## What is the Phase diagram for the 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. One chemical entity (H2O) represents all these, 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* comprises :

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

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

(c) One triple point, O.

For anyone component system, the maximum 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

*comprises :*

**phase diagram for water system****1. Areas:**Area BOC represents the solid (ice) phase, which is the 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. The phase rule equation can also conclude it.

*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 coexist in equilibrium. Any point on boundary lines has one degree of freedom. This follows from the 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. It has also known oA curve as the 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. The critical point marks the highest temperature at which the liquid can exist. The critical point is a characteristic property of a pure substance.

(ii)

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

coexist in equilibrium along this curve.

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

*F*=

*C*–

*P*+ 2 = 1 – 2 + 2 = 1

Hence the 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 the melting point curve. The inclination of the curve OC towards the pressure axis shows that the melting point of ice slightly decreases by increasing pressure. The reason for this behaviour is the decrease in the volume when the 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 a vapour pressure curve of super-cooled water. As the water does not always freeze 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 the 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 several phases (P) and degrees of freedom (F) is greater than the number of components (C) by two. We express mathematically it :

*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) . It changed if either the temperature or the pressure or both, all phases would no longer coexist and at least one of them would disappear.

**Significance of triple point: **Triple point is a characteristic physical property of a pure substance. The triple point marks the lowest temperature at which the liquid can exist. As for the water system, the solid‐liquid phase boundary slopes in the opposite direction so the triple point criteria are not applicable regarding temperature. But regarding pressure, a liquid can exist as a stable phase if the pressure is above that of the triple point.

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