Thermochemistry and Entropy

Question 1

Define Le Chatelier’s principle

Answer 1

“A system at equilibrium will respond to a change so to relieve the effect of the change”

Question 2

What are the four variables found in equations of state?

Answer 2

Pressure
Volume
Temperature
Number of moles

and p= p(n,v,t)

Question 3

What are the different types of system and what can they exchange with its surroundings? Give examples

Answer 3

Open- exchange energy and matter with surroundings, e.g open test tube
Closed- exchange energy but not matter
e.g closed test tube
Isolated- does not exchange energy nor matter with the surroundings
e.g insulated test tube

Question 4

How can a closed system exchange energy with its surroundings? Define these terms

Answer 4

As heat- the transfer of energy down a temperature gradient
And work- the transfer of energy due to a force

Question 5

In terms of motion, how do heat and work vary?

Answer 5

Work leads to uniform motion, as applying with a force
Heat leads to chaotic motion

Question 6

What do the signs attached to energy mean with respect to the system?

Answer 6

+ = work done on the system or transferred to the system
- = work done by the system or transferred from the system

Question 7

What is the first law of thermodynamics?

Answer 7

Δu = q + w
Change in internal energy= heat added to the system + work done on the system

Question 8

What is the change in internal energy of an isolated system?

Answer 8

0
as heat and work done cannot occur as energy transfer cannot occur with an isolated system

Question 8

What is an isothermal change?

Answer 8

A change where the temperature of a system remains constant
The energy of the system must be constant, and so if heating for example, energy must be transferred between the system and surroundings

Question 9

What is an adiabatic change?

Answer 9

A change where heat energy is not transferred between a system and its surroundings
Temperature can change

Question 10

What is a state function?

Answer 10

A property of a system which is not dependent on how the system was prepared, and instead only on the current. state of the system so V/T…

Question 11

Why is du an exact differential?

Answer 11

U is a state function
The Δu= u(vf,tf) - u(vi,ti), which is independent of the path of the process

Question 12

Are q and w the same for all paths for Δu?

Answer 12

Usually they differ with each path
Not exact differentials
Energy is conserved in an isolated system but heat and work are not, as heat can generate work and vice versa

Question 13

What is the difference between Δu and du?

Answer 13

Δu is the finite change in u, between two different states and can be calculated from
∫du, with limits vf,tf and vi, ti

du is the infinitesimal change in internal energy, used with infinitesimal change in q and w

Question 14

What is the incremental expansion work done on a system when its volume increases by dv?

Answer 14

dW= -Pex x dV

work done= -external pressure x infinitesimal change in volume

Question 15

How is the pressure/force done equation derived?

Answer 15

pressure=force/area
work= force x distance

work= pressure x area x distance
work= -pressure x volume

and - as work done by the system

Question 16

When is dv and Δv used?

Answer 16

For reversible changes where the system and surroundings are in mechanical equilibrium at every stage, dV, and so integrate the expression for pressure with to v

For irreversible changes, when p is much larger than Pex, use Δv, where you do not integrate the pressure equation and instead use change in v

Question 17

What is the work done of free expansion into a vacuum?

Answer 17

irreversible
as external pressure=0 and so -Pex x Δv= 0
so work done=0

Question 18

What is the process of reversible expansion? The calculation

Answer 18

p=Pex + dp

using equation work= Pex dv = p-dp dv
and as dp so small, negligible, p dv

Question 19

Does reversible expansion or irreversible have a greater work done? Why?

Answer 19

Reversible
Area underneath the curve= work done
Much larger for reversible as no large drop to form a rectangle like with irreversible

Question 20

What is the Δu for a perfect gas expansion?

Answer 20

0
Work is done and heat energy transferred for both

Question 21

Derive the heat for a system at constant volume

Answer 21

du= dq + dw
if expansion work the only possibility
du = dq - Pexdv
at constant volume
du=dq
Δu=q for finite changes

Question 22

Why is enthalpy more useful than heat energy? Define enthalpy

Answer 22

Using the assumption q=Δu only works for constant volumes but this is unlikely to be carried out
Constant pressure is more likely

Instead H= u + pv

Question 23

Prove ΔH= q(constant p)

Answer 23

H= u + pv
dH= du + pdv + vdp
dH= dq +dw + pdv + vdp
dH= dq -Pexdv + pdv + vdp
dH= dq + Vdp

at a constant pressure
dH=dq (p)
ΔH=q finite change

Question 24

How does expansion work vary for solids/liquids vs gases, what implications does this have?

Answer 24

Solids/liquid do much less expansion work than gases meaning H is approximately u

Question 25

What are the heat capacities and equations for them?

Answer 25

Cv= dq(v)/dT Cp= dq(p)/dT defined as an infinitesimal change in heat energy at a constant pressure or volume, per infinitesimal change in temperature also can calculated with a small change in each of the variables rather than an infinitesimal change

Question 26

How do the values of Cp/Cv vary for a compound typically and why?

Answer 26

Cp is generally larger than Cv because some of the heat added at a constant pressure is used to do work on the surroundings and less is available to increase the system pressure

Question 27

What is the equation relating Cp and Cv? How does this relate to solids?

Answer 27

Cp= Cv + nR solids Cp~~Cv as less of the heat supplied at constant p is used to do work on the surroundings

Question 28

What are the partial derivatives of Cv and Cp?

Answer 28

Cv=dq(v)/dT= (∂U/∂T)v from the equation relating constant volume and internal energy Cp= dq(p)/dT= (∂H/∂T)p from the equation relating enthalpy to heat energy at constant pressure

Question 29

Define the standard state of a substance

Answer 29

The state of a substance as a pure material at a pressure of 1 bar (10^5 Pa)

Question 30

What is the standard reaction enthalpy?

Answer 30

The sum of the molar (formation) enthalpies of components of a reaction mixture (products and reactants), at 1 bar and a specified temperature multiply the products by the stoichiometric number, and the reactants by - stoichiometric number

Question 31

Define Hess's law and briefly explain why it occurs

Answer 31

The standard reaction enthalpies is the sum of the standard enthalpies of a series of reactions into which the overall reaction may be divided into In other words, the reaction enthalpy is independent of the path taken This is because dH is a closed loop state function

Question 32

What is Kirchhoff's law and explain how to derive it?

Answer 32

ΔrH⦵(T2) = ΔrH⦵(T1) + ∫Δcp,m(T) dT with limits of T2 and T1 Sum the molar enthalpies of the reaction as before, and for Cp, one overall Cp of products-reactants then integrate from the Cp equation, and integrate, rearrange

Question 33

What is a reference state and why is it needed?

Answer 33

The most stable state of the element at p=1 bar, at a specified temperature Needed as we cannot calculate the internal energy/enthalpy of a substance, only changes relative changes, so useful to have a reference point

Question 34

What is the standard enthalpy of formation? How does this relate to elements? Why is this useful?

Answer 34

The standard reaction enthalpy for the formation of the substance from its elements in their reference state The enthalpy of formation of an element in its reference state is zero You can use formation enthalpies to calculate the enthalpy change of a reaction

Question 35

How does the enthalpy of vaporisation tend to different from fusion and why?

Answer 35

Vaporisation much larger There is greater adjustment in the intermolecular potential energy between a liquid and gas than solid and liquid

Question 36

How can Δtrs H be calculated experimentally? Define the enthalpy of vaporisation, and sublimation

Answer 36

Using calorimetry Heat absorbed by a system at a constant pressure can be measured= enthalpy change Defined as the standard enthalpy of gas - enthalpy of liquid for vaporisation Sublimation= fusion + vaporisation

Question 37

What is the second law of thermodynamics?

Answer 37

A spontaneous process in an isolated system is accompanied by an increase in entropy

Question 38

What does it mean if a process is spontaneous? Give an example

Answer 38

It does not need to be driven by doing work, leading to more disorder (either matter or energy dispersing) e.g expansion of a gas into a vacuum, heat flow from hot to cold

Question 39

What is entropy?

Answer 39

The thermodynamic state function which quantifies disorder Entropy measures the disorderliness of the energy

Question 40

Why might a process be spontaneous even if the entropy of the system decreases?

Answer 40

Spontaneous when ΔS total > 0 ΔS system + ΔS surroundings > 0 If the increase in entropy in the surroundings is large enough, then there can be a decrease in entropy of the system but the total entropy increases e.g a puddle freezing

Question 41

What is the Clausius inequality?

Answer 41

dS≥ dq/T where dS = dS system and with a reversible process: dS=dq rev / T

Question 42

What is the equation for reversible heat? How can we justify the equation for dS?

Answer 42

dq rev = TdS Reversibility ensures no extraneous disorder is introduced And dq is not an exact differential, but using an integrating factor of 1/T, it is an exact differential, therefore dS is exact and S a state function

Question 43

How can you prove S is a state function for a perfect gas?

Answer 43

For a perfect gas (∂u/∂v)T= 0 du= (∂u/∂v)T dV + (∂u/∂T)v dT du= Cv(T) dT also du= dq + dw dq= du + pdv dq= Cv(T)dT + nRT/v dv dS= dq/T dS= Cv(T)/T dT + nR/V dv As so with the test for exactness, both are equal and =0 so an exact differential, meaning S is a state function

Question 44

How do you calculate the entropy change for an isothermal expansion of a perfect gas? Show the derivation

Answer 44

From previously, dq rev = pdv + Cv(T)dT = nrt/v dv + Cv(T)dT ds= dq rev / t = nrt/v dv + Cv(T)dT / T ds= nr/v dv + Cv(T)/T dT and comparing to the exact differential ds= (∂S/∂V) dV + (∂S/∂T) dT (∂S/∂V)T= nr/v ΔS= ∫ nr/v dV = nrh ln (Vf/Vi) for reversible and not reversible Can't use U as a variable as not a state function

Question 45

How do you calculate the entropy change for increasing temperature at constant volume? Show the derivation

Answer 45

ds= (∂S/∂V) dV + (∂S/∂T) dT ds= nr/v dv + Cv(T)/T dT by comparing the differentials (∂S/∂T)v = Cv(T)/T ΔS= ∫ Cv(T)/T dT from Tf to Ti

Question 46

How do you calculate the entropy change for increasing temperature at constant pressure? Show the derivation

Answer 46

dq rev= Cp(T) ds= Cp(T)/T dt ΔS= ∫ Cp(T)/T dt from Tf to Ti

Question 47

How do you calculate the entropy change at a phase transition?

Answer 47

Phase transitions occur reversibly ΔS= qrev/T trs = Δtrs H / T trs

Question 48

What is Tranton's rule?

Answer 48

A comparable amount of disorder is generated when any liquid boiled (with the exception of liquids with lots of internal structure like water (H-bonds 109jkmol) Normally around 85J/kmol

Question 49

How can you calculate overall entropy change of heating with constant pressure from t=0?

Answer 49

ΔS= S(0) + ∫ Cp(T)/T dT + sum of Δtrs H / T trs with the integral from T to 0

Question 50

How can the entropy of a solid close to 0K be calculated?

Answer 50

In this region, Cp(T)= aT³ S(T)= S(0) + ∫ Cp(T)/T dT = S(0) + a ∫ T² dT =S(0) + 1/3 Cp(T)

Question 51

What is the 3rd law of thermodynamics? What is the Nernst heat theorem?

Answer 51

The entropy of all perfectly crystalline substances tends to 0 as T tends to 0 ---/ sets origin of the entropy scale The entropy change of any transformation between internally stable substances tends to 0 as T tends to 0 e.g converting between rhombic and monoclinic sulphur

Question 52

What is the standard molar enthalpy?

Answer 52

The entropy of 1 mole of substance at p=1 bar Absolute, relative to entropy at T=0

Question 53

How would you calculate the adiabatic expansion of a gas?

Answer 53

Both temperature and volume are changing dq = 0 So use Cv to replace dU, and dw with -pdV and then the ideal gas form Move t from ideal gas over to the left, and integrate on both sides, rearrange where needed

Question 54

How can you calculate the molar entropy change and enthalpy change from a bomb calorimeter?

Answer 54

First the heat capacity of the calorimeter needs to be calculated Has a constant volume Cv= dq/dT=du/dT Using a known combustion value (mol x molar value) / temperature change Then for the species we are investigating, calculate dq by multiplying Cv by the temperature increase This is equivalent to U, and scale up per molar To calculate H, H= U + pV, pv=nrt, and use the starting temperature

Question 55

What should be done with B when carrying out the calculation?

Answer 55

1000B = values given so multiply the values by 10^-3, /1000

Question 56

What are the units for enthalpy with pv work? If you need to calculate the internal energy change using this equation for a temperature change, how do you calculate volume?

Answer 56

H= u + pv H=joules, pv= standard from ideal gas equation Use the change in temperature to calculate the change in volume, for change in energy

Question 57

How would you approach a question on entropy of a sample rather than entropy change ?

Answer 57

Need to calculate entropy changes using equations Then add on the change to a known entropy value at the lower bound

Question 58

What are the Cv and Cp values of common substances?

Answer 58

At room temperature, and ideal gases Monatomic: Cv= 3/2R, Cp= 5/2R Diatomic: Cv=5/2 R, Cp = 7/2 R Polyatomic: Cv= 3R, Cp=4R

Question 59

What is the entropy change for adiabatic expansion?

Answer 59

0 As dq=0 for adiabatic

Question 60

How do you calculate entropy changes from their derivations?

Answer 60

Use inequality as base and replace variables U, when Cv/Cp dependent on what is constant, and -pdV Use the exact differential with s and dT for temp, dV for volume, ideal gas where needed

Question 62

How do you calculate the enthalpy of a reaction from internal energy?

Answer 62

Delta H=Delta U + Delta pv Delta H= Delta U + Delta nRT Where n is the number of gaseous moles, so products - reactants from the stoichiometric equation