# What is the Phase diagram for water system? What is the Gibbs phase rule?

Answer:

**The water system :**

**The water system :**

Under normal conditions the water system is a three phase and one component system. The three phases are liquid, ice and vapour. All these are represented by one chemical entity (H2O), hence it is one component system. **Phase diagram for water system**

The three forms of water (ice, water and vapour) constitute the following equilibrium :

### 1. Single phase equilibrium :

(a) Solid (ice) : represented by area BOC.

(b) Liquid (water) : represented by area AOC.

(c) Gas (vapour) : represented by area AOB.

### 2. Two phase equilibrium :

(a) Solid (ice) –><– Liquid (water) : represented by curve OC.

(b) Liquid (water) –><– Gas (water vapour) : represented by curve OA.

(c) Solid (ice) –><– Gas (water vapour) : represented by curve OB.

### 3. Three phase equilibrium :

Solid (ice) –><–Liquid (water) –><– Gas (Vapour) : represented by triple point O.

The * phase diagram* consists of :

(a) Three areas, BOC, AOC and AOB.

(b) Three curves, OB, OA and OC.

(c) One triple point, O.

For any one component system, the maximum number of degree of freedom is two. Therefore such

a system can be represented completely by a two dimensional diagram. The most convenient

variables are pressure and temperature. The

*consists of :*

**phase diagram for water system****1. Areas :**Area BOC represents the solid (ice) phase which is thermodynamically most stable state

under these conditions. Area AOC represents the liquid (water) phase in the system and similarly

area AOB represents the gas (vapour) phase in the system. Thus these areas represent one phase

equilibria.

In order to define the system completely at any point in the area, it is essential to specify both

the temperature and pressure. Therefore areas have two degrees of freedom and are called

bivariant systems. It can also be concluded by the phase rule equation.

*F*=

*C*–

*P*+ 2 = 1 – 1 + 2 = 2 (Bivariant system)

**2. Curves or boundary lines :**Separating the areas are lines OA, OB and OC, connecting the point

at which two phases can co‐exist in equilibrium. Any point on boundary lines has one degree of

freedom. This follows from phase rule equation :

F = 3-P = 3-2=1 (Univariant system)

**(i) The curve OA (Vapour pressure curve) :**Curve OA represents the equilibrium between the two phases, liquid water and vapour. Along this curve water and vapour coexist in equilibrium. The curve shows the vapour pressure of liquid water at different temperatures. OA curve is also known as vapour pressure curve of water()l . A is the critical point having temperature 3740 C and pressure 218 atm. At this critical point the liquid and vapour are indistinguishable from each other and thus only one phase is left. Critical point marks the highest temperature at which the liquid can exist. Critical point is a characteristic property of pure substance.

(ii)

**Curve OB (Sublimation curve)**: Curve OB represents the equilibrium between ice and vapour and it is called as sublimation curve of ice. The two phases namely ice and vapour

coexist in equilibrium along this curve.

Along the curve OC, OA and OB, the number of phases present in equilibrium is two,

*F*=

*C*–

*P*+ 2 = 1 – 2 + 2 = 1

Hence system is univariant along the curve.

(iii)

*The curve OC represents the equilibrium between ice and water (two phase equilibria) and it is known as melting point curve. The inclination of the curve OC towards the pressure axis indicates that melting point of ice slightly decreases by increasing pressure. The reason for this behaviour is the decrease in the volume when ice melts into water. Thus ice transforms into denser water when the pressure is raised. Phase diagram for water system*

**Curve OC (Melting or fusion curve) :****Curve**The dotted curve*OA*’ (Metastable curve) :*OA*’ is the continuation of vapourization curve*OA*. It is vapour pressure curve of supercooled water. As the water does not always freezes at 0^{0}C, therefore if the vessel containing water and vapour is thoroughly clean and dust free, it is possible to super cool water several degrees below its freezing point.

** **Super cooled –><–liquid vapour

On adding nucleus of ice (stable state) the system reverts to true stable system i.e.

Solid–><–Vapour

**Triple Point :**The point*O*where all the three curves*OC*,*OA*and*OB*meet is known as triple At the triple point all the three phases of water system namely solid ice, liquid water and gas vapour are in equilibrium. The equilibrium in three phases is attained at 0.0076^{0}C temperature and 4.58 mm Hg pressure. The degree of freedom will be :

** ***F *=* C *–* P *+ 2 = 1 – 3 + 2 = 0

** **Hence, the system is non‐variant.

**Gibbs phase rule** :

* Gibbs phase rule* states that if a heterogeneous system is influenced by temperature, pressure and concentration and not by any other action like gravity, electrical, magnetic forces or by surface action, then the sum of number of phases (P) and degrees of freedom (F) is greater than the number of components (C) by two. It is expressed mathematically as follows :

*P*+

*F*=

*C*+ 2

F =* C *–* P *+ 2

Where, P = the number of phases; C = number of components

F = number of degrees of freedom

The Gibbs phase rule provides a general relationship among the degree of freedom of a system F, the number of phases P and the number of components C.

**Triple point : **The point at which all the phases of the system coexist in equilibrium is called the triple point of the system. System is invariant at triple point (since *F* = 0) . If either the temperature or the pressure or both are changed, all phases would no longer coexist and at least one of them would disappear.

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