Question

Use these data to draw a qualitative phase diagram for ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right) .\) Is \(\mathrm{C}_{2} \mathrm{H}_{4}(s)\) more or less dense than \(\mathrm{C}_{2} \mathrm{H}_{4}(l) ?\) bp at 1 atm: \(-103.7^{\circ} \mathrm{C}\) \(\mathrm{mp}\) at \(1 \mathrm{~atm}:-169.16^{\circ} \mathrm{C}\) Critical point: \(\quad 9.9^{\circ} \mathrm{C}\) and \(50.5 \mathrm{~atm}\) Triple point: \(-169.17^{\circ} \mathrm{C}\) and \(1.20 \times 10^{-3} \mathrm{~atm}\)

Short answer

C₂H₄(s) is denser than C₂H₄(l) because the solid-liquid boundary slopes negatively.

Step-by-step solution

- Identify Key Data Points

Record the given data points: - Boiling point at 1 atm: -103.7°C - Melting point at 1 atm: -169.16°C - Critical point: 9.9°C and 50.5 atm - Triple point: -169.17°C and 1.20 × 10^-3 atm

- Plot the Axes

On a graph, label the y-axis as Pressure (in atm) and the x-axis as Temperature (in °C).

- Mark the Data Points

Plot the given data points on the graph: - Boiling point at 1 atm (-103.7°C) - Melting point at 1 atm (-169.16°C) - Critical point (9.9°C, 50.5 atm) - Triple point (-169.17°C, 1.20 × 10^-3 atm)

- Draw Phase Boundaries

Based on the data points, draw the lines representing the phase boundaries: 1. Solid-liquid boundary from the triple point upward. 2. Liquid-gas boundary from the boiling point at 1 atm to the critical point. 3. Solid-gas boundary from the triple point to the left and upward.

- Label the Regions

Label the different regions of the phase diagram that correspond to solid, liquid, and gas.

- Determine Density Comparison

Compare the slopes of the solid-liquid boundary. If the boundary slopes positively (to the right), the solid is less dense than the liquid. If it slopes negatively, the solid is denser than the liquid.

Key concepts

phase diagram

A phase diagram shows the states of matter for a substance at various pressures and temperatures.
It has different regions representing solid, liquid, and gas phases.
The lines separating these regions are called phase boundaries. In the case of ethylene, we plot the temperature on the x-axis and pressure on the y-axis.
Important data points such as the boiling point, melting point, critical point, and triple point are used to construct this diagram.
Each phase boundary indicates the conditions under which two phases coexist in equilibrium.
Understanding a phase diagram helps visualize how changing pressure and temperature affects the state of a substance.

critical point

The critical point on a phase diagram marks the endpoint of the liquid-gas boundary.
Beyond this point, the liquid and gas phases become indistinguishable from each other.
For ethylene, this critical point is at 9.9°C and 50.5 atm.
This means that at temperatures and pressures higher than these values, ethylene will exist as a supercritical fluid.
A supercritical fluid has properties of both liquids and gases, making it versatile for various applications.
Understanding the critical point is essential for processes that involve high temperatures and pressures, such as chemical reactions and extractions.

triple point

The triple point of a substance is the unique set of conditions at which solid, liquid, and gas phases coexist in equilibrium.
For ethylene, the triple point occurs at -169.17°C and 1.20 × 10^-3 atm.
At this specific temperature and pressure, any small change can shift the balance to one of the three phases.
The triple point provides vital information for understanding the fundamental properties of a substance.
In practical terms, knowing the triple point helps in calibrating thermometers and understanding phase transitions under various conditions.

density comparison

Density comparison in a phase diagram involves analyzing the slope of the solid-liquid boundary.
For ethylene, if the slope of this boundary is positive (rightward), it indicates that the solid phase is less dense than the liquid phase.
Conversely, a negative slope would mean the solid is denser.
In our case, since the solid-liquid boundary slopes positively, ethylene in its solid form is less dense than its liquid form.
This knowledge is useful in predicting behaviors such as floating or sinking of the solid in the liquid and other physical properties.