do not interact except for perfect, elastic collisions

Front 46

Kinetic Energy =

Back 46

T = 1/2 mv^2

Front 47

Define "force"

Back 47

The rate of change in momentum

Front 48

mean square speed =

Back 48

c^2 = 3RT/M

Front 49

root mean square speed =

Back 49

c = (3RT/M)^1/2

Front 50

To calculate mean square speed

Back 50

integrate x^2 . f(x) dx

Front 51

On a Maxwell- Boltzmann distribution, as temperature increases

Back 51

maximum speed increases

Front 52

On a Maxwell-Boltzmann distribution, as atomic mass increases

Back 52

most probable speed gets slower

Front 53

To calculate most probable speed,

Back 53

differentiate df/ds = 0

Front 54

To calculate mean speed

Back 54

integrate x . f(x) dx

= (8kT/pi . m)^1/2

Front 55

c rel =

Back 55

rt 2 . c

Front 56

reduced mass =

Back 56

Ma + Mb / MaMb

Front 57

Collision frequency =

Back 57

Z = sigma . c rel . N/V

Front 58

Typical range of collision frequency

Back 58

sigma = 0.2 - 1 nm^2

Front 59

Mean free path =

Back 59

lambda = c / Z

distance between collisions

Front 60

Total number of collisions =

Back 60

Zaa = Za (Na/2V)

Front 61

Define "elementary reaction"

Back 61

single step reaction

Front 62

Define "molecularity"

Back 62

no of molecules taking part in an elementary reaction

Front 63

Assumptions of theoretical rate of reaction

Back 63

Reactants must collide
Reactants must have energy more than or equal to the activation energy
Reactants collide in the correct orientation/are hard spheres

Front 64

Boltzmann Distribution

Back 64

x axis --> energy, E
y axis --> f(E)

integrate to find number of molecules with energy specified

Front 65

Theoretical rate constant

Back 65

k = (sigma . c rel . Na^2)/2 . exp(-epsilon/kT)

Front 66

Arrhenius equation

Back 66

k = A exp(-Ea/RT)

Front 67

Steric factor =

Back 67

P = Aexp / Atheory

usually, P < 1

Front 68

Define "effusion"

Back 68

the emergence of gas from a small hole in a container

Front 69

Rate of effusion =

Back 69

Zw . Ao

number of molecules hitting wall x area of hole

Front 70

Define "flux"

Back 70

transfer of momentum

Front 71

Flux formula

Back 71

J = -n . dv/dz

Front 72

What does U(R) show?

Back 72

the potential energy of interaction as a function of molecular separation, R

Front 73

What do van der Waals interactions depend on?

Back 73

Polarisability of molecules
Ionisation potential, I (control of electrons)
Separation, R

Front 74

Lennard-Jones Potential =

Back 74

U(R) = 4. epsilon ( sigma^12/R^12 - sigma^6/R^6 )

Front 75

Total energy, E =

Back 75

E = T + V

total = kinetic + potential

Front 76

State Newton's first law of motion

Back 76

F = 0, v = constant

Front 77

State Newton's 2nd law of motion

Back 77

F = ma, F = dp/dt

Front 78

Potential energy of a simple harmonic oscillator

Back 78

V(x) = 1/2 Dx^2

stronger spring --> larger D --> more energy required

Front 79

When does a standing wave occur?

Back 79

A standing wave occurs when a wave travelling left and a wave travelling right are superimposed. There is a node where the wave crosses the x axis.

Front 80

Raleigh's graph of Black Body Radiation formula

Back 80

p = 8 . pi. kT / lambda^4

Front 81

Classical formula for heat capacity

Back 81

C = 3R

Front 82

Quantised formula for heat capacity

Back 82

C = 3Rf^2

as T --> infinity, f--> 1

Front 83

What is the photoelectric effect?

Back 83

when a photon collides with a metal and an electron is emitted

Front 84

de Broglie's principle

Back 84

lambda = h/p

= h/mv

Front 85

Bohr model

Back 85

mvr = nh/2pi

Front 86

Momentum operator, p^

Back 86

p^ = hbar/i . d/dx

Front 87

Examples of a free particle

Back 87

Gas molecule in a large space
Electrons conducting in a metal
An electron beam

Front 88

Potential energy of a free particle =

Back 88

V = 0

Front 89

Solutions to Schrodinger must obey

Back 89

operator on function = constant x function

Front 90

Example of a particle in a box

Back 90

Atom in a small container
Electrons in a conjugated pi system
Electrons in a bond

Front 91

Potential energy of a particle outside the box =

Back 91

V = infinity

Front 92

Potential energy of a particle inside the box =

Back 92

V = 0

Front 93

State the Born Interpretation

Back 93

the probability of finding a particle in an infinitesimally small region of space between x and x+dx is proportional to the wave function squared

Front 94

To normalise the wavefunction

Back 94

multiply by its complex conjugate = 1

Front 95

Define "quantum tunnelling"

Back 95

regions where a particle can exist that are classically forbidden

Front 96

Example of a particle on a ring

Back 96

Rotating diatomic molecule

Front 97

Angular momentum formula

Back 97

J = pr = mvr

Front 98

Moment of inertia formula

Back 98

I = mr^2

Front 99

Properties of a well-behaved wavefunction

Back 99

Finite
Continuous
Cannot take multiple values, e.g. sin can take more than one value