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.