Thermodynamics 2 Flashcards
Laws of thermodynamics: Zeroth law
if two systems have different temperatures, they exchange heat, q, until they are in thermal equilibrium
Laws of thermodynamics: First law
internal energy, U, is the sum of a system’s potential and kinetic energies
Laws of thermodynamics: Second law
entropy of an isolated system increases in a spontaneous process: ΔS>0
Entropy, S
a measure of the dispersal of energy
Laws of thermodynamics: Third law
the entropy of all perfect crystalline substances is 0 at T = 0K
When is enthalpy H a more useful measure than internal energy U?
at constant pressure because change in enthalpy is just the flow of heat
dH < 0
process is exothermic
dH > 0
process is endothermic
Isolated system
no exchange of energy or matter with the surroundings
Closed system
exchange of energy with the surroundings but not matter
Open system
exchange of energy and matter with the surroundings
Equal pressure
mechanical equilibrium
Equal temperature
(heat flows to give…) thermal equilibrium
Equal number of molecules, N i
( species i diffuse, phase transform or react to give…) chemical equilibrium of species i
What can chemical potential of i be thought as in a mixture?
the change in free energy of a VERY large system when you add one mole of component i
(has to be a very large system so when one mole is added, it doesn’t affect the system)
How does chemical potential relate with vapour pressure?
Chemical potential decreases if vapour pressure decreases
A perfect (or ideal) gas
gas with no interactions between its molecules
An ideal solution or ideal liquid mixture
has identical interactions between its molecules, irrespective of the molecules’ identity
A non-ideal solution or non-ideal liquid mixture
has different interactions between like and unlike molecules
Why does chemical potential decrease when vapour pressure and mole fraction decreases?
due to the increase in molar entropy arising from the increased accessible volume (a larger accessible volume means a greater dispersion of energy)
Criteria for equilibrium
chemical potential is the same in all phases present
What is the Clapeyron Equation used for?
- To find gradient of p-T boundary lines -> gives sign of Δ tr V
- Estimate Δ tr H or the effect of pressure on mp’s
What is the Clausius-Clapeyron Equation used for?
- To estimate vapour pressures, T b , or T sub
- To find Δ tr H via plotting ln p vs 1/T
Perfect (or ideal) gas
NO interactions between its molecules
Ideal solution or ideal liquid mixture
IDENTICAL interactions between its molecules, irrespective of the molecules’ identity
Non-ideal solution/ liquid mixture
DIFFERENT interactions between like and unlike molecules
Raoult’s Law
- Solutions and liquid mixtures obeying Raoult’s law are known as ideal
- Raoult’s law holds increasingly well as x A → 0
Why does chemical potential decrease as the partial pressure of A and the mole fraction of A decrease?
due to the increase in molar entropy arising from the increased accessible volume (a larger accessible volume means a greater dispersion of energy)
Chemical potential of a species
the energy that can be absorbed or released due to a change of the particle number of the given species
Effect of adding solute into solvent regarding T m and T b
- Adding solute lowers the melting point and raises the boiling point because the entropy of solution state is higher than the pure liquid
- Change in boiling point is SMALLER than change in melting point
What do the changes in melting and boiling points depend upon?
- the mole fraction of the solute, not its identity
- the number of particles so for molecules that dissociate (e.g. salts) it is the total number of particles that matter
What is a colligative property important for biology?
Osmotic pressure
Osmotic pressure defined
the pressure that when applied to a solution, prevents the influx of solvent through a semipermeable membrane
Colligative properties
solution properties that depend only on the number of solute particles present and not their identity. They arise because the presence of a solute (B) reduces the chemical potential of the solvent (A)
Osmometry
a sensitive way of determining molar masses of macromolecules using dilute solutions
What can reverse osmosis be used for?
purifying sea water
Effects of solutes being added to solvent
Raises the boiling point and depresses the melting point of a solvent. For dilute solutions, the change in b.p. or m.p. is proportional to the mole fraction of solute. Solutes lower the melting point more than they raise the boiling point.
What is the eutectic point (e)?
it is the minimum melting point of the mixture
What is the composition at e known as and what does it mean?
the eutectic composition - mixtures with the eutectic composition melt and freeze without changing their composition
What happens at the eutectic point in binary mixtures?
the liquid mixture is in equilibrium with solid A and solid B
What sort of systems give lower eutectic points?
Non-ideal systems with A-B interactions more favourable than A-A and B-B ones
What is the liquid-vapour coexistence line?
where the liquid mixture is in equilibrium with the vapours A and B at total pressure p
What is y A ?
the mol fraction of A in the gas phase
Phase diagrams for ideal binary mixtures: how does vapour pressure link to boiling point?
a higher vapour pressure corresponds to a lower boiling point, so a T-z phase diagram looks roughly like an inverted p-z phase diagram
What are phase diagrams useful for discussing?
fractional distillation
Why does the Gibbs phase rule arise?
directly from the requirement of the chemical potential to be the same in all phases that are in equilibrium
What do tie-lines (horizontal lines in two-phase region) do on phase diagrams?
they connect two phases in equilibrium (i.e. with the same chemical potentials)
What mole fraction classifies a dilute solution?
when mole fraction «_space;0.1
Molality and molarity in dilute aqueous solutions
we often substitute molarity (moles per litre of solution) for molality since the two are almost identical
≈ 1 kg dm -3
What is 𝛾?
The activity coefficient (it is dimensionless).
𝛾 measures the deviation from ideality
𝛾 = 1 for an ideal system
(for gases, 𝛾p is the ‘fugacity’ and 𝛾 is the fugacity coefficient)
What is the activity for pure solids and liquids?
1
How can you find activity coefficients in solution?
by measuring partial vapour pressures
What do p-composition graphs show?
they show deviations from Raoult’s law for real (non-ideal) solutions
What measures the non-ideality of a liquid-liquid mixture?
the ratio of Henry’s constant, K H , to the pure liquid vapour pressure, p*
Is internal energy independent of pressure for an ideal gas?
Internal energy is the sum of the systems kinetic and potential energies. Kinetic energy depends upon temp but not pressure and an ideal gas has no interactions between the gas molecules so no potential energy.
Internal energy is independent of pressure.
Is enthalpy independent of pressure for an ideal gas?
H = U + pV, which for an ideal gas becomes H = U + nRT so its enthalpy is independent of pressure
Is gibbs free energy independent of pressure for an ideal gas?
δG/ δp = V and since V is positive, G increases with pressure therefore G depends upon p
What is a simple model of non-ideality?
the regular solution model
How are β and T related to one another in the regular solution model?
β is independent of T
What does the lever rule determine?
the lever rule determines relative amounts of n ɑ / n β of the two phases
Phase behaviour of regular solutions: temperature dependence of mixing
Enthalpic term: independent of temperature in the regular solution model
Entropic term: more weighting at higher temperatures, and so mixing is favoured at higher T.
Upper critical solution temperature (UCST)
the highest temperature at which two liquids phases can coexist (T uc )
Regular solutions: how can you find the composition of two phases using a tangent?
the composition of two phases are given by the common tangent to the Δ mix G vs x a curve
Phase behaviour of regular solutions: Unstable region
a single phase mixture in this region will spontaneously separate via spinodal decomposition into two phases, usually with domains on the nanometre scale
Phase behaviour of regular solutions: Metastable region
it can only phase separate by a process of nucleation and growth of a phase with a different composition
On a Δ mix G against x A graph, what is the spinodal?
the line separating the unstable and metastable regions (i.e. the line that passes through the inflection points)
- the locus of the inflection points
On a Δ mix G against x A graph, what is the binodal?
the line separating the thermodynamically stable one and two phase regions (with compositions given by the common tangent)
- the phase coexistence curve
What occurs in the unstable region of a Δ mix G against x A graph?
in the unstable region, a one phase mixture immediately phase separates by spinodal decomposition
What occurs in the metastable region of a Δ mix G against x A graph?
in the metastable region, a one phase mixture can persist for long times - need to wait for a nucleation event for phase separation to occur
What does the curve of Δ mix G against x A give information on?
for a binary mixture, it provides thermodynamic and kinetic information (i.e. how fast a mixture will phase separate and the mechanism)
Spinodal decomposition
composition fluctuations spontaneously grow, so phase separation proceeds everywhere
Phase separation via nucleation
most fluctuations decay, until nucleation occurs, so phase separation is limited to nucleation locations
Why do some system phase separate on heating?
- They show a lower critical solution temperature (LCST)
- This occurs for systems where the components can form weak complexes at lower T but not at higher T
Example of a LCST (lower critical solution temperature) system
water and triethylamine (hydrogen bonding between the two occurs at lower T because at high T, the H-bonding breaks thus 2 phases arise)
Closed loop system
systems which possess both a LCST and an UCST (e.g. nicotine and water)
Liquid-Vapour Equilibrium: for the ideal case
the vapour phase is richer in the more voltaile component
Liquid-Vapour Equilibrium: deviations from ideality, β>0
- For β>0, if β is large enough, a maximum arises in the vapour pressure.
- At this point the vapour and liquid compositions are the same
- The mixture with this composition is called an AZEOTROPE
The vapour pressure increases due to less favourable A-B interactions. The liquid excludes the minority component more to minimise less favourable A-B liquid interactions
Liquid-Vapour Equilibrium: deviations from ideality, β<0
- For β<0, there is a minimum in vapour pressure.
The vapour pressure reduces due to more favourable A-B liquid interactions. The liquid retains the minority component more to maximise the more favourable A-B liquid interactions
Relationship of vapour pressure and boiling point in a temperature-composition phase diagram
in a temperature-composition phase diagram, the maximum in the vapour pressure corresponds to a minimum in the boiling point
Pressure-composition curves if |β| is sufficiently large
- pressure-composition curves can have a maximum (β>0) or minimum (β<0) at which the vapour and liquid composition curves touch
- the vapour and liquid mixtures have the same composition at this point
- the mixture with this composition is called an AZEOTROPE
What is the azeotrope in a T-composition phase diagram?
the mixture with the minimum boiling point (β>0) or maximum boiling point (β<0)
Purification by distillation in liquid-vapour equilibrium mixtures
the composition of the distillate cannot exceed the azeotropic composition
Can ionic solutions be ideal?
Ionic solutions are always non-ideal, even at low concentrations
Theory for the activity of ions in solution
Debye-Hückel Theory - able to determine the chemical potentials of ionic solutions
What is the charge of ionic solutions?
neutral
Ionic atmosphere
the distribution of charge around a central ion
How do the ‘haze’ of ions act around a central ion?
the time-averaged ‘haze’ of ions around a central ion has a net charge equal and opposite to the central ion in order to preserve overall charge neutrality
How does the ionic atmosphere impact the chemical potential of ions?
since the atmosphere has the opposite charge to the central ion, the interaction with the atmosphere is favourable, reducing the chemical potential of the ions
How does ionic strength vary with charge?
Ionic strength depends on the square of the charge, therefore multivalent ions have a disproportionately larger effect on I
How can activity coefficients, 𝛾 ± , be measured most easily?
electrochemically through the Nernst equation, where
E cell = -G m / F
Can ionic solutions ever be treated as dilute?
No, the coulomb interaction between ions is long-range so ions interact even in dilute solutions
When do ionic activities deviate from the Debye-Hückel Limiting Law?
Ion activities deviate increasingly from the D-H limiting law as the valency of the ions or the ionic strength increases
What can the Debye-Hückel Limiting Law be used to determine?
- solubilities of sparingly soluble salts with and without a common ion added
- pH with and without added salt
How do real gases act at low pressures, intermediate pressures and high pressures?
Low pressures: intermolecular forces play no significant role (behaviour expected like ideal gas)
Intermediate pressures: attractive forces dominate
High pressures: repulsive forces dominate as gas molecules cannot overlap - excluded volume effects
Real gases (gas-liquid critical point):
T>T c
there are no gas ↔︎ liquid phase transitions
Real gases (gas-liquid critical point):
T<T c
the gas will undergo a phase transition to the liquid upon compression, and the liquid → gas phase transition will take place upon decompression
Fugacity (f)
effective pressure (𝛾p)
How does pressure and temperature effect how real gases compare to ideal ones?
- Real gas deviated from ideal gas as pressure increases due to the attractive van der waals forces.
- As temperature gets much higher, real gases deviate in another way due to repulsive forces being dominant.
How does non-ideal behaviour arise?
due to collisions between molecules
Perfect gas
molecules are assumed to occupy no volume and not interact - pV=nRT
What are the two adjustable parameters of the van der Waals equation of state?
- the excluded volume term b
- term a accounts for the attractive interactions between molecules
What is the virial equation of state?
a power series expansion of the compression factor, Z
What is an equation of state?
equation relating p, V and T
How do real gases behave at low T compared to high T?
At low T, attractive forces dominate more whereas repulsive forces dominate at high T
Effect of real gases at the Boyle temperature at low p
Real gases behave like perfect gases
What are assumptions with the Clausius-Clapeyron Equation?
- The vapour behaves like an ideal gas
- The molar volume of the liquid is negligible compared to that of the vapour
- ΔH vap is constant over the temperature range
How to convert from bar to Pa (or N m -2 )?
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