Changes of State and the Gas Laws

7.1 Changes of State

A substance can change from one state of matter to another:
- Solid \leftrightarrow liquid \leftrightarrow gas
- Solid \leftrightarrow gas
Transition terms:
- Solid \rightarrow liquid: melting/fusion
- Liquid \rightarrow solid: freezing
- Liquid \rightarrow gas: vaporization/evaporation
- Gas \rightarrow liquid: condensation
- Solid \rightarrow gas: sublimation
- Gas \rightarrow solid: deposition
States of matter differ in:
- Kinetic energy (depends on temperature).
- Intermolecular forces of attraction – potential energy (solid > liquid > gas).
- Intermolecular forces of attraction vary depending on the element or compound.
During a change of state:
- Intermolecular forces of attraction are formed or disrupted.
- Covalent bonds are NOT changed.
- This is a physical change.
Strongest intermolecular forces of attraction occur in compounds that undergo hydrogen bonding.
Hydrogen bonding occurs between polar molecules containing O–H, N–H bonds, or H–F.
Substances at the same temperature have the same amount of kinetic energy.
The strength of the intermolecular forces of attraction between molecules determines the state of matter for a substance at a given temperature.
Polar molecules have stronger intermolecular forces of attraction than nonpolar molecules.
Heat energy is transferred to or from the surroundings during a change of state.
Vaporization:
- Energy is transferred from the surroundings to the substance evaporating.
- Increases kinetic energy of liquid molecules.
- Disrupts (breaks) intermolecular forces of attraction.
- Molecules enter the gas phase.
Heat absorbed from surroundings during:
- Melting.
- Vaporization.
- Sublimation.
Heat is released to surroundings during:
- Freezing.
- Condensation.
- Deposition.
Melting, vaporization, and sublimation are endothermic physical changes (heat must be added).
Freezing, condensation, and deposition are exothermic physical changes (heat must be removed).
Gases are compressible and can be liquefied by applying pressure.
Boiling point: temperature at which a substance undergoes a phase change from liquid to gas at normal atmospheric pressure (sea level).
Melting point: temperature at which a substance undergoes a phase change from solid to liquid at normal atmospheric pressure (sea level).
A heating curve shows how the temperature of a substance increases or remains constant as heat energy is added.
Horizontal plateaus on a heating curve represent changes of state (constant temperature).
Heat is absorbed for phase change instead of increasing temperature.
A cooling curve starts with the gas phase and records the decrease in temperature as heat is removed.
Condensation occurs at the boiling point.
Freezing occurs at the melting point.
At the melting and boiling points on a heating curve, heat continues to be added, but the temperature remains constant.
The energy added goes into breaking intermolecular forces of attraction, and a change of state occurs rather than a temperature change.
Heat of fusion, \,\Delta H_{fus}, is the amount of energy required to melt a solid at its melting point. Remove this same energy to freeze a liquid.
Heat of vaporization, \,\Delta H_{vap}, is the amount of energy required to boil a liquid at its boiling point. Remove this same energy to condense a gas.
\Delta H{vap} >> \Delta H{fus} because all intermolecular forces of attraction must be disrupted to enter the gas phase.
The heat of vaporization is the heat that must be added per gram of liquid at its boiling point for vaporization or removed from the gas for condensation.
The heat of fusion is the heat that must be added to a solid at its melting point for melting or removed from the liquid for freezing.
Evaporation is a change from the liquid to the gas phase below the boiling point.
Evaporation is endothermic and requires \,\Delta H_{vap}.
- Evaporation cools your skin when you step out of a shower because it absorbs the heat energy from your skin.
- Sweating is evaporative cooling.
Exothermic phase changes add heat to the body.
- Steam burns are more severe than boiling water burns because \,\Delta H_{vap} energy is released by the steam condensing.
- 100 °C steam transfers 538 calories of heat per gram during condensation.
Evaporation (l \rightarrow g) causes the surroundings to become cooler (evaporative cooling) because it is an endothermic process.
Condensation is an exothermic process, causing the surroundings to absorb heat.
Specific heat of a substance is the amount of heat required to raise the temperature of 1 g of the substance by 1 °C.
Units of specific heat = cal/g°C
Heat equation: (cal) = \text{specific heat} \,\,\left(\frac{cal}{g \cdot {}^{\circ}C}\right) \times \text{mass} \,(g) \times \Delta T \,\,\left({}^{\circ}C \right)
- Heat = amount of energy added or removed
- Mass = amount of sample
- \Delta T = change in temperature
Specific heat is the physical property of a substance that indicates the amount of heat required to raise the temperature of 1 g of the substance by 1 °C.
The heat equation can be used to calculate the amount of heat transferred to or from a substance from the mass, change in temperature, and specific heat of the substance.

7.2 Properties of Gases and the Gas Laws

Focus is on substances that are gases at room temperature.
- Examples:
  - Gases in a breath: oxygen and carbon dioxide
  - Common combustion gases: methane, propane
  - Anesthetics that cross the blood-brain barrier
Kinetic-molecular view describes the behavior of gases at the molecular level.
- Gaseous atoms and molecules are in constant motion, moving at high speeds.
  - Greater speeds = greater kinetic energy = higher temperatures
- Gaseous atoms or molecules move in straight lines in random directions, collide with the walls of their container, and fill the entire container.
- Gaseous atoms or molecules are far apart from one another and have negligible intermolecular forces of attraction.
The kinetic-molecular view of a gas describes the atoms and molecules moving at high speed, in straight lines, random directions, colliding with the walls of their container, and exhibiting negligible intermolecular forces of attraction.
Gases are compressible. Due to the compressibility of gases, they can be liquefied by the application of pressure, giving them unique properties that are different from solids and liquids.
Gas particles collide with the walls of the container, creating pressure.
Pressure = \frac{force}{area}
Units of Pressure:
- 1 atmosphere (atm) = 760 millimeters of mercury (mmHg)
- 760 torr (exact)
- 14.70 pounds per square inch (psi)
- 101,325 pascals (Pa)
Pressure is defined as force per unit area.
- Common units of pressure include atmospheres (atm), millimeters of mercury (mmHg), pounds per square inch (psi), and pascals (Pa).
Atmospheric Pressure:
- Air is a mixture: 78% nitrogen, 21% oxygen plus H2O, CO2, and argon
- Atmospheric pressure is the force of air molecules pressing on Earth due to gravity.
- At sea level, atmospheric pressure = 1 atm.
Air pressure forces mercury into an empty tube (no air in tube).
At sea level, the height of the mercury in the tube is 760 mm Hg, or 760 torr.
Higher Altitudes:
- Higher altitudes = lower atmospheric pressure
- Fewer molecules pressing down
- Less oxygen per breath
- Airplanes have cabins pressurized to ~0.75 atm.
The decreased atmospheric pressure at high altitude means that less oxygen is inhaled with every breath. Cylinders of oxygen provide supplemental oxygen at a higher pressure.
The Gas Laws involve the mathematical relationships among four variables that describe the macroscopic properties of a gas:
- pressure (P),
- volume (V),
- temperature (T), and
- moles (n).
The Simple Gas Laws – Two Variables:
- The pressure-volume relationship (Boyle’s law): pressure and volume are inversely proportional when n and T are constant.
- The volume-temperature relationship (Charles’s law): volume and temperature are directly proportional when n and P are constant.
- The pressure-volume relationship (Gay-Lussac’s law): pressure and temperature are directly proportional when n and V are constant and T is given in kelvins.
Boyle’s Law: Pressure-Volume Relationship:
- Pressure and volume are inversely related.
- A graph of P vs. 1/V is a straight line.
- Pi Vi = Pf Vf (n and T are constant.)
Boyle’s law describes the inverse relationship between the pressure and volume of a gas when the amount of gas and the temperature are constant.
- Boyle’s law expressed in terms of initial and final conditions is Pi Vi = Pf Vf .
Solving an Initial/Final Gas Law Problem:
- Step 1: Determine the three given variables and the variable that is asked for.
- Step 2: Determine which gas law applies, and write its mathematical expression (equation).
- Step 3: Rearrange the equation to isolate the asked for variable.
- Step 4: Substitute the given variables and carry out the math.
- Step 5: Check that the answer makes sense.
Charles’s Law: Volume-Temperature Relationship:
- Volume and temperature are directly proportional.
- A graph of V vs. T is a straight line crossing x-axis at 0 K (or −273 °C).
- \frac{Vi}{Ti} = \frac{Vf}{Tf} (n and P are constant; T is in kelvins.)
Charles’s law describes the direct relationship between volume and temperature, given in kelvins, when n and P are constant.
- Charles’s law expressed in terms of initial and final conditions is \frac{Vi}{Ti} = \frac{Vf}{Tf}.
Gay-Lussac’s Law: Temperature-Pressure Relationship:
- Pressure and temperature are directly proportional.
- A graph of pressure versus temperature produces a straight line.
- \frac{Pi}{Ti} = \frac{Pf}{Tf} (n and V are constant; T is in kelvins.)
Gay-Lussac’s law describes the direct relationship between pressure and temperature, given in kelvins, when n and V are constant.
- Gay-Lussac’s law expressed in terms of initial and final conditions is \frac{Pi}{Ti} = \frac{Pf}{Tf}.
The Combined Gas Law: Pressure, Volume, and Temperature:
- Incorporates all the simple gas laws into one law; can be used to remember the individual ones.
- Used when there is a fixed amount of gas, n, and the variables P, V, and T are changing.
- \frac{Pi Vi}{Ti} = \frac{Pf Vf}{Tf} (n is constant.)
The combined gas law provides the relationship among pressure, volume, and temperature for a fixed amount of gas (n is constant), in terms of initial and final conditions, when P, V, and T are changed.
- Temperature must be given in units of kelvins when using the combined gas law: \frac{Pi Vi}{Ti} = \frac{Pf Vf}{Tf} (n is constant).
Avogadro’s Law: Volume-Mole Relationship:
- Avogadro’s law: moles of gas, n, is directly proportional to the volume, V, of the gas (constant T and P).
- \frac{Vi}{ni} = \frac{Vf}{nf}
The moles of a gas are directly proportional to the volume when the temperature and the pressure are constant (Avogadro’s law).
- \frac{Vi}{ni} = \frac{Vf}{nf} (T and P are constant.)
Molar Volume:
- Standard temperature and pressure (STP ): 0 °C (273.15 K) and 1 atm of pressure
- Molar volume of a gas at STP = 22.4 L
One mole of any gas at 0°C and 1 atm occupies a volume of 22.4 L, known as the molar volume of a gas.
Density of a Gas at STP:
- For a gas at STP, Density = \frac{molar \, mass}{molar \, volume}
The density of a gas is proportional to its molar mass.
- Gases with a molar mass less than air float in air.

7.3 Gas Mixtures and Partial Pressures

Gas mixtures contain two or more gases.
- Dry air is a good example.
Dalton’s Law of Partial Pressures:
- Each gas in a mixture exerts a pressure independent of other gases, behaving as if it alone occupied the total volume.
- Dalton’s law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas in the mixture.
- P{total} = P1 + P2 + P3 + …
- P1, P2, P3, . . . , Pn are partial pressures of the gases in the mixture.
Dalton’s law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each of the gases.
- P{total} = P1 + P2 + P3 + …
- P1, P2, P3, . . . , Pn are partial pressures of the gases in the mixture.
Henry’s Law:
- Blood serum contains dissolved gases: oxygen, nitrogen, and carbon dioxide.
- Henry’s law states that the number of moles of gas, n, dissolved in a liquid is directly proportional to the partial pressure, P, of the gas.
C = K_H P (T is constant.)
- P = the partial pressure of the gas,
- KH = Henry’s constant, which is unique for each gas,
- C = the concentration of the dissolved gas (mol/L).
Anesthetics have different KH values.
- KH value determines how quickly the anesthetic reaches the brain.
- It also determines the time needed to regain consciousness.
Henry’s law shows that the moles of gas dissolved in solution are proportional to the partial pressure of the gas.
- C = K_H P (T is constant.)
  - P = the partial pressure of the gas,
  - KH = Henry’s constant, which is unique for each gas,
  - C = the concentration of the dissolved gas (mol/L).
Hyperbaric Oxygen Therapy (HBOT):
- Use of high-pressure oxygen is used to treat the bends, CO poisoning, healing of diabetic wounds, and treating some infections.
- Conditions involve hypoxia (oxygen deprivation) of certain tissues.
How HBOT Works:
- HBOT chamber has an atmosphere with a higher oxygen partial pressure and a total pressure of 1.5–3 atm.
- The bends: A diver is put in a chamber so that nitrogen bubbles redissolve. The pressure in the chamber is gradually reduced, and nitrogen gas is gradually released and exhaled.
- CO poisoning: CO replaces O2 on hemoglobin. Exposure to higher partial pressure O2 helps to displace the CO.
- Diabetic wounds are due to hypoxia in the extremities. Exposure to oxygen stimulates blood vessel growth and healing.