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 \(1 \mathrm{~atm}\) ? Under what temperature conditions can liquid bromine never exist? What phase changes occur as the temperature of a sample of bromine at \(0.10 \mathrm{~atm}\) is increased from \(-50^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C} ?\)

Short answer

The phases of Br2 are ordered from least dense to most dense as: Gas < Liquid < Solid. The stable phase of Br2 at room temperature (20-25°C) and 1 atm is liquid. Liquid Bromine can never exist above the critical point's temperature, which is 320°C. As the temperature of a sample of Bromine at 0.10 atm is increased from -50°C to 200°C, the phase changes from solid to gas (sublimation) directly.

Step-by-step solution

Phase Diagram Construction

To construct the phase diagram for Br2, we need to plot the phases of Br2 (solid, liquid, and gas) along the pressure (y-axis) and temperature (x-axis) axes. The first step is to draw the lines indicating the phase transitions.

Marking the Triple Point

The triple point is the unique point on the phase diagram where all three phases of matter exist in equilibrium. It is given as -7.3°C and 40 torr. Mark this point on the phase diagram.

Marking the Melting Point

The normal melting point is the temperature at which a substance changes from solid to liquid at 1 atm pressure. It is given as -7.2°C. Mark the point on the phase diagram where the temperature is -7.2°C and pressure is 1 atm.

Marking the Boiling Point

The normal boiling point is the temperature at which a substance changes from liquid to gas at 1 atm pressure. It is given as 59°C. Mark the point on the phase diagram where the temperature is 59°C and the pressure is 1 atm.

Marking the Critical Point

The critical point is the point on the phase diagram above which the gas and liquid phases become indistinguishable. It is given as 320°C and 100 atm. Mark this point on the phase diagram.

Ordering the Phases by Density

Looking at the phase diagram, we can see that: 1. Solid phase: Since the solid-liquid phase boundary line has a positive slope, the solid phase is more dense than the liquid phase. 2. Liquid phase: Since the solid-liquid phase boundary line has a positive slope and liquid lies below the line, it is less dense than solid, but denser than the gas phase. 3. Gas phase: As gases are the least dense phase of matter, the phase is least dense in the gas phase. Thus, the order of phases from least dense to most dense is: Gas < Liquid < Solid

Stable Phase of Bromine at Room Temperature and 1 atm

Room temperature is typically around 20 to 25°C. Looking at the phase diagram, we see that 1 atm and around 20-25°C is in the liquid phase. Therefore, the stable phase of Bromine at room temperature and 1 atm is liquid.

Temperature Conditions for Liquid Bromine Nonexistence

For liquid Bromine to never exist, we need to be above the critical point's temperature, which is 320°C.

Phase Changes at 0.10 atm from -50°C to 200°C

At 0.10 atm and -50°C, we are in the solid phase. As we increase the temperature to 200°C: 1. The solid phase will transition to the gas phase directly (sublimation) since we never cross the solid-liquid phase boundary line. 2. After entering the gas phase, Bromine stays as a gas throughout the temperature increase. Thus, the phase changes occurring when increasing the temperature from -50°C to 200°C are solid to gas (sublimation).

Key concepts

Phase Transition

A phase transition is the transformation of a substance from one state of matter to another, such as solid to liquid or liquid to gas. These transitions occur when energy, typically in the form of heat, is added or removed from a system. When bromine is heated from -7.2°C (its normal melting point) at a constant pressure of 1 atm, it undergoes a phase transition from solid to liquid. Similarly, at its boiling point of 59°C, bromine transitions from liquid to gas. The phase diagram of bromine maps these changes, showing the conditions of pressure and temperature under which each phase is stable.

In the context of bromine, if the temperature is raised at a constant pressure below 1 atm, the substance may skip the liquid phase entirely and transition directly from solid to gas through a process called sublimation. This versatile understanding of phase transitions allows us to predict the behavior of substances under different conditions.

Triple Point

The triple point of a substance is an exclusive set of conditions where all three phases—solid, liquid, and gas—coexist in thermodynamic equilibrium. For bromine, the triple point occurs at -7.3°C and 40 torr. At this precise point on the phase diagram, solid bromine, liquid bromine, and bromine vapor can be found together without transitioning from one to another. In other words, the energy exchange between these phases is perfectly balanced. This concept is fundamental to understanding the properties of materials and is often a reference point in scientific calibration standards.

Knowing the triple point of bromine is crucial for high-precision temperature measurements and for industrial applications where bromine must be stored or used in different phases under controlled conditions.

Critical Point

The critical point marks another unique condition on the phase diagram characterized by a specific temperature and pressure where a substance's gas and liquid phases meld into one another and become indistinguishable. For bromine, this occurs at 320°C and 100 atm. Above this critical point, bromine exists in a supercritical fluid state, which means that it shares properties of both gases and liquids. When referring to the phase diagram, the critical point signals the end of the liquid-gas boundary or the so-called 'critical line,' an important characteristic for understanding the complete range of a substance's phases.

Beyond this point, the concepts of 'liquid' or 'gas' lose their usual meaning, and the substance exhibits density and solvation characteristics advantageous for various applications in the field of materials science and extraction processes.

Sublimation

Sublimation is the transition of a substance directly from the solid to the gas phase without passing through the intermediate liquid phase. This endothermic process, requiring energy input, can be observed in the phase diagram of bromine when the conditions include a temperature rise from -50°C to 200°C at a constant pressure of 0.10 atm. Such a low pressure prevents bromine from ever becoming a liquid, and as it absorbs energy, it bypasses the liquid phase entirely and turns directly into gas. Substances like dry ice (solid carbon dioxide) and iodine also exhibit sublimation under certain conditions.

Understanding sublimation is important for several applications, including freeze-drying, where it is applied to preserve perishable materials, and in various manufacturing processes where it's important to avoid liquid-phase related issues.

Phase Density

Phase density refers to how closely packed the molecules of a substance are within a given phase. Generally, solids are the most dense as their molecules are tightly packed, followed by liquids and then gases, which have the least density due to widely spaced molecules. In the case of bromine, at room temperature and a pressure of 1 atm, it exhibits its highest density in the solid phase and is least dense in the gaseous phase. The phase diagram helps us visualize this by indicating the regions of stability for each phase under varying conditions. By understanding the phase density, we can predict how bromine will behave when it's used in different applications, such as in buoyancy, or when bromine's mass per unit volume is a critical factor.

For instance, solid bromine particles would sink in liquid bromine due to their higher density, while bromine gas would rise if contained above liquid bromine.