Chapter 11: Gases – Properties and Laws (Mini-Textbook Study Notes)

Chapter 11: Gases

11.1 Properties of Gases

This section introduces the fundamental properties and behaviors of gases, as well as the kinetic molecular theory and units of measurement used for gases.

• Gases in Our Environment: Common gases at room temperature include H2, N2, O2, F2, Cl2, noble gases, nonmetal oxides (CO, CO2, NO, NO2, SO2, SO3), and low-molecular-weight hydrocarbons (methane, ethane, propane, butane).

• Gas Behavior:

  • Gas particles are much farther apart than those in liquids or solids.

  • Gases have no definite shape or volume and fill any container completely.

  • Gases are less dense and more compressible than solids or liquids.

Gases: Kinetic Molecular Theory

The kinetic molecular theory explains the behavior of gases based on the motion and energy of their particles.

• Gases consist of small particles (atoms or molecules) moving randomly at high velocities.

• Attractive forces between gas particles are very small.

• The actual volume occupied by gas molecules is very small compared to the total volume of the gas.

• Gas particles are in constant, rapid, straight-line motion.

• The average kinetic energy of gas molecules is proportional to the Kelvin temperature.

Pressure (P)

Pressure is the force exerted by gas particles when they collide with the walls of their container. Heating a gas increases the speed and frequency of collisions, raising the pressure.

• Definition: Pressure is defined as force per unit area.

$P = \frac{\text{force}}{\text{area}}$

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the column of air from the top of the atmosphere to the Earth's surface. At sea level, it is about 1 atmosphere (atm).

• Measured using a barometer (typically with mercury).

Volume (V)

The volume of a gas equals the size of its container. In a flexible container, adding more particles increases volume, while lowering temperature decreases volume due to reduced kinetic energy.

Temperature (T)

Temperature is related to the kinetic energy of gas particles and is measured in kelvins (K). Increasing temperature increases particle energy and, in a rigid container, increases pressure.

Amount of Gas (n)

The amount of gas is measured in moles (n). Adding gas increases pressure in a fixed volume. Mass is often measured in grams and converted to moles for calculations.

Properties That Describe a Gas

The main properties used to describe a gas are pressure, volume, temperature, and amount.

Property	Description	Units of Measurement
Pressure (P)	Force exerted by a gas against the walls of the container	atmosphere (atm), millimeter of mercury (mmHg), torr, pascal (Pa)
Volume (V)	Space occupied by a gas	liter (L), milliliter (mL)
Temperature (T)	Determines kinetic energy and rate of motion of gas particles	degree Celsius (°C), kelvin (K)
Amount (n)	Quantity of gas present	gram (g), mole (n)

Measuring Gas Pressure: Units

• 1 atm = 760 mmHg = 760 torr (exact)

• 1 mmHg = 1 torr (exact)

• SI unit: pascal (Pa); 1 atm = $1.01325 \times 10^5$ Pa = 101.325 kPa

Unit	Abbreviation	Unit Equivalent to 1 atm
atmosphere	atm	1 atm (exact)
millimeters of Hg	mmHg	760 mmHg (exact)
torr	Torr	760 Torr (exact)
inches of Hg	inHg	29.9 inHg
pounds per square inch	lb/in2 (psi)	14.7 lb/in2
pascal	Pa	101,325 Pa
kilopascal	kPa	101.325 kPa

Altitude and Atmospheric Pressure

Atmospheric pressure decreases as altitude increases. This is because there is less air above the surface at higher elevations.

Location	Altitude (km)	Atmospheric Pressure (mmHg)
Dead Sea	-0.40	800
Sea level	0.00	760
Los Angeles	0.09	752
Las Vegas	0.70	700
Denver	1.60	630
Mount Whitney	4.50	440
Mount Everest	8.90	253

11.2 Pressure and Volume (Boyle's Law)

Boyle's Law describes the inverse relationship between the pressure and volume of a gas when temperature and amount of gas are constant.

• Statement: The pressure (P) of a gas is inversely related to its volume (V) when T and n are constant.

• If pressure increases, volume decreases, and vice versa.

$P_1 V_1 = P_2 V_2$

• Indirect Relationship: As one variable increases, the other decreases.

Steps for Boyle's Law Calculations

1. State the given and needed quantities.

2. Rearrange the equation to solve for the unknown.

3. Substitute values and calculate.

Example:

If a 12-L tank of oxygen at 3800 mmHg is released to a final pressure of 570 mmHg, the final volume is:

$V_2 = V_1 \times \frac{P_1}{P_2} = 12\,L \times \frac{3800\,mmHg}{570\,mmHg} = 80\,L$

Chemistry Link to Health

• Inhalation: Lungs expand, pressure decreases, air flows in.

• Exhalation: Lungs contract, pressure increases, air flows out.

11.3 Temperature and Volume (Charles's Law)

Charles's Law describes the direct relationship between the temperature and volume of a gas when pressure and amount of gas are constant.

• Statement: The temperature (K) of a gas is directly related to its volume (V) when P and n are constant.

• If temperature increases, volume increases.

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Direct Relationship: Both variables increase or decrease together.

• All temperatures must be in Kelvin for calculations.

Example:

If a gas at 5.40 L and 15°C (288 K) is heated to 42°C (315 K), the final volume is:

$V_2 = V_1 \times \frac{T_2}{T_1} = 5.40\,L \times \frac{315\,K}{288\,K} = 5.91\,L$

Learning Check:

• Temperature decreases when volume decreases.

• When temperature decreases, volume decreases.

• Temperature decreases when volume changes from 12 L to 4 L.

• Volume increases when temperature changes from 15°C to 45°C.