Chapter 4, Problem 4B.4ST

Interpretation Introduction

Interpretation:

The minimum pressure at which the liquid water is the thermodynamically stable phase at ${\text{25}}^{\text{ο}}\text{C}$ has to be calculated.

Concept Introduction:

Phase:

A phase is defined as a homogeneous and physically distinct part of a system which is bounded by a surface and is mechanically separable from the other parts of the system.

Phase rule:

Phase rule is very important to predict the conditions that must be specified for a system to exhibit equilibrium.  According to phase rule, for system in internal equilibrium,

$\begin{array}{l}\text{F}\text{=}\text{C}-\text{P}\text{+}\text{2}\\ \\ \text{F}\text{=}\text{no}\text{.}\text{of}\text{degrees}\text{of}\text{freedom}\\ \\ \text{C}\text{=}\text{no}\text{.}\text{of}\text{components}\\ \\ \text{P}\text{=}\text{no}\text{.}\text{of}\text{phases}\end{array}$

Clausius Clapeyron equation:

On a pressure temperature diagram the line separating the two phases is known as the coexistence curve and the Clausius Clapeyron equation gives the slope of the tangents to this curve.

The equation is given as,

  $\frac{\text{dP}}{\text{dT}}\text{=}\frac{\text{ΔH}}{\text{TΔV}}$

Where,

$\text{P}$ is the pressure

$\text{T}$ is the temperature

$\text{V}$ is the volume

$\text{ΔH}$ is the enthalpy change

Phase diagram for water:

Figure-1

According to the figure BD represents the solid liquid equilibrium, BC represents the liquid vapor equilibrium and AB represents the solid vapor equilibrium.

Using Clausius Clapeyron equation from this phase diagram it can be predicted that, as the volume of the liquid water is less than the volume of ice so the slope for solid-liquid equilibrium boundary will be negative and as the difference is less so the value will be more.  Thus it can be concluded that the melting point decreases with increase in pressure.

As the volume of vapor is more than volume of liquid hence the slope for the liquid vapor equilibrium will be positive but value of slope is less as the volume difference is more.  Hence with increase in pressure the boiling point will increase.