Divisional Foundation exam: Physical Chemistry

Assumptions for an gas to be ideal

1) No interactions
2) Particles <<< space occupied

How can a gas loose its ideality?

1) Large variation of temperature
2) Pressure (increase = crowding)

What are the three core properties of gases?

1) High compressibility
2) Low density
3) No defined shape or volume

Define and explain: Isothermal

Constant Temperature (ΔT = 0)
Internal energy ΔU = 0

Solve for Heat: q=W
Solve for Work: W = nRTln(V2/V1)

Define and explain: adiabatic

Heat exchange is 0: Q = 0
ΔU = -W

Solve for W = (P2V2 - P1V1)/ 1 - γ
OR using internal energy:
ΔU = nCvΔT

Define and explain: Isochloric

Constant Volume: ΔV =0
W = 0

ΔU = q
q = nCvΔT

Define and explain: Isobaric

Constant pressure: ΔP = 0
ΔU = W - q

W=PΔV
q = nCvΔT

What is the first law of thermodynamics?

Energy cannot be created or destroyed only transferred or transformed

Define a path function and provide an example

It is a property where the value depends on the specific path taken between the two states

if you have a hard time understanding: a path function is the energy you used to get to the summit

Define a state function

It is a property where the value does NOT depend on the path taken between the two states

if you have a hard time understanding: a state function is the elevation at the summit of the mountain. No matter which way you took

Explain the conceptual points of Work

1) Work is the transfer of mechanical energy
2) When the external pressure is 0 the work on the system is 0 also
3) Path function

W = -PexΔV
W= -nRTln(V2/V1)

Explain the conceptual points of Heat

1) Transfer of thermal energy
2) Path function

q = smΔT
q = CΔT

Explain the conceptual points of enthalpy

1) Usable energy absorbed or released under constant pressure conditions
2) State function
3) Constant pressure (open atmopshere)

ΔH = Qp
H = U + PV

Define endothermic

ΔH > 0

Heat is being absorbed

ex. melting ice

Define exothermic

ΔH < 0

Heat is being released

ex. combustion

Define and provide the equations for heat capacity

Heat capacity is the amount of heat required to raise the temperature of an object or substance by 1 degree C or K. This explains how resistant a material is to temperature change.

Equations:
C = q/ΔT

Explain a thermodynamic cycle

Thermodynamic cycle is a cycle of processes that returns the system back to its original state

ΔUcycle = 0

BUT heat and work are exchanged during the cycle

ex. Carnot engine

Define hess' law

The total enthalpy change of a reaction is independent of the route taken.

This can be mathematically done through half reactions and taking the summation of the enthalpies to provide the ΔH of the overall reaction.

What is the second law of thermodynamics?

Entropy of the universe will increase for any spontaneous reaction

BUT this reaction does not have to be fast to be spontaneous

Define spontaneous

A reaction that can proceed without sustained external influence

For a REVERSIBLE system what is ΔS?

Always 0 for both system and surroundings

Explain which of the three phases will present the largest entropy?

Gas will present the highest entropy

What is the base equation for entropy

ΔS universe = ΔS system + ΔS surroundings

What conditions does ΔS universe to be spontaneous? At equilibrium? Nonspontaneous?

Spontaneous: ΔS universe > 0
Equilibrium: ΔS universe = 0
Nonspontaneous: ΔSuniverse < 0

This is nonspontaneous because it requires external work or energy to be put into the system to be greater than 0.

What is the third law of thermodynamics?

As a system approaches absolute zero

What are the equations for an absolute entropy phase change math problem for any substance?

Non-phase change: ΔS=nCpln(T2/T1)
Phase change: ΔS = ΔH/T
20 K to absolute 0K: ΔS= a/3 T^3

Explain the conceptual points of internal energy (U)

This represents the total energy of the system

Explain the conceptual points of Helmholtz (A)

This represents the maximum work obtainable from a system.

This is held at constant temperature and volume.

A = U - TS

Explain the conceptual points of gibbs free energy (G)

This represents the quantification of how much useful work can be extracted and directly relates to equilibrium shift.

G = H - TS

What are the differences between Helmholtz and Gibbs Free Energy?

Helmholtz:
1) Constant T

What conditions does ΔG to be spontaneous? At equilibrium? Nonspontaneous?

Spontaneous: ΔG > 0
Equilibrium: ΔG = 0
Nonspontaneous: ΔG > 0

Explain the conceptual points of Chemical Potential

This represents the change in a systems energy when an additional particle is introduced.

Essentially the energy cost or benefit of adding a particle

To measure a chemical potential a species has to move from one phase to another

Define chemical equilibrium

This is the state of a reversible chemical reaction where the rate of the forward and reverse reactions are equal resulting a no net change in concentration of product and reactants over time.

This must be a closed system and temperature and pressure must remain constant.

How does gibbs free energy relate to equilibrium constant?

When ΔG = 0

ΔG^o = -RTlnK

If ΔG is negative: product favored and spontaneous
If ΔG is positive: reactant favored and non-spontaneous

aA + bB ⇌ cC + dD what is the equilibrium constant equation?

K = [C]^c [D]^d / [A]^a [B]^b

If more product is introduced to the system where will the equilibrium go towards?

Reactants

Increasing temperature does what to equilibria?

Go towards products

Decreasing pressure does what to the equilbria?

Go towards the reactants

What is the difference between Q and K ?

Q is the reaction quotient and it is mathematically the same as K but it can be at any moment of the reactions life

Q = [products]^n / [reactants]^n

What does the following mean for equilibrium:
Q = K
Q > K
Q < K

Q = K : Reaction is in equilbrium
Q > K : Reaction will form more reactants
Q < K : Reaction will form more products

What does the Van't Hoff equation represent for equilibrium?

This equation relates temperature change to equilibrium

Increasing pressure does what to the equilibrium?

This will favor the side with less moles

Introducing a catalyst does what to the equilibrium?

Nothing. Catalyst reduce the activation energy but does not effect the position of the equilibrium.

What are the equations for a zeroth order rate law?

Differential rate law: rate = k
Integrated rate law: [A] = [A]o - kt
Half life: t 1/2 = [A]o / 2k

Units: M/s

What are the equations for a first order rate law?

Differential rate law: rate = k[A]
Integrated rate law: [A] = [A]o(e^-kt)
Half life: t 1/2 = 0.693/k

Units: 1/s

What are the equations for a second order rate law?

Differential rate law: rate = k[A]^2 OR rate = k [A][B]
Integrated rate law: 1/[A] = 1/[A]o + kt
Half life: t 1/2 = 1/k[A]o

Units: 1/M*s

Define a reaction mechanism

A step by step molecular pathway by which a chemical reaction occurs

Define molecularity

Number or molecules coming together in a elementary reaction which helps determine the rate order of an elementary reaction

Define unimolecular

Typically a first order reaction that is one species decomposes or rearranges

Define bimolecular

Typically a second order reaction that is the collision between two species with a short living intermediate

Define trimolecular

Typically a third order reaction that is rare. This is a three body collision.

What are the steps of a chain reaction? Explain what each step does?

Step one: Initiation. This is where a highly reactive species is formed (free radical typically)

Step two: Propagation. This where the reactive species interacts with a stable molecule to produce a intermediate

Step three: Termination. This is where the reactive intermediate combines to form stable products (Stopping the chain)

What are the postulates of kinetic energy?

Hint there are 5

1) Gases are made of particles

Define hermitian

Type of operator that represents physical observables (ex. position

Define eigenvalue

This is the scaler that is provided when an operator acts on a wavefunction.

This cannot be complex due to the nature of it being a scaler.

Define eigenfunction

A function that satisfies a differential equation of the form: O^ψ(x)=λψ(x)

These do not change shape or mathematically vary at all

What is a wavefunction?

It is a function that provides all the information on the quantum system (momentum

What are the main mathematical properties for wavefunctions?

Hint there are 5

1) Normalization: The function must be normalized to ensure the probabilistic nature of QM.

2) Expectation value (): This is the mean/average of the system

3) Second moment (

4) Variance: This is the measurement of the spread of values for x. IE

5) Standard deviation: This is the square root of the variance.

Explain the conceptual information on particle in a box

1) This covers the translation movement of a particle
2) This is made under defined boundaries. With this

Explain quantum tunneling? What model does this disrupt the basis of?

This is where a particle goes through a classically forbidden region causing a reduced probability but not a reduced energy.

This disrupts the particle in a box method.

What are the five postulates for quantum mechanics?

1) State postulate: A quantum state is described by a wavefunction

2) Observable postulate: Every observable is represented by a Hermitian operator

3) Measurement postulate: The probability of measuring the eigenvalue of an observable is determined by the born interpretation

4) Time evolution postulate: Governed from Schrodinger's equation where as time moves the probability is conserved

5) Composite system postulate: If two quantum systems are intertwined you must take the tensor product space

Define the superposition principle

This states that if two wavefunctions are solutions to a linear equation then any linear combination is also a valid solution.

What does complementarity mean in quantum mechanics?

You cannot observe or precisely measure certain pairs of observables (ex position and momentum).

These must be non commuters.

Define the uncertainty principle

A quantitative limit of how precisely you can know two observables at once.

Explain the conceptual information on the harmonic oscillator?

1) This covers the vibrational movement

2) Energy levels are equally spaced due to the model being governed by hooks law (ie how tight or loose the 'spring' is determines the spacing)

3) The wavefunctions in this model represent the spring

4) Potential energy creates the polynomial because there is both kinetic and potential

Explain the conceptual information on the rigid rotor?

1) This covers the rotational movement

2) This model works because the two masses are connected by a fixed-length bond

3) This model rotates

Explain how the rigid rotor helps with spectroscopy?

This provides the line spacing and structure we see in microwave and IR regions.

Rotational movement leads to the spacing selection rule J+1 or J-1 and for each line

What are the three approximation methods? Explain what each do.

1) Perturbation method: This starts with a solvable system and adding correction terms (parameters) expanding the system to reduce error.

2) Variation method: Estimates the ground state energy of a quantum system by choosing a trial wavefunction and minimizing the expectation value (so mean) of the Hamiltonian.

3) Hartree-flock method: Computational method that compares a guessed charge density to the solved SE charge density and modified until a reduced error overlap.

What are the three quantum numbers?

Principle quantum number (n)
Orbital quantum number (l)
Magnetic quantum number (m)

What is the Pauli Exclusion Principle?

No two electrons can have the same quantum numbers

What is the Aufbau principle?

Fill from the lowest energy state to the highest

What is Hund's rule?

Fill empty orbitals fully prior to pairing with alternate spin

Why do we need a slater determinant to provide a antisymmetric wavefunction?

This ensures that there are no two electrons at the same quantum state (supports the pauli exclusion principle)

What are the two bonding types in diatomics?

1) Sigma: head on head interactions

2) Pi bonds: Side by side interactions

What are the three integrals that the foundation of MO diagrams?

1) Overlap integral (S): Measures how much two orbitals share space. Ties to MO: determines how strongly atomic orbitals combine to form bonding and antibonding molecular orbitals

2) Columbic integral (J): Quantifies the classical electrostatic repulsion between two electrons. Ties to MO: determines the electron-electron repulsion

3) Exchange integral (K): Spin correlation that arises from the antisymmetry of the wavefunction. Ties to MO: Stabilization of certain orbitals and effects orbital ordering

What is the difference between valence bond theory and molecular orbital theory?

VBT:
1) Starts with atomic orbitals and modifies to get hybridized orbitals
2) Hybridized orbitals are still atomic orbitals that belong to the individual atoms on that molecule

MO Theory:
1) Belongs to the molecule as a whole
2) More flexible for accommodating what molecules do