Question

Referring to Figure \(9.7,\) state what phase(s) is (are) present at (a) \(1 \mathrm{~atm}, 10^{\circ} \mathrm{C}\). (b) \(3 \mathrm{~mm} \mathrm{Hg}, 20^{\circ} \mathrm{C}\) (c) \(1000 \mathrm{~mm} \mathrm{Hg}, 75^{\circ} \mathrm{C}\).

Short answer

Answer: (a) At \(1 \mathrm{~atm}, 10^{\circ} \mathrm{C}\), the substance is in the liquid phase. (b) At \(3 \mathrm{~mm} \mathrm{Hg}, 20^{\circ} \mathrm{C}\), the substance is in the gas phase. (c) At \(1000 \mathrm{~mm} \mathrm{Hg}, 75^{\circ} \mathrm{C}\), the substance is in the liquid phase.

Step-by-step solution

Locate each point on the phase diagram

First, we need to find the point on the phase diagram that corresponds to each given set of pressure and temperature conditions. (a) \(1 \mathrm{~atm}, 10^{\circ} \mathrm{C}\) (b) \(3 \mathrm{~mm} \mathrm{Hg}, 20^{\circ} \mathrm{C}\) (c) \(1000 \mathrm{~mm} \mathrm{Hg}, 75^{\circ} \mathrm{C}\)

Determine the phase region(s) for each condition

Now that we have located the points on the phase diagram, we need to determine which phase region each point falls into. Each region represents a specific phase of the substance: solid, liquid, or gas. (a) For the condition \(1 \mathrm{~atm}, 10^{\circ} \mathrm{C}\), the point falls in the liquid phase region. (b) For the condition \(3 \mathrm{~mm} \mathrm{Hg}, 20^{\circ} \mathrm{C}\), the point falls in the gas phase region. (c) For the condition \(1000 \mathrm{~mm} \mathrm{Hg}, 75^{\circ} \mathrm{C}\), we need to convert \(1000 \mathrm{~mm} \mathrm{Hg}\) to atmospheres where 1 atmosphere = 760 mm Hg. So, \(1000 \mathrm{~mm} \mathrm{Hg} = \frac{1000}{760} \mathrm{~atm}\). The point falls in the liquid phase region.

State the phase(s) present for each condition

Based on the phase region each point falls into, we can state the phase(s) present for each given condition: (a) At \(1 \mathrm{~atm}, 10^{\circ} \mathrm{C}\), the substance is in the liquid phase. (b) At \(3 \mathrm{~mm} \mathrm{Hg}, 20^{\circ} \mathrm{C}\), the substance is in the gas phase. (c) At \(1000 \mathrm{~mm} \mathrm{Hg}, 75^{\circ} \mathrm{C}\), the substance is in the liquid phase.