Chapter 6: Gases and Pressure

Properties of Gases and the Kinetic-Molecular Theory

• A gas consists of particles (atoms or molecules) that move randomly and rapidly.

• The size of gas particles is extremely small compared to the space between the particles.

• Gas particles exert no attractive forces on each other.

• The kinetic energy of gas particles increases as the temperature increases.

• When gas particles collide with each other, they rebound and travel in new directions.

Understanding Gas Pressure

• Pressure ($P$) is defined as the force ($F$) exerted per unit area ($A$).

• Gas particles exert pressure when they collide with the walls of a container.

• The mathematical formula for pressure is:     $\text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{F}{A}$

• Common units for pressure and their relationships to 1 atmosphere ($atm$):

  • $1\,atm = 760.\,mm\,Hg$

  • $1\,atm = 760.\,torr$

  • $1\,atm = 14.7\,psi$

  • $1\,atm = 101,325\,Pa$

Boyle’s Law: Relationship Between Pressure and Volume

• Definition: For a fixed amount of gas at a constant temperature, the pressure and volume of the gas are inversely related.

• When one quantity (pressure or volume) increases, the other decreases.

• The product of pressure and volume is a constant ($k$):     $\text{Pressure} \times \text{Volume} = \text{constant}$     $P \times V = k$

• If the volume of a cylinder of gas is halved, the pressure of the gas inside the cylinder doubles.

• The relationship for initial and new conditions is expressed as:     $P_1V_1 = P_2V_2$

Application: Boyle’s Law and Breathing

• Inhalation:

  • The rib cage expands and the diaphragm lowers.

  • This increases the volume of the lungs.

  • The increase in volume causes internal pressure to decrease.

  • Air is drawn into the lungs to equalize the pressure difference with the atmosphere.

• Exhalation:

  • The rib cage contracts and the diaphragm is raised.

  • This decreases the volume of the lungs.

  • The decrease in volume causes the internal pressure to increase.

  • Air is expelled out of the lungs to equalize the pressure.

Charles’s Law: Relationship Between Volume and Temperature

• Definition: For a fixed amount of gas at constant pressure, the volume of the gas is proportional to its Kelvin temperature.

• If the temperature increases, the volume increases as well.

• The ratio of volume to temperature is a constant ($k$):     $\frac{V}{T} = k$

• Temperature must always be expressed in Kelvins ($K$).

• The relationship for initial and new conditions is expressed as:     $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• If the temperature of a cylinder is doubled, the volume of the gas inside the cylinder doubles.

• Practical Example (Density and Convection):

  • Heated air expands (per Charles's law), which decreases its density.

  • As hot air rises, cooler air moves in to take its place. Cooler air has a higher density because the same number of air molecules occupies a smaller volume.

Gay–Lussac’s Law: Relationship Between Pressure and Temperature

• Definition: For a fixed amount of gas at constant volume, the pressure of a gas is proportional to its Kelvin temperature.

• If the temperature increases, the pressure increases as well.

• Mechanism: Increasing the temperature increases the kinetic energy of the gas particles, which causes the pressure exerted by the particles to increase.

• The ratio of pressure to temperature is a constant ($k$):     $\frac{P}{T} = k$

• The relationship for initial and new conditions is expressed as:     $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

The Combined Gas Law

• The three individual gas laws (Boyle’s, Charles’s, and Gay-Lussac’s) can be unified into a single equation:     $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

• This equation is used to determine the effect of changing two factors (such as Pressure and Temperature) on the third factor (Volume).

Summary of Gas Laws (Table 6.1)

• Boyle's Law: $P_1V_1 = P_2V_2$ (As $P$ increases, $V$ decreases for constant $T$ and $n$).

• Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (As $T$ increases, $V$ increases for constant $P$ and $n$).

• Gay-Lussac's Law: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ (As $T$ increases, $P$ increases for constant $V$ and $n$).

• Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ (Shows the relationship of $P$, $V$, and $T$ when two quantities are changed).

Avogadro’s Law: Relationship Between Volume and Moles

• Definition: When pressure and temperature are held constant, the volume of a gas is proportional to the number of moles present.

• If the number of moles increases, the volume increases as well.

• The ratio of volume to number of moles is a constant ($k$):     $\frac{V}{n} = k$

• The relationship for initial and new conditions is expressed as:     $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

Standard Temperature and Pressure (STP)

• Gases are often compared at standard conditions of temperature and pressure.

• STP Conditions:

  • Standard Pressure = $1\,atm$ ($760\,mm\,Hg$).

  • Standard Temperature = $273\,K$ ($0^{\circ}C$).

• Standard Molar Volume: At STP, $1\,mole$ of any gas occupies a volume of $22.4\,L$.

• Properties of 1 mole of gas at STP:

  • $1\,mol\,N_2$ occupies $22.4\,L$, contains $6.02 \times 10^{23}\text{ particles}$, and weighs $28.02\,g$.

  • $1\,mol\,He$ occupies $22.4\,L$, contains $6.02 \times 10^{23}\text{ particles}$, and weighs $4.003\,g$.

The Ideal Gas Law

• All four properties of gases ($P$, $V$, $n$, and $T$) are combined into the Ideal Gas Law:     $PV = nRT$

• The Universal Gas Constant ($R$):

  • Using atmospheres: $R = 0.0821\,\frac{L \cdot atm}{mol \cdot K}$

  • Using millimeters of mercury: $R = 62.4\,\frac{L \cdot mm\,Hg}{mol \cdot K}$

Physiological Focus: The Lungs

• Humans possess two lungs containing a vast system of air passages for gas exchange between the atmosphere and the bloodstream.

• The lungs contain approximately $1,500\text{ miles}$ of airways.

• The total surface area of the airways is roughly the size of a tennis court.

Dalton’s Law and Partial Pressures

• Dalton’s Law: The total pressure ($P_{total}$) of a gas mixture is the sum of the partial pressures of its component gases.

• For a mixture of three gases (A, B, and C):     $P_{total} = P_A + P_B + P_C$

• Example Calculation (Exhaled Air):

  • $P_{N_2} = 563\,mm\,Hg$

  • $P_{O_2} = 118\,mm\,Hg$

  • $P_{CO_2} = 30.\,mm\,Hg$

  • $P_{H_2O} = 50.\,mm\,Hg$

  • $P_{total} = 563 + 118 + 30. + 50. = 761\,mm\,Hg$

Environmental Science and Gases

• The Ozone Layer:

  • Ozone ($O_3$) is formed in the upper atmosphere by the reaction of oxygen molecules ($O_2$) with oxygen atoms ($O$).

  • It acts as a shield protecting Earth by absorbing destructive ultraviolet radiation.

  • Chlorofluorocarbons (CFCs), formerly used as refrigerants and aerosol propellants, destroy ozone in the upper atmosphere.

• Carbon Dioxide and Global Warming:

  • $CO_2$ is categorized as a greenhouse gas because it absorbs thermal energy that radiates from the Earth's surface.

  • Increased levels of $CO_2$ contributes to global warming, which is the increase in the average temperature of the Earth's atmosphere.