Mehran University of e

Mazhar Ali Soomro (K13PG43)

Presented by:

Mehran UET SZAB Campus Khair pur Mir’s

Gibb’s Phase Rule and Degree of freedom

Contents

Phase Rule Degree of freedom Thermodynamic of solutions Phase diagram Types of phase diagram Thermodynamic properties

The Phase Rule describes the possible number of degrees of freedom in a (closed) system at equilibrium, in terms of the number of separate phases and the number of chemical constituents in the system. It was deduced from thermodynamic principles by J. W. Gibbs in the 1870s.The Gibbs phase rule describes the degrees of freedom available to describe a particular system with various phases and substances.

f p c 1 2 pc p 2 pp 21 cc c c p

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Phase Rule

Degree of freedom

single phase (pi=1) F=1-1+2=2

two phases (pi=2) F=2+1-2=1

three phase (pi=3) F=2+1-3=0

The Degrees of Freedom [F] is the number of independent intensive variables (i.e. those that are independent of the quantity of material present) that need to be specified in value to fully determine the state of the system. Typical such variables might be temperature, pressure, or concentration.The rule is:

F = C - P + 2.

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3 Phases (solid, liquid-vapor and solid-liquid-gas)3

For example:A system with one component and one phase (a balloon full of carbon dioxide, perhaps) has two degrees of freedom: temperature and pressure, say, can be varied independently.If you have two phases -- liquid and vapor for instance -- you lose a degree of freedom, and there is only one possible pressure for each temperature.Add yet one more phase -- ice, water and water vapor in a sealed flask -- and you have a "triple point" with fixed temperature and pressure

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Thermodynamics of Solutions

• Phases: Part of a system that is chemically and physically homogeneous, bounded by a distinct interface with other phases and physically separable from other phases.

• Components: Smallest number of chemical entities necessary to describe the composition of every

phase in the system. The number of components are determined by the formula

C=N-X-R Where N= total no: of chemical constituents, X=chemical

reactionAnd R= total number of chemical constraints(neutrally charged)

on complete system

Ex: For the reduction of nickel oxide, NiO, NiO(s) + CO(g) = Ni(s) + CO2(g)

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Solutions: Homogeneous mixture of two or more

chemical components in which their concentrations may be freely varied within certain limits.

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Can four phases exist together (as in two solid phases, a liquid phase and the gaseous phase?

Phase diagram

A figure which summarizes the effect of temperature and pressure on a substance in a closed container. Every point in this diagram represents a possible combination of temperature and pressure for the system. The diagram is divided into three areas, which represent the solid, liquid, and gaseous states of the substance.

The best way to remember which area corresponds to each of these states is to remember the conditions of temperature and pressure that are most likely to be associated with a solid, a liquid, and a gas. Low temperatures and high pressures favor the formation of a solid. Gases, on the other hand, are most likely to be found at high temperatures and low pressures. Liquids lie between these extremes.

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Phase Diagram8

Applications of PD

Phase diagrams are useful tools to determine:

--the number and types of phases, --the wt% of each phase, and the

composition of each phase for a given T and composition of the system.

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Phase diagram cont.

Triple points: Points where equilibrium boundary lines meet.

All phases in the adjacent stability fields must coexist.

Critical point – the point on a phase diagram at which the substance is indistinguishable between liquid and gaseous states.

Fusion(melting) (or freezing) curve – the curve on a phase diagram which represents the transition between liquid and solid states.

Vaporization (or condensation) curve – the curve on a phase diagram which represents the transition between gaseous and liquid states.

Sublimation (or deposition) curve – the curve on a phase diagram which represents the transition between gaseous and solid states

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2D Phase Diagram

The simplest phase diagrams are pressure-temperature diagrams of a single simple substance, such as water. The axes correspond to the pressure and temperature. The phase diagram shows, in pressure-temperature space, the lines of equilibrium or phase boundaries between the three phases of solid,liquid, and gas.

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2D Phase Diagram

Pressure vs. Temperature

3D phase diagrams

It is possible to envision three-dimensional (3D) graphs showing three

thermodynamic quantities. For example for a single component, a 3D Cartesian

coordinate type graph can show temperature (T) on one axis, pressure (P) on a second axis, and specific volume (v) on a third. Such a 3D graph is sometimes called a P-v-T diagram.

The equilibrium conditions would be shown as a 3D curved surface with areas for solid, liquid, and vapor phases and areas where solid and liquid, solid and vapor, or liquid and vapor coexist in equilibrium.

A line on the surface called a triple line is where solid, liquid and vapor can all coexist in equilibrium. The critical point remains a point on the surface even on a 3D phase diagram.

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3D Phase Diagram cont.

An orthographic projection of the 3D P-v-T graph showing pressure and temperature as the vertical an horizontal axes effectively collapses the 3D plot into a 2D pressure-temperature diagram. When this happens, the solid-vapor, solid-liquid, and liquid-vapor surfaces collapse into three corresponding curved lines meeting at the triple point, which is the collapsed orthographic projection of the triple line.

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3D phase diagram15

Types of Liquids

Saturated Liquid: a liquid whose temperature and pressure are such

 that any decrease in pressure without change in temperature causes it to boil.

Unsaturated Liquid: A Liquid which is not about to vaporize. Saturated Vapor: A vapor that is about to condense. Super heated Vapor: A vapor that is not about to condense.

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Super critical Fluid

A supercritical fluid is any substance at a temperature and pressure above its critical point, where distinct liquid and gas phases do not exist. It can effuse through solids like a gas, and dissolve materials like a liquid. In addition, close to the critical point, small changes in pressure or temperature result in large changes in density, allowing many properties of a supercritical fluid to be "fine-tuned". Supercritical fluids are suitable as a substitute for organic solvents in a range of industrial and laboratory processes.

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Thermodynamic properties

The properties define the thermodynamic state of a system.

a. Intensive property: does not depend on the mass (m) or does not change with subdivision of the system, denoted by lowercase letters, e.g., z.

b. Extensive property: does depend on the mass (m) or does change with subdivision of the system, denoted by uppercase letters, e.g., Z.

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m

Zz

* An intensive property is also called a specific property if

For example, volume V is an extensive property, so v=V/m (i.e., volume per unit mass) is a specific property and an intensive property.

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