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Physical & Analytical Chemistry

A Hofmann · 2106NSC Physical & Analytical Chemistry · Thermodynamics 7 · Phase diagrams 2017

Thermodynamics 7

Phase diagrams


Phase transitions

Plus: conversion of different solid states, e.g. graphite to diamond


Phases and phase transitions

A form of matter that is uniform throughout in chemical composition and physical state is called a phase.

Phases include: solid, liquid, gas; there may be various solid phases, conducting and superconducting phases, superfluid phases.

Examples: Ice, liquid water, water steam.

A phase transition is the conversion of one phase into another.

When two or more phases are in equilibrium, the chemical potential of a substance is thesame in each phase and at all points in each phase.

(This is a consequence of the 2nd Law of Thermodynamics.)


The phase rule

The phase rule allows one to calculate the number of intensive parameters that can be varied independently (F) while the number of phases (P) remains constant, given a system with a particular number of components (C) of a system:

F = C – P + 2

Intensive parameters are independent of the amount of substance (e.g. p, T).

For example, if two phases (P= 2) in a system consisting of one component (C= 1) are in equilibrium

F = 1 – 2 + 2 = 1

one parameter (e.g. T) can be changed, but other parameters (e.g. p) will follow suit. Systems with F= 1 are called univariant.


The phase rule: F = C – P + 2

Example: Water steam

C = 1, P = 1

=> F = 2

This is a bivariant system. It corresponds to an area in an x-y-plot.

We can vary the temperature of the steam without having to change the pressure at the

same time (but still maintain the gas phase).

Example: Liquid water in equilibrium with its vapour

C = 1, P = 2

=> F = 1

This is a univariant system. It corresponds to a line in an x-y-plot.

The temperature can be varied, but the pressure needs to be varied accordingly to

preserve the equilibrium.


Phase diagrams

We will consider phase diagrams for 1, 2 and 3- component systems, uni- and bi-variant systems.

We will discuss critical, triple and eutectic points.

We will also consider how the shapes of the phase diagrams are derived from thermodynamic relations.


One component systems

Boiling point: temperature at which the vapour pressure of the liquid is equal to the external pressure. If

p = 1 atm = 1013.25 hPa, this is called the normal boiling point; pnormal

p = 1 bar = 1000.0 hPa, this is called the standard boiling point; pØ

Melting point: temperature at which the liquid and solid phases coexist; equals the freezing temperature. If

p = 1 atm, this is called the normal freezing or melting point; pnormal

p = 1 bar, this is called the standard freezing or melting point; pØ


One component systems

Critical temperature

At this temperature, there is no interface between the liquid and the vapour (there is no liquid phase).

Triple point

At a single definite pressure and temperature, three phases exist in equilibrium.

This corresponds to a point in an x-y-plot.

Water triple point: T3= 273.16 K, p3= 611 Pa

solid, liquid and gaseous water exist at the same time

used to define the thermodynamic temperature scale


One component systems: CO2


Supercritical CO2


Fossil power

Figure from: Service (2017) Science 356, 796-799.

Coal-fired power plants burn coal to generate steam which drives a turbine to generate electricity. CO2 is emitted into the atmosphere and much of the heat is lost in the cooling towers where water steam is condensed into the liquid phase. Only ~38% of the coal's energy is converted into electricity.


Supercritical CO2: The Brayton/Allam cycle

Figure from: Service (2017) Science 356, 796-799.

Instead of water steam/liquid, this cycle uses supercritical/gaseous CO2 to drive a turbine. Such turbines are much smaller and more efficient than conventional steam turbines. Fuel is burnt to heat the cycling CO2 to 1150°C. However, the resulting CO2 from the combustion is still going to exhaust(but may be sequestered). Disadvantages: chilled air, compressed CO2 (requires a lot of energy); advantages: produces water (in contrast to the conventional steam cycle).


Atmospheric CO2 capture at industrial scale

June 2017: World's first commercial plant for capturing carbon dioxide directly from the air.

The plant sits on top of a waste heat recovery facility that powers the process. Fans push air through a filter system that collects CO2. When the filter is saturated, CO2 is separated at temperatures above 100°C. The gas is then sent through an underground pipeline to a greenhouse to help grow vegetables, like tomatoes and cucumbers. [Marshall, C. (2017) Science 356, 990]


Some concepts

Phase transition Spontaneous change from one phase to another.

Transition temperature Temperature at which two phases are in equilibrium and the Gibbs free energy is minimised (for a given pressure).

Phase boundary Lines (in the phase diagram) that separate regions where various phases are thermodynamically stable.They show values of p and T where two phases coexist in equilibrium.Phase boundaries are univariant.


One component systems: H2O

Water Structure and Science (M Chaplin, London South Bank University)


http://www1.lsbu.ac.uk/water/phase.html

One component systems: H2O

Note steep slope of solid-liquid boundary.

Various solid phases.

More than 1 triple point.

Unusual: negative slope of the solid-liquid boundary at lower pressures.

This is due to the liquid having a smaller volume (i.e. higher density) than the solid.


One component systems: Helium

The phase diagram for helium shows other unusualbehaviour.

The two isotopes of helium, 3He and 4He, have different phase diagrams.

4He has two liquid phases with a transition between them (the l-line).

Helium's low temperature triple point is the point where He-II (l), He-I (l) and He (g) coexist.

He-II is a superfluid. It flows with zero viscosity.

hcp: hexagonal closed packing, bcc: body-centred cubic packing



Unusual behaviour at low temperatures.

Solid and gas are never in equilibrium, due to the light He atoms having large amplitude vibration – they need high pressures to form a solid.

Isotopes 3He and 4He have different phase diagrams.

He-I is like a normal liquid.

He-II is a superfluid – no viscosity (single quantum state).



Left: Helium II will "creep" along surfaces in order to find its own level—after a short while, the levels in the two containers will equalize. The Rollin film also covers the interior of the larger container; if it were not sealed, helium II would creep out and escape.

Right: Liquid helium is in the superfluid phase (He-II). As long as it remains superfluid, it creeps up the wall of the cup as a thin film. It comes down on the outside, forming a drop which will fall into the liquid below. Anotherdrop will form—and so on—until the cup is empty. (2nd Law of Thermodynamics ...)

http://en.wikipedia.org/wiki/Superfluid


http://en.wikipedia.org/wiki/Superfluid

One component systems: Hydrogen

Hydrogen is classified as a non-metal under conventional circumstances.

In 1935, Eugene Wigner and Hillard Bell Huntington proposed that hydrogen might exist in a phase where it behaves like an electrical conductor: metallic hydrogen.

At high pressures and temperatures, a metallic liquid hydrogen phase might exist (such as e.g. in the interiors of Jupiter, Saturn and other extrasolar planets).

In 2016, claims have been made that metallic hydrogenhad been prepared 'permanently' in the laboratory at apressure of about 495 GPa using a diamond anvil cell. Aserendipitous in situ preparation by means of a shockwave compression had been done in 1996 at LLNL.

Diamond anvil (Photo by Max Alexander/Science Photo Library)



Temperature (K)

Press

ure

(G

Pa)

100

0

300

400

200

500 15001000 20000

liquid H2

metallic liquid H2

critical point

solid H2

metallic solid H 2

Suggested phase diagram of hydrogen at high pressures and temperatures, according to Dias & Silvera (2017) Science 355, 715-718.



(A) At pressures up to 335 GPa, hydrogen was transparent. (B) At this stage of compression, the sample was black and nontransmitting. (C) Photo of metallic hydrogen at a pressure of 495 GPa. The sample is nontransmitting and observed in reflected light. The sample dimensions are ~8 to 10 μm, with thickness of ~1.2 μm. Figure from Dias & Silvera (2017) Science 355, 715-718.



Several researchers in the field doubt the claim of the prepared metallic hydrogen in 2016 (see Castelvecci (2017) Nature 542, 17).


Stability and phase transitions

The shapes of the phase diagrams are determined by the relative thermodynamic stability of the phases, i.e. by the chemical potential m (molar Gibbs free energy Gm).

Therefore, the chemical potential m can be thought of as the potential of a substance to bring about a physical change.

All parts of an equilibrium system have the same chemical potential.

Under different conditions, different forms of the same system become more stable.


Suggested ReadingHofmann, A (2016) Introduction to Physical Chemistry, 2nd Edition, Structural Chemistry Program, Griffith University.Sections III.3.3-III.3.8

Atkins, PW & de Paula, J (2010) Physical Chemistry, 9th Edition, Oxford University Press.Sections 4.1 – 4.3 (pp. 135-143)


2106nsc physical & analytical chemistry a hofmann · 2106nsc physical & analytical chemistry...

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