Thermomdynamics Flashcards
What is another way of saying molar gibbs energy. Intensive/extensive?
Chemical potential μ, intensive
What is an extensive property
They are proportional to the amount of substance (at const T, P and composition) for example volume!
What is an intensive property
They are independent of of the amount of substance eg density, temp
The ratio of 2 extensive properties gives what
An intensive prop
How can you easily turn for example U, S and V into intensive properties
Devide by mols so its molar volume etc
What has no well-defined 0 value
Energy
What does isothermal mean
Constant temp but pressure variation
What happens to chemical potential when pressure increases
Chem pot increases too
For an ideal gas, does internal energy depend on pressure?
NO
What is Am
Molar Helmholtz energy
What does isobaric mean
Constant pressure, variation with T
Equation of molar internal energy of an ideal monatomic gas
Um = 3/2 RT + constant where constant is independent of P and T
What does adiabatic mean
Constant entropy and no heat change - thermally insulated system is compressed/expanded quickly
What happens during adiabatic heating
Rapid compression of a fluid raises its temp. Mechanicl E into heat E. Process that occurs without transferring heat or mass to environment.
Equation for temperature rise of ideal gas
dT = dU / Cv where dU is amount fo mechanical (compression) work done on gas
What is the enthalpy change of a mixture of ideal gases + why
0 bc they don’t interact
How is a pure liquid denoted to distinguish it from a component of a mixture
- for example μ*
What is assumed to be constant for ideal mixtures
Temp and Press
What is Raoult’s law in words
The vapour pressure of a solvent above solution = The mole fraction of solvent * Vapour pressure of pure solvent
When is G minimised in relation to a pure solvent + its vapour
If the chemical potential of liquid = vapour aka at equilibrium
When is the boiling point of a liquid
The temp when its vapour pressure is equal to the pressure of the gas above it eg 1bar in STP (P*A = P0)
In an ideal mixture, how is the vapour pressure compared to the pure vap press?
Pa < Pa, raoults law says vapour pressure is equal to mole fractionpure vapour pressure
Why is partial pressure in a mix less than pure vapour pressure in ideal? 2 reasons
- Fewer A molecs at surface = slower evaporation rate = slower condense rate at eq BUT equal condensation rate than pure A.
- Condensation rate only influenced by collisions of gas qith liquid surface = Since T and intermolecular forces = const then only lower vapour pressure can affect the rate
How does BP and freezing temp change if solute A is dissolved in solvent
BP increases and freezing point decreases
Whta is the Gibbs-Duhem equation?
Using dG equation, at const P and T, nAdμA + nBdμB + … = 0 so chemical potentials of different components in a mix are related.
Short way to explain why adding solute A to liquid B increases BP + decreases freezing temp
μ of B in vapour + solid remains the same but decreases in the liquid, stabilising the liquid.
What causes non-ideal behaviour
Attraction + repulsion between molecules eg becasue of large molecules or strong intermolecular forces
What equations are used for non-ideal gases
Van der Waal and virial equation of state
VdW equation: P = RT / (Vm - b) - a/(Vm)^2. What is a, b and what value do they take if gas/liquid is ideal?
A is attraction, b is molecular size. They are 0 if ideal.
Virial equation: P/RT = 1/Vm + B2(T) / (Vm)^2 + B3(T) / (Vm)^3 + … What if B2, B3 < 0, what if > 0? When are their values more important/not important?
If B2, B3 < 0: attraction as P will decrease since they don’t hit container at expected speed. B2, B3 > 0: repulsion. Attraction important at low T, at high T they don’t have time to interact. Repulsion doesn’t depend on temperature.
What state can virial equation be used for
Only gas!
What is meant by excess quantities in for example gases + ideal gases
Gases only ideal at P -> 0 so before that, Vm(excess) = Vm - Vm(ideal) = Vm = RT/P
What types of mixtures does Gibbs-Dunhem equation apply to
All mixtures, not just ideal ones
What is Gibbs-Dunhem equation
For changes at constant pressure and temperature
𝑛Ad𝜇A + 𝑛Bd𝜇B … = 0
What do regions of a P/T phase diagram show
Phase with lowest chemical potential
What do the lines separating eg liquid and gas mean in a phase diagram
μ (gas) = μ (liquid) < μ (solid) aka where phases are in equilibrium
What happens at the end of the liquid/gas line
It is called critical point, it becomes a supercritical fluid
What happens at triple point
All phases chemical potential is equal
What is different about a solid/liquid line in water compared to most other compounds
The gradient of the line is negative, almost always positive
What are polymorphs
Multiple solid phases observed eg many different ice structures depending on pressure etc
What are the 3 regions in a T/Vm or P/Vm phase diagram
Compressed liquid, saturated liquid-vapour, superheated vapour
What is the critical point on a T/Vm phase diagram
Where saturated liquid and vapour curves meet. The highest temp and press in which vapour and liquid can coexist
What do the lines straight across a T/Vm diagram show
Constant pressure
Phase rule: F + P = C + 2. What does F, P and C mean
F: No. of degrees of freedom. P: Phases in equilibrium. C: Independent components
In a P/T diagram, what does F (degrees of freedom) = 0, 1, 2 and 3 look like
0: point, 1: line, 2: area, 3: volume
How many C (independent components) does CO + 1/2O2 <-> CO2 have
The reaction at equilibrium has 2. If it was a mixture of the 3 gases that didnt interact it would be 3
What is the change in Gibbs energy at phase change
0 because const T, P and chemical potential is same in both phases
What is the Clausius-Clapeyron equation. When can you only use it
2nd eq in eq sheet under “chemical equilibirum” but instead of K it’s P and they are almost equal to, not equal. Use for gradient of ONLY phase equilib lines involving the GAS phase
3 variables to consider in mixtures
Temp, Press, composition
How are phase diagrams normally shown
They are 3D so a slice through it is shown in 2D
What is the Lever rule (in words)
Start at the point that corresponds to the composition of your mixture and temp/pressure. Then go horizontally left and right until it reaches phase lines. This shows the composition of liquid and gas in that moment. The inverse lengths of the line segments give the relative amounts of the two phases.
What do areas and lines show in phase diagrams
Area: Minimum G, Line: Equal G
T/x diagram: What is important when drawing the L+G mixed phase area lines
They always have a negative gradient - never max/minimums
What is different between T/x and P/x phase diagrams
In P/x, the upper liquid line is straight becasue of Raoults law (baso BP - vapour press - is proportional to mole fraction so straight line)
What is the lever rule in an equation for T/x
Lb/Lc = amount of gas / amount of liquid. Lb is the line length to the left
Why can sometimes 2 liquids form instead of a mixture at low temperatures
Gibbs energy of mixing is less negative (less favourable) than separate ideal mixtures
Why does heating assist mixing
ΔG = ΔH - TΔS so as temp rises, gibbs becomes more negative. Also S favours mixing so it increaes too.
What does it mean on a P/x diagram that has many different loops
They are of constant temp
What happens if loop of const temp in p/x temp hits top but does not hit the right side.
Look contains G+L phase. Top left is only L, bottom is G but to the right of it is supercritical fluid. This because it has hit the critical temp of component B. There is no visible transition between the liquid + gas bc no separation
What happens to mixture during fractionla distillation
Vapour has different composition to liquid. During boiling, most volatile liquid is distilled so new liquid has higher conc of the volatile one. Repeat: concentrates liquid further
Problems with an azeotrope during fractional distillation
This means that the mixture cannot be separated into its individual components by simple distillation. When you heat an azeotrope and collect the vapor, the composition of the vapor will be the same as that of the liquid mixture.
What is an azeotrope
Mixture that will have the same composition of liquid as the vapour, nothing changes when it is heated baso
When should you use Henrys law instead of Raoults
When it’s not an ideal mix. Use when solute has really low concentration.
What does a larger K mean in solubility from Henrys law
Smaller solubility
How to calculate Henrys law constant K from P/x diagram
At x=very low, calculate partial pressure of solvent with raoults law. Then partial pressure of solute with henrys law. Add them together. Rearrange to find the gradient. Measure gradient and work out K. (Check lecture 8 recording + handwritten notes by teacher and probs me)
What is the activity of an ideal gas
a = oartial pressure/bar (P/P0) where P0 is pressure at standard conds = 1 bar
What is the activity of a liquid or solvent in excess or a solid
Assume a = 1 so μ=μ0
What is reaction quotient
Like K but activities of produ/react
What is the activity for a solute
Conc / M where M is mol dm^-3
Unit for gases in reaction quotients
Bar
Gibbs energy of any reaction under any conditions equation!!
ΔG = Δ G0 + RTlnQ where Q is measured in activities
What is Q (equilib ratio) when it is standard state?
Q = 1
What is ΔG at equilibrium
0 otherwise it would keep reacting
How are vertical lines treated in phase diagrams
As 1 phase region with very small width, but it is 3D. Eg an atom of B will dissolve in A and be 1 phase but the solubility is too low to show
What has to exist between 2 phase regions on phase diagrams
A one phase region which is normally a very small width (a line)
What is eutectic
Mixture that melts/freezes at a lower temperature then both consitutents
What is increase in energy of a liquid exposed to air proportinal to
Surface area of liquid
What does it mean if surface tension (γ) is negative
It is favourable as energy of liquid is lowered when it forms a surface with other substance
Explain capillary rise
γ < 0 for water/glass so energy of water decreases the more contact it has with glass tube so there is an upward force on the water. But gravity causes downward force. Balance of fores = equilibrium of the rise
How can an object float even if it is denser than water.
aγ(water-air) > 0 so water wants to minimise contact with air = flat surface. Therefore surface energy exerts an upward force on the object. Gravity exerts downward force on object bc its denser than H2O. Balance is equilibrium when it floats. Not always reached.
What factors affect if a drop of water will bead or spread out on glass
Surface tension of water/air > 0 (wants to minimise contact) and water/glass < 0
What is the surface tension for liq/gas
Always > 0 because cohesive forces between molecules in a liquid are generally stronger than the adhesive forces between the liquid and gas molecules. This is bc there are much fewer molecules by the surface of the liquid. So less favourable interactions! There are very few gas
molecules close enough to have any attractive or repulsive interaction with the liquid.
What are 4 energy states for a molecule
Electronic (energy), vibrational, rotational, translational
What is Q in Boltzmann equation
Partition constant. All exponentials added together
How to convert between energy levels to thermodynamic quanities
From energy levels + T -> Q -> A (helmholtz) from equation -> any other quantities
What is another way to call the Partition constant Q
Number of accessible states IF ε(0) = 0 bc then e^(-ε/kT) = 1
Why does S = kln(w) have limited use
All states must have the same energy. True for ideal gases bc no interaction betw molecules therefore same internal E in system regardless of where molecs get placed
For ideal gas, what is (dV/dT)P equal to. (PV=nRT exists)
nR/P. bc if you plot V against T then the gradient will be nR/P
Meaning of evaporation
Evaporation refers to the exchange of molecules between the surface of the liquid and the gas
Difference between Raoults law and Henrys law
Henrys is for a solute in dilute solution. The vapour pressure depends on the chemical indentity of both components, not just mole fraction (Raoults). Raoults just predicts the vapour pressure for the solvent at x% of its pure value where x = mole fraction
What does Henrys law predict about vapour pressure of a sufficiently dilute solute
It is proportional to its concentration but proportinality constant is different to Raoults law + diff for diff solvents
Why is Henrys law needed for a solute at low conc
Solute can interact with solution molecules - forces hindering it from evaporating
Why is vapour pressure lower in a mixture
Mixing reduces chemical potential (or molecular level: only x% at surface of liquid so evaporation rate only at x%)
What does a larger K in Henrys law mean
Lower solubility of solute
P vs mole fraction diagram if mixture is ideal
Straight line connecting between the vapour pressures on either side
How does Henrys law show up in P vs mole faction diagrams when it is a non-ideal mixture
Straight line all the way to the left and right separately (by the vapour pressures) but then afterwards, line begins to curve
How to find K from Henrys law
On p vs mole fraction mixture. Calculate P of solvent A + P of solute B. Add together then rearrange gives gradient K - P*A at low concs.
What does it mean if there is a positive deviation from Raoult’s Law on P vs mole fraction. Relate to Gibbs
The liquid line is above an ideal straight line joining the end-points. This means that
the Gibbs energy of mixing is not as negative as it would be for an ideal mixture. However, the Gibbs energy of mixing is still negative, since the liquids mix; there is no two-phase liquid region.
What is the activity proportional to in an ideal mixture and ideal gas
Mix: concentration. Gas: prop to partial pressure
Explain in molecular terms why water adheres to glass
Water adheres to glass because water molecules are polar and glass consists of charged ions. Thus the electropositive hydrogen atoms of water are attracted to anions in the glass, and the water oxygen atom is attracted to cations
What is W in 𝑆 = 𝑘B ln(𝑊)
W is the number of ‘accessible states’ of the system.
What is Stirlings approximation
ln(x!) = xln(x)
Why is it reasonable that all perfect crystalline substances have the same entropy at absolute zero, but not the same enthalpy?
They have perfect order (only one way of packing the atoms, so W=1 and S=0). However, the bonding between the atoms, and hence the internal energy and enthalpy in the form of “chemical energy”, is different between different substances.
What is ΔmixG equal to for an ideal mixture
ΔA because PV is constant
What does ideal mixing to do S, G, A, chem potential, P, V, U, H?
Ideal mixing involves an increase in S, a decrease in G, A and chemical potential, and no change in P, V, U or H.
What is the change in gibbs during melting
0!! Because it is an equilibrium process (nothing changes or something idk what it means)
What type of phase diagram would show the change in volume when methane melts?
P/V and T/V
A P/T phase diagram would show the melting point, but not the volume change.
What is the critical temprature
Critical temperature is the temperature above which the liquid and gas no longer form separate phases.
What are vertical lines in a T/x diagram
Single solids
When is using concentration instead of activity as an approximation more accurate (for equilibrium calcs)
At low concentrations
WHat can a horizontal line mean on T/x diagram when the phase doesn’t go to liquid
A phase transition between two different solid structures
Why is a freezing point of a solute depressed when it forms a liquid mixture?
Because its chemical potential in the liquid is lowered, whereas its chemical potential in the (PURE) solid is unchanged.
Why is internal energy expected to be the same for an ideal gas at const temp being compressed?
Internal energy is the sum of kinetic and
potential energies. The kinetic energy doesn’t change at constant temperature, and an ideal gas has no interactions between the molecules, so the potential energy doesn’t change when the molecules get closer. :)
What is internal energy a sum of
Internal energy is the sum of kinetic and
potential energies (such as electrostat attraction)
What is the change in gibbs during change of phase as the gas and liquid are in equilibrium + const P and T
0
What is change in enthalpy during phase change
The value of - change in enthalpy of vaporisation if it’s going from gas to liq eg
When doing calculations on vapour pressure, what 3 assumptions can you make
Assume ideal gas, liquid volume negligable and constant delta H
What is a metastable phase
Thermodynamically unstable phases that persist because the transition is kinetically hindered are called metastable phases
How does chemical potential change as temp is raised
chemical potential of a pure substance decreases as the temperature is raised
Equation for pressure-volume work
W = pΔV
What is 𝑁𝑘B equal to with gases
nR and kB is boltzmann constant and N is number of molecules in the gas
