Problem 106 - Chemistry An Atoms First Approach

Question

Like most substances, bromine exists in one of the three typical phases. \(\mathrm{Br}_{2}\) has a normal melting point of \(-7.2^{\circ} \mathrm{C}\) and a normal boiling point of \(59^{\circ} \mathrm{C}\). The triple point for \(\mathrm{Br}_{2}\) is \(-7.3^{\circ} \mathrm{C}\) and 40 torr, and the critical point is \(320^{\circ} \mathrm{C}\) and 100 atm. Using this information, sketch a phase diagram for bromine indicating the points described above. Based on your phase diagram, order the three phases from least dense to most dense. What is the stable phase of \(\mathrm{Br}_{2}\) at room temperature and 1 atm? Under what temperature conditions can liquid bromine never exist? What phase changes occur as the temperature of a sample of bromine at 0.10 atm is increased from \(-50^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

The phase diagram of bromine can be sketched using the given information, and the density order can be determined as Gas < Liquid < Solid. The stable phase of Br₂ at room temperature and 1 atm is Liquid. Liquid bromine cannot exist at temperatures above the critical point, i.e., \(320\ ^\circ \mathrm{C}\). As the temperature increases from \(-50\ ^\circ \mathrm{C}\) to \(200\ ^\circ \mathrm{C}\) at \(0.10\ \mathrm{atm}\), bromine experiences phase transitions from solid to liquid and then from liquid to gas.

Step 1: Draw the axes for the phase diagram

On the x-axis, represent the temperature in degrees Celsius. On the y-axis, represent the pressure in torr for the negative and atmospheric (atm) pressure range for positive values.

Step 2: Plot the triple and critical points

Mark the triple point at the coordinates \((-7.3\ ^\circ \mathrm{C}, 40\ \mathrm{torr})\) and the critical point at the coordinates \((320\ ^\circ \mathrm{C}, 100\ \mathrm{atm})\).

Step 3: Plot the melting and boiling points

The normal melting and boiling points correspond to 1 atm of pressure. Mark the solid-liquid equilibrium line by connecting the triple point to the melting point at \((-7.2\ ^\circ \mathrm{C}, 1\ \mathrm{atm})\). Similarly, mark the liquid-gas equilibrium line by connecting the triple point to the boiling point at \((59\ ^\circ \mathrm{C}, 1\ \mathrm{atm})\).

Step 4: Complete the phase diagram

Draw the solid-gas equilibrium line connecting the triple point with the x-axis at a very low temperature. To mark the different phases of the substance, label the regions above the solid-liquid equilibrium line as "Liquid", below the solid-gas equilibrium line as "Solid", and to the right of the liquid-gas equilibrium line as "Gas".

Step 5: Identify the density order of the different phases

Since the solid-liquid equilibrium line has a negative slope, the solid phase is denser than the liquid phase. Therefore, the order of density from least dense to most dense is: Gas < Liquid < Solid.

Step 6: Identify the stable phase at room temperature and 1 atm

Room temperature is around \(20\ ^\circ \mathrm{C}\), and since \(20\ ^\circ \mathrm{C}\) falls above and to the left of the liquid-gas equilibrium line, the stable phase of Br₂ at room temperature and 1 atm pressure is Liquid.

Step 7: Identify the conditions where liquid bromine cannot exist

Liquid bromine cannot exist at temperatures above the critical point, which is \(320\ ^\circ \mathrm{C}\).

Step 8: Identify the phase changes as temperature increases from -50℃ to 200℃ at 0.10 atm

As the temperature increases from \(-50\ ^\circ \mathrm{C}\) to \(200\ ^\circ \mathrm{C}\) at \(0.10\ \mathrm{atm}\): 1. Initially, bromine is in the solid phase (\(-50\ ^\circ \mathrm{C}\)). 2. It goes through a solid to liquid transition at the melting point (-7.2℃). 3. The bromine exists as a liquid until it reaches its boiling point, which is located between the triple point and normal boiling point. 4. Finally, it goes through a liquid to gas phase transition and ends up as a gas at \(200\ ^\circ \mathrm{C}\).

Key Concepts

Melting Point

The melting point is a fundamental thermal property wherein a solid turns into a liquid. For bromine (\(\mathrm{Br}_2\)), this occurs at \(-7.2^{\circ}\mathrm{C}\) under standard atmospheric pressure (1 atm). At this precise temperature, both the solid and liquid phases of bromine can coexist, making it a crucial part of a phase diagram that shows the balance between different phases based on temperature and pressure. This transition point provides critical insights into how substances behave under varying thermal conditions. In the context of bromine, the melting point indicates when ice-like bromine becomes a liquid, an understanding pivotal for grasping other thermal transitions such as the boiling point.

Boiling Point

The boiling point represents the temperature at which a liquid becomes a gas. For bromine, this occurs at \(59^{\circ}\mathrm{C}\) at 1 atm pressure. During this transformation, the liquid phase transforms into vapor as intermolecular forces break down and allow molecules to escape into a gaseous state. The boiling point is an essential component of a phase diagram, showing the line where liquid turns into gas across different pressures. Understanding this helps in visualizing how bromine behaves from a molecular perspective during phase transitions and under varied atmospheric pressures.

Triple Point

Unique and significant, the triple point of a substance is where solid, liquid, and gas phases coexist in thermodynamic equilibrium. For bromine, the triple point occurs at \(-7.3^{\circ}\mathrm{C}\) and 40 torr. Phase diagrams depict this vital intersection point, demonstrating the specific conditions under which all three phases can exist simultaneously. Realizing the importance of this point aids in conceptualizing phase transitions and understanding substance behavior under controlled conditions typically used in scientific experiments.

Critical Point

The critical point on a phase diagram marks the conditions beyond which distinct liquid and gas phases do not exist. For bromine, it is located at \(320^{\circ}\mathrm{C}\) and 100 atm. Beyond this temperature and pressure, bromine transforms into a supercritical fluid, where the liquid-gas boundary ceases to exist. This is crucial for understanding phenomena such as supercritical fluid extraction or the behavior of substances at high pressure and temperature, beyond everyday experiences. It highlights the theoretical limits of states of matter and phase changes.

Density

Density, a property that measures mass per unit volume, varies across different phases of a substance. In the case of bromine, the gas phase is the least dense, while the solid phase is the most dense, as indicated by the phase diagram's solid-liquid line having a negative slope. This order: Gas < Liquid < Solid, tells us that as bromine transitions from gas to solid, its molecules pack closer together, increasing density. Understanding density and how it shifts with state changes is essential for predicting how a material behaves in different phases, crucial in fields ranging from material science to engineering.