Question

Like most substances, bromine exists in one of the three typical phases. Br_ 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 \(200^{\circ} \mathrm{C} ?\)

Short answer

In the phase diagram of bromine, the order of phases from least dense to most dense is gas, liquid, and solid. The stable phase of Br2 at room temperature (25°C) and 1 atm is liquid. Liquid bromine cannot exist above the critical point (320°C) or below the triple point temperature (-7.3°C). When the temperature of a sample of bromine at 0.10 atm is increased from -50°C to 200°C, it undergoes phase changes starting from solid to liquid, and finally to gas.

Step-by-step solution

1. Plot the given data points

To start, we need to plot the four data points given: the normal melting point, normal boiling point, triple point, and critical point on a P-T graph. The given points are: - Normal melting point: -7.2°C - Normal boiling point: 59°C - Triple_point: (-7.3°C, 40 torr) - Critical point: (320°C, 100 atm) Remember to convert the pressure units consistently, either using torr or atm for all points.

2. Understand the phase diagram

We can now identify the three regions in the phase diagram corresponding to the solid, liquid, and gas phases of Br2. The lines separating the phases represent phase transitions: - The line between the solid and liquid phases represents melting and freezing. - The line between the liquid and gas phases represents vaporization and condensation. - The line between the solid and gas phases represents sublimation and deposition. The triple point is where all three phases coexist in equilibrium, and the critical point is the point above which the liquid and gas phases cannot be distinguished.

3. Order the phases by density

To order the phases by density, we can observe how the phase regions are positioned with respect to the triple point: - If the slope of the solid-liquid boundary line is positive, the solid phase is denser than the liquid phase. This is because an increase in pressure would cause the liquid to turn into a solid. - If the slope is negative, the liquid phase is denser than the solid. An increase in pressure would cause the solid to turn into a liquid. - The gas phase is always the least dense.

4. Determine the stable phase at room temperature and 1 atm

Room temperature is approximately 25°C, and 1 atm is the standard atmospheric pressure. To determine the stable phase of Br2 at these conditions, locate the point on the phase diagram that corresponds to this temperature and pressure. The phase in which this point resides is the stable phase.

5. Find the temperature conditions where liquid bromine cannot exist

Liquid bromine cannot exist above the critical point or below the triple point temperatures.

6. Describe phase changes when increasing the temperature at 0.10 atm

At 0.10 atm, we need to determine the phase changes that occur as the temperature increases from -50°C to 200°C. Start at the left side of the phase diagram and trace the path as you move to the right at 0.10 atm. Observe when phase transitions occur along this path.

Key concepts

Bromine Phases

Bromine, like most other elements, can exist in distinct phases: solid, liquid, and gas. These phases depend on both temperature and pressure conditions. Each phase is characterized by its own unique structural arrangement and energy level.

• Solid Phase: Occurs at low temperatures and typically high pressures. Atoms are closely packed and only vibrate in place.
• Liquid Phase: Exists between the solid and gas phases, at moderate temperatures and pressures. In this phase, particles are closely packed but can move freely, allowing for fluidity.
• Gas Phase: Happens at high temperatures or low pressures, where particles are very far apart and move quite freely.

Understanding these phases is crucial for analyzing bromine's behavior in different environmental conditions.
By comparing conditions such as temperature and pressure against a phase diagram, we can predict what phase bromine will be in at any given point.

Critical Point

The critical point is a specific condition in a phase diagram where the distinction between liquid and gas phases of a substance vanishes. For bromine, this point is at 320°C and 100 atm.
At this combination of temperature and pressure:

• The properties of the liquid and gas phases become indistinguishable. The substance exists as a single phase called a supercritical fluid.
• Above the critical temperature, no amount of pressure increase can liquefy the gas.
• Above the critical pressure, increasing temperature will not convert the liquid to a vapor.

Understanding the critical point helps in industrial applications where supercritical fluids are used, such as extraction processes.

Triple Point

The triple point of a substance is a unique state where solid, liquid, and gas phases coexist in equilibrium. For bromine, this is at -7.3°C and 40 torr.
This point is significant because:

• It represents the only set of conditions where all three phases can coexist.
• At pressures below the triple point, liquefaction is not possible; solid bromine sublimates directly into gas.
• Understanding the triple point assists in accurately calibrating temperature measurement devices since it serves as a reference point.

The triple point offers a foundational concept for thermodynamic studies and practical systems that need stable multi-phase interactions.

Phase Transitions

Phase transitions refer to the changes between different states of matter—such as from solid to liquid (melting), liquid to gas (vaporization), or solid to gas (sublimation). Each transition involves energy change and is characterized by specific conditions on a phase diagram.
In the case of bromine:

• Melting/Freezing: Occurs around the normal melting point. As energy is added, solid bromine becomes liquid.
• Vaporization/Condensation: As temperature increases and exceeds the boiling point, liquid bromine turns to gas.
• Sublimation/Deposition: At conditions below the triple point pressure, solid bromine transitions directly to gas.

These transitions are essential to processes such as purification, chemical synthesis, and other industrial applications where state changes allow for the manipulation of materials' properties.