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

Step by step solution

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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.

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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.

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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.

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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.

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5. Find the temperature conditions where liquid bromine cannot exist

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

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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.

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