Problem 75 - Chemistry: An Atoms-Focused Approach

Question

Predict the phase of water that exists under the following conditions: a. 2 atm of pressure and \(110^{\circ} \mathrm{C}\) b. 0.5 atm of pressure and \(80^{\circ} \mathrm{C}\) c. \(7 \times 10^{-3}\) atm of pressure and \(3^{\circ} \mathrm{C}\)

Step-by-Step Solution

Answer

Based on the given conditions and using the phase diagram of water, identify the phase of water in the following cases: a. 2 atm pressure and \(110^{\circ} \mathrm{C}\) temperature. b. 0.5 atm pressure and \(80^{\circ} \mathrm{C}\) temperature. c. \(7 \times 10^{-3}\) atm pressure and \(3^{\circ} \mathrm{C}\) temperature. Answer: a. Liquid b. Gas c. Solid

Step 1: Understanding the Phase Diagram of Water

To predict the phase of water under the given conditions, we need to know the phase boundaries in a phase diagram for water. On this diagram, we can find the conditions (pressure and temperature) at which water can be solid, liquid, or gas. Take note of the phase boundaries and critical points in the diagram, particularly the points where water either freezes/melts, evaporates/condenses, or boils/reaches maximum temperature.

Step 2: Determining the Phase for 2 atm Pressure and \(110^{\circ} \mathrm{C}\)

For part (a), we have 2 atm of pressure and \(110^{\circ} \mathrm{C}\). If we look at the phase diagram, this pressure is above the normal boiling point of water (\(100^{\circ} \mathrm{C}\)) at 1 atm, which means that under these conditions, the water will be in a liquid state.

Step 3: Determining the Phase for \(0.5\) atm Pressure and \(80^{\circ} \mathrm{C}\)

For part (b), we have 0.5 atm of pressure and \(80^{\circ} \mathrm{C}\). At this pressure, the boiling point of water is below \(80^{\circ} \mathrm{C}\), meaning the water's temperature is high enough to reach the vapor phase. Under these conditions, water will be in a gaseous state.

Step 4: Determining the Phase for \(7 \times 10^{-3}\) atm Pressure and \(3^{\circ} \mathrm{C}\)

For part (c), the pressure is \(7 \times 10^{-3}\) atm and the temperature is \(3^{\circ} \mathrm{C}\). This pressure lies within the region where the phase transition between solid and gas happens, meaning water will be in the solid state under these conditions. In conclusion, for the given conditions: a. 2 atm and \(110^{\circ} \mathrm{C}\): liquid b. 0.5 atm and \(80^{\circ} \mathrm{C}\): gas c. \(7 \times 10^{-3}\) atm and \(3^{\circ} \mathrm{C}\): solid

Key Concepts

Phase Transitions

Phase transitions are fascinating changes in the state of matter that occur when specific temperature and pressure conditions are met. During these transitions, a substance moves from being one form of matter to another. For instance, when water freezes, it transitions from a liquid to a solid. Conversely, when it boils, it changes from a liquid to a gas.
Factors such as temperature and pressure significantly influence these transitions. Water, for example, boils at a lower temperature when the atmospheric pressure decreases. Unique points on the phase diagram of water, like the triple and critical points, highlight conditions where phases coexist or where transitions occur in distinct manners.

• Freezing/Melting: Transition between solid and liquid.
• Evaporation/Condensation: Transition from liquid to gas and vice versa.
• Sublimation/Deposition: Direct transition between solid and gas.

Each transition has its energetic requirements, usually involving heat absorption or release, shaping the physical behavior of water under various conditions.

Pressure-Temperature Conditions

Pressure and temperature are two critical variables that control the state of a substance at any given time. The relationship between these factors is beautifully illustrated in a phase diagram.
Water’s phase diagram showcases regions where water can exist as a solid, liquid, or gas, depending on the specific pressure and temperature. For example, under normal atmospheric conditions (1 atm and around 100°C), water boils. However, at a pressure of 0.5 atm, water will boil at much lower temperatures.
The phase diagram helps predict what phase water will be in when subject to unusual pressure and temperature combinations:

• High pressure and high temperature, like 2 atm at 110°C, keep water in liquid form.
• Low pressure and lower temperatures, such as 0.5 atm at 80°C, lead water to become gas.
• Extremely low pressures, for instance, at 3°C with 0.007 atm, cause water to remain solid.

Understanding this pressure-temperature interplay allows us to predict and determine the phase of water under different environmental conditions.

States of Matter

The primary states of matter that most of us are familiar with are solid, liquid, and gas. Each state represents different molecular arrangements and interactions. For water, these states are particularly insightful for understanding its behavior under varying conditions.

• Solid (Ice): In this state, water molecules are tightly packed in a fixed structure, limiting their motion except for vibration.
• Liquid (Water): Molecules are more loosely bonded than in a solid and can slip past one another, giving liquids their characteristic ability to flow.
• Gas (Water Vapor): Molecules move freely and are widely spaced, which allows them to fill any container they are in.

Understanding each state's characteristics and behaviors helps us determine how water acts under different conditions. This knowledge is crucial, especially in tasks that need water manipulation across states, such as heating, cooling, and pressurization in various scientific and industrial applications.