Chapter 9, Problem 116QRT

(a)

Interpretation Introduction

Interpretation:

The number of solid phases that exist in the phase diagram of sulfur has to be determined.

Concept Introduction:

Every pure substance that exists in all three phases has a characteristic phase diagram like below.

Figure 1

Solid phase of the material is found at very low temperature and very high pressure.  Gaseous phase of the material is found at very high temperature and very low pressure.  Liquid phase of the material is found at other pressures and temperatures.

Explanation of Solution

The phase diagram of sulfur is given below.

Figure 2

From the above phase diagram, it is clear that there are two solid phases in the range of very high pressure and very low temperature.  These two are rhombic and monoclinic which are two allotropic forms of sulfur.

(b)

Interpretation Introduction

Interpretation:

The number of triple points that exist in the phase diagram of sulfur has to be determined.

Concept Introduction:

Triple point:

The triple point of a substance is the temperature and pressure at which all the three phases of that substance coexist in thermodynamic equilibrium.  In other words, it can be defined the meeting point of sublimation curve, fusion curve and the vaporization curve.

Explanation of Solution

There are three triple points in the phase diagram of sulfur which are labeled as $B,EandC.$

(c)

Interpretation Introduction

Interpretation:

The phase of sulfur at $1atmand{80}^{\circ }C$ and $1atmand{125}^{\circ }C$ has to be determined.

Concept Introduction:

Refer to part (a).

Explanation of Solution

The phase diagram of sulfur is given below.

Figure 3

The horizontal line from $1atm$ and the vertical line from ${80}^{\circ }C$ meets at a point which lies in the solid region.  Hence, sulfur exists in the solid phase at $1atmand{80}^{\circ }C.$

The horizontal line from $1atm$ and the vertical line from ${125}^{\circ }C$ meets at a point which lies in the liquid region.  Hence, sulfur exists in the liquid phase at $1atmand{125}^{\circ }C.$

(d)

Interpretation Introduction

Interpretation:

The phase of sulfur at ${151}^{\circ }C$ has to be determined.

Concept Introduction:

Refer to part (a).

Explanation of Solution

The phase diagram of sulfur is given below.

Figure 4

The phase diagram of sulfur at ${151}^{\circ }C$ can be divided into three parts.

1. 1) Region below pressure ${10}^{-4}atm$
2. 2) Region between pressure ${10}^{-4}atm$ and ${10}^{3}atm$
3. 3) Region above pressure ${10}^{3}atm$

Hence, at ${151}^{\circ }C$ and pressure lower than ${10}^{-4}atm$, sulfur exists as a gas, between ${10}^{-4}atm$ and ${10}^{3}atm$, it exists as a liquid and above ${10}^{3}atm$, it exists as a solid.

(e)

Interpretation Introduction

Interpretation:

The condition of sublimation of sulfur has to be determined.

Concept Introduction:

Sublimation:

The process of direct conversion of solid phase of a substance to a gaseous phase without any intermediate phase is called as sublimation.

Explanation of Solution

The phase diagram of sulfur is given below.

Figure 5

Sulfur will sublime at a temperature and pressure where there exists a solid $/$ gas equilibrium on the phase diagram.  This can be clearly seen from the diagram that pressure should be below $10^{-4}atm$ and temperature should be below $120^{o}C.$

(f)

Interpretation Introduction

Interpretation:

The most stable phase of sulfur at $1atmand{100}^{\circ }C$ has to be determined.

Explanation of Solution

The phase diagram of sulfur is given below.

Figure 6

A horizontal line from $1atm$ and a vertical line from ${100}^{\circ }C$ meets at a point which lies in the region of monoclinic solid.  Hence, the most stable phase at $1atmand{100}^{\circ }C$ is monoclinic solid.

(g)

Interpretation Introduction

Interpretation:

The phases present at ${10}^{-4}atm$ as the temperature changes from ${50}^{\circ }Cto{200}^{\circ }C$ has to be identified sequentially.

Explanation of Solution

The phase diagram of sulfur is given below.

Figure 7

By drawing a horizontal line from ${10}^{-4}atm$, the sequential changes that happens can be identified easily.  The sulfur starts as a rhombic solid at ${50}^{\circ }C$, then changes to a monoclinic solid, then touches the triple point $E$ at which all the phases coexist and then to a vapor as shown above

(h)

Interpretation Introduction

Interpretation:

The normal melting point of sulfur has to be determined from the phase diagram.

Concept Introduction:

Melting point:

The temperature at which the conversion of the solid phase of a substance to a liquid phase is known as melting point.  At this point both solid and liquid phases of a substance exist in equilibrium.  The pressure is generally taken as standard pressure such as $1atm$.

Explanation of Solution

The phase diagram of sulfur is given below.

Figure 8

The horizontal lone from $1atm$ is touching the curve at a point from where a vertical line can be drawn which will touch the temperature axis at ${120}^{\circ }C.$  Hence, the normal melting point of sulfur is $120^{o}C.$