Question

Referring to Figure \(9.7,\) state what phase(s) is/are present at (a) \(1 \mathrm{~atm}, 100^{\circ} \mathrm{C}\). (b) \(0.5 \mathrm{~atm}, 100^{\circ} \mathrm{C}\). (c) \(0.8 \mathrm{~atm}, 50^{\circ} \mathrm{C}\).

Short answer

Question: Using the phase diagram in Figure 9.7, determine the phase or phases present in a substance under the following conditions: (a) \(1 \mathrm{~atm}, 100^{\circ} \mathrm{C}\), (b) \(0.5 \mathrm{~atm}, 100^{\circ} \mathrm{C}\), and (c) \(0.8 \mathrm{~atm}, 50^{\circ} \mathrm{C}\). Answer: (a) At \(1 \mathrm{~atm}, 100^{\circ} \mathrm{C}\), both solid and liquid phases are present. (b) At \(0.5 \mathrm{~atm}, 100^{\circ} \mathrm{C}\), only the liquid phase is present. (c) At \(0.8 \mathrm{~atm}, 50^{\circ} \mathrm{C}\), only the solid phase is present.

Step-by-step solution

Identify the coordinates for each condition

For each part of the exercise, we need to locate the corresponding point on the phase diagram. The pressure values will be on the Y-axis, while the temperature values will be on the X-axis. (a) \(1 \mathrm{~atm}, 100^{\circ} \mathrm{C}\): Point is at \((100, 1)\) (b) \(0.5 \mathrm{~atm}, 100^{\circ} \mathrm{C}\): Point is at \((100, 0.5)\) (c) \(0.8 \mathrm{~atm}, 50^{\circ} \mathrm{C}\): Point is at \((50, 0.8)\)

Determine the phases at the given coordinates

Using the phase diagram in Figure \(9.7\), find what phases the points fall into. (a) At \((100, 1)\): The point lies on the solid-liquid phase boundary. Here, both solid and liquid phases are present. (b) At \((100, 0.5)\): The point lies within the liquid phase region. Thus, only the liquid phase is present. (c) At \((50, 0.8)\): The point lies within the solid phase region. Therefore, only the solid phase is present.

Write the answer

Based on the analysis of the phase diagram, we can state the following: (a) At \(1 \mathrm{~atm}, 100^{\circ} \mathrm{C}\), both solid and liquid phases are present. (b) At \(0.5 \mathrm{~atm}, 100^{\circ} \mathrm{C}\), only the liquid phase is present. (c) At \(0.8 \mathrm{~atm}, 50^{\circ} \mathrm{C}\), only the solid phase is present.