Question

A pure substance \(\mathrm{X}\) has the following properties: \(\mathrm{mp}=90^{\circ} \mathrm{C}\), increasing slightly as pressure increases; normal bp \(=120^{\circ} \mathrm{C}\); liquid vp \(=65 \mathrm{~mm} \mathrm{Hg}\) at \(100^{\circ} \mathrm{C}, 20 \mathrm{~mm} \mathrm{Hg}\) at the triple point. (a) Draw a phase diagram for X. (b) Label solid, liquid, and vapor regions of the diagram. (c) What changes occur if, at a constant pressure of \(100 \mathrm{~mm} \mathrm{Hg}\), the temperature is raised from \(100^{\circ} \mathrm{C}\) to \(150^{\circ} \mathrm{C}\) ?

Short answer

Answer: When the temperature is raised from 100°C to 150°C at a constant pressure of 100 mmHg, substance X changes its phase from liquid to vapor.

Step-by-step solution

Draw the phase diagram

To start drawing the phase diagram for substance X, we need to gather the information related to its properties. The given information is: - Melting point: \(90^{\circ}\)C, - Normal boiling point: \(120^{\circ}\)C, - Liquid vapor pressure: \(65\) mmHg at \(100^{\circ}\)C, \(20\) mmHg at the triple point. Using these values, plot the phase diagram by placing the points related to the melting point (solid-liquid equilibrium), the boiling point (liquid-vapor equilibrium), and the triple point (solid-liquid-vapor equilibrium).

Label regions

After placing the points related to the properties given, label the solid, liquid, and vapor regions of the phase diagram. The solid region will be on the left side of the solid-liquid equilibrium line, the liquid region will be between the solid-liquid and liquid-vapor equilibrium lines, and the vapor region will be on the right side of the liquid-vapor equilibrium line.

Identify changes in phase

Now, we need to identify the changes in phase that occur if, at a constant pressure of \(100\) mmHg, the temperature is raised from \(100^{\circ}\)C to \(150^{\circ}\)C. Locate the point on the phase diagram with a pressure of \(100\) mmHg and a temperature of \(100^{\circ}\)C in the liquid region as given (liquid vapor pressure). Next, raise the temperature to \(150^{\circ}\)C with the constant pressure of \(100\) mmHg. Observe the phase diagram to see if the point moves from one phase region to another. For example, see if it crosses the liquid-vapor equilibrium line. If it does, then there is a phase change from liquid to vapor. In this case, as we raise the temperature from \(100^{\circ}\)C to \(150^{\circ}\)C at a constant pressure of \(100\) mmHg, the substance X changes its phase from liquid to vapor.

Key concepts

Melting Point

The melting point of a substance is the temperature at which it changes from a solid to a liquid. In the case of substance X, the melting point is given as 90°C. The melting process requires heat energy to break the bonds that hold the solid structure together. As the temperature reaches the melting point, particles gain enough kinetic energy to overcome the forces keeping them in a solid structure, leading to a phase transition into a liquid.

For most substances, the melting point can vary with pressure, but for substance X, it increases slightly with pressure. This behavior is somewhat common—under high pressures, particles are pushed closer together, making the solid state more stable and raising the temperature necessary to produce a phase change. Understanding the melting point is crucial, as it provides insights into the thermal properties and stability of a substance.

Boiling Point

The boiling point is another critical thermal property defined as the temperature at which a substance's vapor pressure equals the surrounding atmospheric pressure, causing the substance to form vapor bubbles within the liquid and transition to a gaseous state. Substance X has a normal boiling point of 120°C, which occurs under standard atmospheric pressure, typically 760 mmHg.

Just like melting points, boiling points are also pressure-dependent. The boiling point will be lower at higher altitudes where atmospheric pressure is reduced. Conversely, increasing the pressure can raise the boiling point. This pressure dependence is explained by Le Chatelier's Principle, where the system adjusts to minimize the pressure change by favoring the phase that occupies less volume when pressure is increased.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. When the liquid’s vapor pressure reaches the surrounding pressure, boiling occurs. Substance X exhibits a liquid vapor pressure of 65 mmHg at 100°C. This indicates the equilibrium pressure exerted by the vapor arising from its liquid at this temperature.

As the temperature increases, so does vapor pressure, because more molecules have enough kinetic energy to escape the liquid's surface. At the triple point, the vapor pressure of substance X is 20 mmHg, which represents the unique set of conditions where solid, liquid, and vapor phases coexist in equilibrium. Understanding vapor pressure is essential for predicting at what conditions a liquid will boil and how temperature changes influence this phase transition.

Phase Transition

A phase transition refers to the transformation of a substance from one state of matter to another. These transitions occur due to changes in temperature and pressure, as depicted in a phase diagram. In the scenario involving substance X, raising the temperature from 100°C to 150°C at a constant pressure induces a phase transition from liquid to vapor.

Phase transitions happen when the internal energy of a substance allows particles to change their organization, hence, their state. This energy is generally provided by heat. Common examples of phase transitions include melting (solid to liquid), freezing (liquid to solid), vaporization (liquid to vapor), and condensation (vapor to liquid). Each of these transitions involves a specific type of energy change—latent heat of fusion for melting and freezing, and latent heat of vaporization for vaporization and condensation.