One substance, three phases
Lesson 1.2.1 introduced the three states of matter with a particle model. AP topic 3.3 asks for more precise particulate diagrams: solids can be crystalline or amorphous; the particles of a solid and of a liquid are both in close contact; and the spacing and collision frequency of gas molecules change with temperature, pressure, and volume. Questions often show several particle diagrams and ask you to choose the correct one.
Solids: crystalline and amorphous
- A crystalline solid晶体 has its particles arranged in a regular, repeating three-dimensional pattern, as in table salt, ice, and metals. Crystalline solids have a definite melting point.
- An amorphous solid非晶体 has its particles packed closely but with no long-range order, as in glass and most plastics and rubbers. Amorphous solids soften gradually over a range of temperatures instead of melting at one temperature.
In both kinds of solid, the particles only vibrate about fixed positions; they don’t move past one another. The structure of a solid depends on the forces between its particles and on how well the particles can pack together.
Liquids
The particles of a liquid are also in close contact, but they move and collide constantly and slide past one another, with no fixed positions. So a liquid has a definite volume but no definite shape, and it flows. The forces between particles (polarity, hydrogen bonding, and so on) and the temperature affect how the particles are arranged and how they move: the stronger the forces, the less easily the liquid flows and evaporates.
Because the particles of both solids and liquids are in close contact, the solid and liquid of the same substance have similar molar volumes: 1 mol of water is about 18 mL as a liquid and about 20 mL as ice. (Ice is actually a little larger: hydrogen bonds hold its water molecules in an open network, as in 2.4.8. Most substances are slightly denser as solids than as liquids.)
Vapor pressure
In a closed container, higher-energy molecules at the surface of a liquid keep escaping into the vapor, and vapor molecules keep striking the surface and rejoining the liquid. At first evaporation outpaces condensation and the vapor builds up; once the two rates are equal, the amount of vapor stops changing, a dynamic equilibrium. The pressure of the vapor then is the equilibrium vapor pressure平衡蒸气压.
- The equilibrium vapor pressure depends only on the substance (its intermolecular forces) and the temperature: weaker forces and higher temperature mean higher vapor pressure. For example, water’s equilibrium vapor pressure at 25 °C is 3.17 kPa (IAPWS-95).
- It doesn’t depend on the amount of liquid, the area of its surface, or the volume of the container: a larger surface lets more molecules escape but also catches more coming back, so the equilibrium vapor pressure is unchanged.
- A liquid boils when its vapor pressure equals the external pressure. The boiling point at 1 atm is the normal boiling point: the weaker the intermolecular forces, the higher the vapor pressure and the lower the normal boiling point.
Gases
Gas molecules are in constant random motion, with distances between them far larger than the molecules themselves, and intermolecular forces have little effect. So a gas has neither a definite shape nor a definite volume, and it is easily compressed. The average distance between molecules and how often they collide depend on temperature, pressure, and volume:
- Compression (smaller volume or higher pressure): the molecules get closer together and collide more often.
- Heating at constant volume: the average spacing stays the same, but the molecules move faster and collide more often and harder.
At 100 °C and 1 atm, 1 mol of water as steam occupies about 30.6 L, roughly 1700 times its volume as a liquid, and the average distance between molecules is more than 10 times that in liquid water.
Switch among the three states to see how the particles are arranged and move, then press the piston:
| Spacing | Very close, in a regular pattern |
|---|---|
| Motion | Vibrate in fixed positions |
| Shape | Fixed |
| Volume | Fixed |
| Compressible? | Hardly at all |
Compare the volume of 1 mol of water in each phase, then drag the temperature and pressure to see how the spacing and collision frequency of gas molecules change:
Volume of 1 mol of water (about 18 g) in each phase, drawn to scale
1 mol of an ideal gas: drag the temperature and pressure
Example 1: The volume of steam
Calculate the volume of 1.00 mol of water as steam (treated as an ideal gas) at 100 °C and 1.00 atm, compare it with 1.00 mol of liquid water (about 18 mL), and explain with the particle model.
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Use the ideal gas law for the steam. Convert the temperature to kelvins, T = 100 + 273.15 = 373.15 K; with R = 0.08206 L·atm/(mol·K), the volume comes out in liters:
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Compare with liquid water. About 18 mL = 0.018 L of liquid:
The steam takes up about 1700 times the volume of the same amount of liquid water.
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Explain with the particle model. In liquid water the molecules are touching; the steam has the same number of molecules of the same size, but they are much farther apart, so almost all of its volume is empty space between molecules.
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A consequence. This is why gases are easy to compress and liquids are nearly incompressible.
Example 2: Compressing and heating a gas
For a flask of gas (treated as ideal), (1) the volume is halved at constant temperature; (2) it is heated from 300 K to 600 K at constant volume. Describe how the average distance between molecules, the average speed, and the collision frequency change in each case.
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How spacing depends on volume. Each molecule has an average space of V/N, and the average distance d is proportional to its cube root:
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(1) Half the volume at constant temperature. The number of molecules is unchanged, so the average distance becomes
its original value, not half. The temperature is unchanged, so the average speed is too; twice as many molecules per unit volume means twice the collision frequency, and twice the pressure.
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(2) Double the temperature at constant volume. The average distance doesn’t change. The average speed is proportional to :
The molecules hit the walls more often and harder, and the pressure doubles.
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What stays the same. In both cases the molecules themselves don’t change size; what changes is their spacing (compression) or how fast they move (heating).
- Particles only vibrate about fixed positions
True for both crystalline and amorphous solids.
- Particles are in close contact but slide past one another
That's why liquids flow.
- No definite shape and no definite volume
A gas fills its whole container.
- Easily compressed
There is a lot of space between the molecules.
- Definite volume but no definite shape
A liquid takes the shape of its container.
- The average distance between particles changes greatly with temperature and pressure
In solids and liquids the particles stay in close contact.
- Glass (no long-range order)
Glass is an amorphous solid.
- 1 mol occupies about 24.5 L at 25 °C and 1 atm
V = RT/P applies only to gases.
- Forces between particles have little effect on their arrangement and motion
Gas molecules are far apart.
- 1 mol of water occupies about 18 mL
Liquid water has a density of about 1.0 g/mL.
Common mistakes
Mistake 1: “Particles in a liquid are much farther apart than in a solid.” In both solids and liquids the particles are in close contact, and the molar volumes are similar. What distinguishes a liquid is that its particles can slide past one another, not the distance between them.
Mistake 2: “Particles in a solid are completely still.” The particles of a solid vibrate constantly about fixed positions; they just can’t slide past one another. The higher the temperature, the more vigorously they vibrate.
Mistake 3: “A gas expands when heated because its molecules get bigger.” The molecules don’t change size. Heating makes them move faster; if the pressure stays constant, the gas expands because the distance between molecules increases.
Quick check
Which diagram best represents the particles in a liquid?
In a liquid the particles are in close contact and disordered, with a definite volume, and the liquid flows to the bottom of its container. A is a crystalline solid; B is a gas, with particles far apart; D is an amorphous solid, packed and disordered but only vibrating, so it needs no container.
Glass is an amorphous solid. Which diagram best represents the particles in glass?
The particles of an amorphous solid are packed closely but without a regular repeating pattern. B is crystalline; C and D are a gas and a liquid.
Four liquids are each sealed in a container at the same temperature and have reached equilibrium (only some of the molecules are drawn). Which liquid has the weakest intermolecular forces?
At the same temperature, the weaker the intermolecular forces, the more easily molecules escape, so at equilibrium there are more vapor molecules above the liquid and the vapor pressure is higher. B has the most vapor molecules.
At constant temperature, a liquid and its vapor are moved from one sealed container to a larger sealed container (some liquid remains). After equilibrium is restored, how has the vapor pressure changed?
Right after the move the vapor pressure drops for a moment, but more liquid evaporates until evaporation and condensation are again balanced, and the vapor pressure returns to its original value. C: a larger surface also catches more molecules coming back.
The solid and liquid of the same substance usually have similar molar volumes. Which is the best explanation?
Solids and liquids differ in whether particles can slide past one another, not in how far apart they are. A, C, and D are all false.
The temperature of a gas in a rigid, sealed container is raised. Which statement is correct?
The number of molecules and the volume are unchanged, so the average spacing is unchanged; at the higher temperature the molecules move faster and collide more often and harder, so the pressure rises. The molecules don't change size.
A sample of gas is compressed to half its volume at constant temperature. Which statement is correct?
The number of molecules per unit volume doubles, so the molecules are closer and collide more often. At constant temperature the average speed is unchanged (B is wrong). Halving the volume shrinks the spacing only to about 0.79 of its value (a cube root), not to half (D is wrong).
Most substances are slightly denser as solids than as liquids, yet ice floats on water. Which is the best explanation?
In ice each water molecule hydrogen-bonds to 4 others, forming an open network, so the same mass of ice takes up more volume. The size of the molecules and the O–H bonds don't change appreciably.
AP-style free response
1.00 mol of water can exist as ice at 0 °C, as liquid water, or as steam at 100 °C and 1.00 atm. The molar volume of liquid water is about 18 mL.
(a) Treating steam as an ideal gas, calculate the volume of 1.00 mol of steam at 100 °C and 1.00 atm.
(b) About how many times the volume of the liquid is the volume of the steam? Explain with a particle model.
(c) Describe how particle diagrams of liquid water and of steam should differ.
(d) At constant temperature, the steam is compressed to half its volume (it remains a gas). How do the average distance between molecules and the collision frequency of each molecule change?
Model answer and scoring
(a) V = nRT/P = 1.00 × 0.08206 × 373.15 ÷ 1.00 ≈ 30.6 L.
(b) 30.6 L ÷ 0.018 L ≈ 1.7 × 10³ times. In liquid water the molecules are in close contact; in steam they are far apart, and the volume is almost all space between molecules.
(c) Liquid water: particles touching, disordered, gathered at the bottom of the container with a surface. Steam: the same number of particles, far apart and spread evenly through the whole container. The particles are the same size in both diagrams.
(d) The average distance decreases (to about 0.79 of its original value); the number of molecules per unit volume doubles and the average speed is unchanged, so the collision frequency of each molecule roughly doubles.
Scoring: (a) correct substitution, with the answer in L; (b) about 1.7 × 10³ times, citing the distance between molecules; (c) liquid closely packed, gas spread out, particle size unchanged; (d) spacing decreases and collisions become more frequent.
Summary
- Solids: particles only vibrate about fixed positions; crystalline solids have a regular repeating structure and amorphous solids don’t.
- Liquids: particles are in close contact, moving constantly and sliding past one another; solids and liquids have similar molar volumes.
- The equilibrium vapor pressure depends only on temperature and intermolecular forces, not on the amount of liquid, its surface area, or the container volume.
- Gases: molecules are far apart in constant random motion, with no definite shape or volume; the average spacing and collision frequency depend on temperature, pressure, and volume.
AP tip: When choosing a particle diagram, check each feature: Do the particles stay the same size? Are the particles of solids and liquids touching? Does the gas fill the whole container? Is the crystal orderly? Are the numbers of atoms and molecules conserved? Changing only temperature or pressure never makes molecules bigger or smaller.