Physical Chemistry 2

Question 1

What is thermodynamics?

Answer 1

The study of energy transformations

Question 2

What is energy and work?

Answer 2

Work - a form of energy which can transfer in and out of a system, stored in the organized motion of molecules.
It is done when an object is moved against as opposing force.

Energy - capacity to do work. Energy of a system can be changed by work and heat.

Question 3

How is work done calculated / defined?

Answer 3

W = Fx

By definition;
dW = -Fdz
and pressure, P = F/A

So by substitution,
dW = -PAdz
and Adz has units of volume (x³)

Therefore dW = -PdV
Which can then be integrated

Question 4

What’s a diathermic and adiabatic system?

Answer 4

Diathermic - energy can transfer in and out as heat

Adiabatic - no heat can be transferred in and out

Question 5

What’s internal energy?

Answer 5

Total energy of a system, as a function of state, and is an extensive property (dependent on the amount of matter).

Question 6

For an adiabatic process, what is internal energy equal to?

Answer 6

Overall energy balance:
ΔU = Q + W

However ΔQ is 0 as there is no transfer of heat so:
ΔU = W

Question 7

For an isobaric process, what is internal energy equal to?

Answer 7

Overall energy balance:
ΔU = Q + W

Both still exist for this process (although ΔP is 0)

Question 8

What is an isochoric process?

Answer 8

One with a constant volume.

ΔV = 0

Question 9

For an isochoric process, what’s internal energy equal to?

Answer 9

Overall energy balance:
ΔU = Q + W

However, ΔV = 0 (and W=PΔV)
Therefore:
ΔU = Q

Question 10

For an isothermal process, what is internal energy equal to?

Answer 10

Temperature is fixed (ΔT = 0) and it’s energy stays constant so ΔU = 0

Therefore:
Q = -W

Question 11

For an cyclic process, what is internal energy equal to?

Answer 11

Certain processes have the same initial and final states, represented by a closed path and ΔU = 0.

Therefore:
Q = -W

Question 12

What’s a reversible and irreversible process?

Answer 12

Reversible - the system is never more than infinitesimally far from equilibrium and an infinitesimal change in external conditions can reverse the process

Irreversible - cannot be reversed by an infinitesimal change in external conditions

Question 13

How can work by an ideal gas be calculated?

Answer 13

Using pV = nRT and W = pΔV

Question 14

How is heat capacity at constant volume defined/calculated?

Answer 14

Cᵥ = (dU/dT)ᵥ = Q v

->

dU = CᵥdT
For a certain range of T where Cv is constant

No work is done

Question 15

What’s molar heat capacity and specific heat capacity (how is it found)?

Answer 15

Molar: C vm = Cv / n

Specific heat is in terms of mass

Question 16

How’s enthalpy found?

Answer 16

H = U + pV

= internal energy + work

Question 17

How is enthalpy found for an isothermal process?

Answer 17

Change in U = 0.

Therefore ΔH = pV = ΔnRT

If no chemical reaction and no change in the # moles, ΔH = 0.
Otherwise ΔH = RTΔn

Question 18

What’s the relation between Cp and Cv?

Answer 18

Cp - Cv = nR

Question 19

What changes occur when a gas expands adiabatically?

Answer 19

Work is done since there’s a change in pV

Internal energy will fall

Temperature will decrease

Microscopic Ek of molecules will fall

Question 20

What’s the standard enthalpy of transition, Δ trs H’?

Answer 20

Standard enthalpy change accompanying a phase change.

Enthalpy is a state function, so ∆H differs only in sign for forward and reverse processes.

Phase changes include: mixing, solution, atomisation, combustion etc.

Question 21

What’s standard reaction enthalpy, ΔrH?

Answer 21

Change in enthalpy when reactants in standard states change to products in standard states
Enthalpies of mixing and separation are usually ignored.

Question 22

How is standard reaction enthalpy found?

Answer 22

= enthalpy of products - enthalpy of reactants

Enthalpy of formation often used

Question 23

What’s the standard enthalpy of formation?

What’s their reference state?

Answer 23

Changein enthalpy for formation of compound from its constituent elements in their reference states, which is the most stable state of an element at a certain temperature and 1 bar.

Question 24

What’s Kirchhoff’s law?

Answer 24

ΔᵣH(T2) = ΔᵣH(T1) + ∫(ΔᵣCp)dt

Where the quantity, ΔᵣCp, is the difference in heat capacities between reactants and products under standard conditions, weighted by stoichiometric coefficients.

ΔᵣCp = ΣvCp * [products] - ΣvCp * [reactants]
(where v is stoichiometric coefficients)

Question 25

What is the difference between exact and inexact differentials?

Answer 25

Exact - there exists a function of two variables
u(x,y) with continuous partial derivatives

– System is taken along a path, with ∆U = Uf – Ui

Inexact - An infinitesimal which is not the differential of an actual function
– System is heated, total energy transferred as heat is the sum of individual contributions along each point of the path
– Do not write ∆Q! Q depends upon the path of integration
– Path dependence is expressed by saying that dQ is an inexact differential

Question 26

What’s the second law of thermodynamics?

Answer 26

The Second Law of Thermodynamics is about the quality of energy. It states that as energy is transferred or transformed, more and more of it is wasted. It also states that there is a natural tendency of any isolated system to degenerate into a more disordered state. Entropy increases.

No process is possible in which the sole result is the absorption of heat from a reservoir and its complete process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.

The total entropy of an isolated system can never decrease over time.
∆S tot> 0

Question 27

What’s entropy?

Answer 27

State function to quantify disorder and randomized motion. Increasing entropy means increasing disorder and randomized motion.

Question 28

How is the change in entropy measured for an infinitesimal change, and for an overall/measurable change?

Answer 28

Infinitesimal:
dS = dQᵣₑᵥ/T

Overall:
ΔS = ∫dQᵣₑᵥ/T

Question 29

What’s the Carnot cycle?

Answer 29

A theoretical thermodynamic cycle with 4 main steps: isothermal expansion, reversible adiabatic, isothermal compression and adiabatic reversible compression.

It’s the most efficient cycle for converting a given amount of thermal energy into work, or conversely, creating a temperature difference (e.g. refrigeration) by doing a given amount of work

The entropy change along any individual path is cancelled by the entropy change along the path it shares.

Question 30

What are the 4 stages of the Carnot cycle and how does entropy change for these stages?

Answer 30

1. Reversible isothermal expansion from A to B
   ΔS = Qh/Th
2. Reversible adiabatic expansion from B to C
   ΔS = 0
3. Reversible isothermal compression from C to D
   ΔS = Q𝒸/T𝒸
4. Reversible adiabatic compression from D to A
   ΔS = 0

Total change in entropy = dS = Qh/Th + Q𝒸/T𝒸

Question 31

How is engine efficiency calculated?

Answer 31

η = work performed / heat absorbed

η = W / Qh

[η = (Qh-Q𝒸)/Qh = 1 - Q𝒸/Qh = 1 -T𝒸/Th)

Question 32

How is entropy at a phase change calculated?

Answer 32

Δ trs S = Δ trs H/T

Question 33

What is the third law of thermodynamics?

Answer 33

The entropy of a system approaches a constant value as its temperature approaches absolute zero.

At zero entropy, there’s no disorder or thermal motion.

Question 34

How is standard reaction entropy defined?

Answer 34

The difference between molar entropies of pure, separated weighted products and reactants.

drS = vSm (prod) - vSm (react)

Question 35

How does the change in entropy relate to Q/T for an ideal cycle, and for a real engine?

Answer 35

For ideal, they’re equal.

For a real engine, dS is greater than dQ/T

Question 36

What’s Helmholtz free energy?

Answer 36

∆A is the part of change in internal energy that we are free to use for work

Question 37

What’s the formula for the standard Gibbs energy of formation?

Answer 37

∆rG = ∆rH - T ∆rS

Question 38

How can the number of moles of a product be determined, with regards to the extent of a reaction?

Answer 38

n = n(0) + v ∆Ê

Question 39

What’s Le Châtelier’s principle?

Answer 39

A system at equilibrium, when subjected to a disturbance, responds in a way that tends to minimize the effect of the disturbance.