Question

A pure substance A has a liquid vapor pressure of 6 atm at \(550^{\circ} \mathrm{C}\). Its triple point is at \(5 \mathrm{~atm}, 350^{\circ} \mathrm{C}\). The solid phase is denser than the liquid phase. (a) Sketch the phase diagram for compound \(A\). (b) From the phase diagram, estimate the temperature at which the compound boils when 6.3 atm of pressure are applied. (c) What changes occur when, at a constant pressure of 4 atm, the temperature drops from \(400^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C} ?\)

Short answer

Question: Based on the phase diagram of substance A, estimate its boiling point at 1 ATM pressure, and describe the phase transitions, if any, that occur when the temperature drops from 150 to 100 degrees Celsius at a constant pressure of 320 mm Hg. Answer: The boiling point of substance A at 1 ATM pressure is approximately _____ degrees Celsius. When the temperature drops from 150 to 100 degrees Celsius at a constant pressure of 320 mm Hg, the substance undergoes a _____ (phase transition, e.g., gas to liquid) phase transition.

Step-by-step solution

Plotting the Triple Point

First, we need to plot the triple point on the phase diagram. The triple point is given at \(85^{\circ} \mathrm{C}\) and \(60 \mathrm{~mm} \mathrm{Hg}\). This is where all three phases (solid, liquid, and gas) coexist.

Plotting the Pressure Points of Liquid and Gas

Next, we need to plot the given pressures for the liquid and gas phases on the diagram. We are given that the vapor pressure is \(320 \mathrm{~mm} \mathrm{Hg}\) at \(125^{\circ} \mathrm{C}\), and \(800 \mathrm{~mm} \mathrm{Hg}\) at \(150^{\circ} \mathrm{C}\).

Plotting the Melting Point at Increasing Pressure

We are given that the melting point of A decreases slightly as pressure increases. We plot this information as a line starting from the triple point, slanting slightly downward to the right.

Sketching the Phase Diagram and Identifying Regions

Now that we have plotted the triple point, pressure points for liquid and gas phases, and the melting point at increasing pressures, we can sketch the phase diagram. On the diagram, identify the regions for solid, liquid, and gas, and sketch the lines separating the three regions.

Estimating the Boiling Point

From the phase diagram, we can estimate the boiling point by analyzing the temperature value at the intersection of the line separating the liquid and gas regions, and a vertical line representing 1 ATM.

Analyzing the Changes at Constant Pressure

Lastly, we need to analyze the changes that occur when the temperature drops from \(150^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\) at a constant pressure of \(320 \mathrm{~mm} \mathrm{Hg}\). To do this, follow the line representing 320 mm Hg on the phase diagram and observe if it crosses the regions of the different phases. Then describe the phase transitions, if any, that occur during the temperature drop.

Key concepts

Triple Point

Understanding the triple point in chemistry is crucial for comprehending how a substance can exist in three different states: solid, liquid, and gas. The triple point is a unique set of conditions—specifically temperature and pressure—where all three phases of a substance coexist in thermodynamic equilibrium. This point on a phase diagram is represented by a single spot where the boundaries between the solid, liquid, and gas phases meet.

For example, for substance A in the exercise, the triple point occurs at 5 atm and 350°C. This information allows us to plot the starting point on a phase diagram from where we can draw phase boundaries, indicating the conditions under which each phase is stable. Phase diagrams are valuable as they give an at-a-glance representation of a substance's state under varying conditions of temperature and pressure.

Vapor Pressure

Vapor pressure is a term that describes the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It's a measure of a substance's tendency to evaporate. As the temperature increases, molecules move more rapidly, thus increasing their likelihood to transition into the gas phase, which results in higher vapor pressure.

In the context of the exercise, substance A has a vapor pressure of 6 atm at 550°C. Plotting this data point on a phase diagram, and other similar points at different temperatures, helps form the curve that separates the gas phase from the liquid phase. The curve itself is critical for understanding at what pressure and temperature phase transitions occur.

Phase Transitions

Phase transitions are transformative changes that occur when a substance goes from one state of matter to another, such as from solid to liquid (melting) or liquid to gas (vaporization). The main types of phase transitions include melting, freezing, sublimation, deposition, vaporization, and condensation.

In the exercise, we're asked to consider the changes that happen when temperature drops from 400°C to 100°C at a constant pressure of 4 atm. A phase diagram helps visualize these changes by indicating the regions of stability for the solid, liquid, and gas phases. By following a line at the given pressure, you can see which phase transitions will occur as the temperature changes.

Melting Point

The melting point of a substance is the temperature at which it changes from a solid to a liquid. At the melting point, the solid and liquid phases of a substance are in equilibrium, so the temperature will remain constant until all the solid has melted. This point varies with pressure; generally, for most substances, the melting point increases with pressure because molecules are forced closer together. However, there are exceptions, such as water.

In the exercise's phase diagram, the melting point at increased pressure is represented by a line descending slightly to the right starting from the triple point. This slope of the line indicates the unique behavior of substance A, suggesting that its melting point slightly decreases with an increase in pressure, contrary to the more common trend.

Boiling Point

The boiling point is the temperature at which a liquid changes to a vapor or gas. At this point, the vapor pressure of the liquid equals the external pressure exerted on the liquid. Like the melting point, the boiling point of a substance can change with pressure but generally increases as pressure increases, causing the liquid to require higher temperatures to reach the boiling state.

According to the exercise, to estimate the boiling point of substance A under the pressure of 6.3 atm, you'd find the intersection of the line that represents this pressure with the curve separating the liquid and gas phases on the phase diagram. This intersection denotes the temperature at which the liquid form of substance A boils under these conditions.