Thermochemistry and Entropy Flashcards
Define Le Chatelier’s principle
“A system at equilibrium will respond to a change so to relieve the effect of the change”
What are the four variables found in equations of state?
Pressure
Volume
Temperature
Number of moles
and p= p(n,v,t)
What are the different types of system and what can they exchange with its surroundings? Give examples
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
How can a closed system exchange energy with its surroundings? Define these terms
As heat- the transfer of energy down a temperature gradient
And work- the transfer of energy due to a force
In terms of motion, how do heat and work vary?
Work leads to uniform motion, as applying with a force
Heat leads to chaotic motion
What do the signs attached to energy mean with respect to the system?
+ = work done on the system or transferred to the system
- = work done by the system or transferred from the system
What is the first law of thermodynamics?
Δu = q + w
Change in internal energy= heat added to the system + work done on the system
What is the change in internal energy of an isolated system?
0
as heat and work done cannot occur as energy transfer cannot occur with an isolated system
What is an isothermal change?
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
What is an adiabatic change?
A change where heat energy is not transferred between a system and its surroundings
Temperature can change
What is a state function?
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…
Why is du an exact differential?
U is a state function
The Δu= u(vf,tf) - u(vi,ti), which is independent of the path of the process
Are q and w the same for all paths for Δu?
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
What is the difference between Δu and du?
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
What is the incremental expansion work done on a system when its volume increases by dv?
dW= -Pex x dV
work done= -external pressure x infinitesimal change in volume
How is the pressure/force done equation derived?
pressure=force/area
work= force x distance
work= pressure x area x distance
work= -pressure x volume
and - as work done by the system
When is dv and Δv used?
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
What is the work done of free expansion into a vacuum?
irreversible
as external pressure=0 and so -Pex x Δv= 0
so work done=0
What is the process of reversible expansion? The calculation
p=Pex + dp
using equation work= Pex dv = p-dp dv
and as dp so small, negligible, p dv
Does reversible expansion or irreversible have a greater work done? Why?
Reversible
Area underneath the curve= work done
Much larger for reversible as no large drop to form a rectangle like with irreversible
What is the Δu for a perfect gas expansion?
0
Work is done and heat energy transferred for both
Derive the heat for a system at constant volume
du= dq + dw
if expansion work the only possibility
du = dq - Pexdv
at constant volume
du=dq
Δu=q for finite changes
Why is enthalpy more useful than heat energy? Define enthalpy
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
Prove ΔH= q(constant p)
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
How does expansion work vary for solids/liquids vs gases, what implications does this have?
Solids/liquid do much less expansion work than gases
meaning H is approximately u
What are the heat capacities and equations for them?
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
How do the values of Cp/Cv vary for a compound typically and why?
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
What is the equation relating Cp and Cv? How does this relate to solids?
Cp= Cv + nR
solids Cp~~Cv as less of the heat supplied at constant p is used to do work on the surroundings
What are the partial derivatives of Cv and Cp?
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
Define the standard state of a substance
The state of a substance as a pure material at a pressure of 1 bar (10^5 Pa)
What is the standard reaction enthalpy?
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
Define Hess’s law and briefly explain why it occurs
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
What is Kirchhoff’s law and explain how to derive it?
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
What is a reference state and why is it needed?
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
What is the standard enthalpy of formation? How does this relate to elements? Why is this useful?
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
How does the enthalpy of vaporisation tend to different from fusion and why?
Vaporisation much larger
There is greater adjustment in the intermolecular potential energy between a liquid and gas than solid and liquid
How can Δtrs H be calculated experimentally? Define the enthalpy of vaporisation, and sublimation
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
What is the second law of thermodynamics?
A spontaneous process in an isolated system is accompanied by an increase in entropy
What does it mean if a process is spontaneous? Give an example
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
What is entropy?
The thermodynamic state function which quantifies disorder
Entropy measures the disorderliness of the energy
Why might a process be spontaneous even if the entropy of the system decreases?
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
What is the Clausius inequality?
dS≥ dq/T
where dS = dS system
and with a reversible process:
dS=dq rev / T
What is the equation for reversible heat? How can we justify the equation for dS?
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
How can you prove S is a state function for a perfect gas?
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
How do you calculate the entropy change for an isothermal expansion of a perfect gas? Show the derivation
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
How do you calculate the entropy change for increasing temperature at constant volume? Show the derivation
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
How do you calculate the entropy change for increasing temperature at constant pressure? Show the derivation
dq rev= Cp(T)
ds= Cp(T)/T dt
ΔS= ∫ Cp(T)/T dt
from Tf to Ti
How do you calculate the entropy change at a phase transition?
Phase transitions occur reversibly
ΔS= qrev/T trs
= Δtrs H / T trs
What is Tranton’s rule?
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
How can you calculate overall entropy change of heating with constant pressure from t=0?
ΔS= S(0) + ∫ Cp(T)/T dT + sum of Δtrs H / T trs
with the integral from T to 0
How can the entropy of a solid close to 0K be calculated?
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)
What is the 3rd law of thermodynamics? What is the Nernst heat theorem?
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
What is the standard molar enthalpy?
The entropy of 1 mole of substance at p=1 bar
Absolute, relative to entropy at T=0
How would you calculate the adiabatic expansion of a gas?
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
How can you calculate the molar entropy change and enthalpy change from a bomb calorimeter?
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
What should be done with B when carrying out the calculation?
1000B = values given
so multiply the values by 10^-3, /1000
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?
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
How would you approach a question on entropy of a sample rather than entropy change ?
Need to calculate entropy changes using equations
Then add on the change to a known entropy value at the lower bound
What are the Cv and Cp values of common substances?
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
What is the entropy change for adiabatic expansion?
0
As dq=0 for adiabatic
How do you calculate entropy changes from their derivations?
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
How do you calculate the enthalpy of a reaction from internal energy?
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
