Question

A pure substance \(X\) has the following properties: \(\mathrm{mp}=90^{\circ} \mathrm{C}\), increasing slightly as pressure increases; normal \(\mathrm{bp}=120^{\circ} \mathrm{C} ;\) liquid \(\mathrm{vp}=65 \mathrm{~mm} \mathrm{Hg}\) at \(100^{\circ} \mathrm{C}, 20 \mathrm{~mm} \mathrm{Hg}\) at the triple point. (a) Draw a phase diagram for \(\mathrm{X}\). (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: As the temperature is increased from 100°C to 150°C at a constant pressure of 100 mmHg, the substance X changes from the liquid phase to the vapor phase.

Step-by-step solution

(a) Determine the triple point and critical point

In order to draw the phase diagram, we need to determine the pressure and temperature of the X's triple point and critical point. We know the vapor pressure at the triple point is 20 mmHg. We also know that the melting point is 90°C and increases slightly with pressure, so the temperature at the triple point is slightly lower, let's assume 89°C. As for the critical point, we don't have enough information to determine it, so we will proceed with the phase diagram without it.

(a) Draw the phase boundaries

Next, we need to draw the boundaries between the solid, liquid, and vapor phases. We know that the normal boiling point is 120°C, and the liquid vapor pressure is 65 mmHg at 100°C. This gives us a point on the liquid-vapor boundary. We can draw a curve to connect that point with the triple point mentioned earlier (89°C, 20 mmHg). The solid-liquid boundary will have a positive slope, as the melting point increases slightly with pressure. Draw a straight line passing through the triple point and having a positive slope.

(b) Label the regions

Having drawn the phase boundaries, we can now label the regions as follows: - The region above the liquid-vapor boundary is the vapor phase. - The region below the solid-liquid boundary is the solid phase. - The region between the two boundaries and to the right of the triple point is the liquid phase.

(c) Determine the state of X

At a constant pressure of 100 mmHg, the initial temperature is 100°C, which is located in the liquid phase based on our phase diagram. If the temperature increases to 150°C, the point moves vertically upwards in the phase diagram while staying at the same pressure. Based on our phase diagram, it crosses over into the vapor phase. So, the substance X changes from liquid to vapor as the temperature is increased from 100°C to 150°C at a constant pressure of 100 mmHg.