Chapter 4, Problem 4.3P

(a)

Interpretation Introduction

Interpretation:

The slope of the solid-liquid phase boundary of water on a pressure-temperature phase diagram has to be determined.

Concept Introduction:

For the solid-liquid phase boundary, Clausius-Clapeyron equation can be written as

  $\frac{dP}{dT}=\frac{{\Delta }_{fus}H}{T_f{\Delta }_{fus}V}=\frac{{\Delta }_{fus}S}{{\Delta }_{fus}V}$

Where,

$\begin{array}{l}{\Delta }_{fus}S=\frac{{\Delta }_{fus}H}{T_f}\\ \\ {\Delta }_{fus}V=V_m\left(l\right)-V_m\left(s\right)\\ \\ V_m=\frac{Mass}{Density}\end{array}$

$V_m\left(s\right)=$ Molar volume of solid

$V_m\left(l\right)=$ Molar volume of liquid

${\Delta }_{fus}V=$ Volume of fusion

${\Delta }_{fus}S=$ Entropy of fusion

${\Delta }_{fus}H=$ Enthalpy of fusion

$T_f=$ Fusion temperature

(b)

Interpretation Introduction

Interpretation:

The pressure required to lower the melting point of ice by $1^{\circ }C$ has to be calculated.

Concept Introduction:

For the solid-liquid phase boundary, Clausius-Clapeyron equation can be written as

Where,

$\begin{array}{l}{\Delta }_{fus}S=\frac{{\Delta }_{fus}H}{T_f}\\ \\ {\Delta }_{fus}V=V_m\left(l\right)-V_m\left(s\right)\\ \\ V_m=\frac{Mass}{Density}\end{array}$

$V_m\left(s\right)=$ Molar volume of solid

$V_m\left(l\right)=$ Molar volume of liquid

${\Delta }_{fus}V=$ Volume of fusion

${\Delta }_{fus}S=$ Entropy of fusion

${\Delta }_{fus}H=$ Enthalpy of fusion

$T_f=$ Fusion temperature