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

01

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.

02

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 \((320\ ^\circ \mathrm{C}, 100\ \mathrm{atm})\).

03

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 \((59\ ^\circ \mathrm{C}, 1\ \mathrm{atm})\).

04

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".

05

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.

06

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.

07

Identify the conditions where liquid bromine cannot exist

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

08

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 \(200\ ^\circ \mathrm{C}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!