Chapter 5: Gases – Properties, Laws, and Applications

Properties of Gases

General Characteristics

Gases are one of the three main states of matter, distinguished by their ability to expand and fill the entire volume of their container. Unlike solids and liquids, gases do not have definite shapes or volumes.

• Indefinite volume and shape: Gases expand to occupy the entire volume and assume the shape of their container.

• Compressibility: The volume occupied by a gas changes significantly with pressure.

• Temperature dependence: The volume of a gas changes with temperature.

• Miscibility: Gases are easily mixed unless they chemically react with one another.

• Low density: Gas densities are typically much lower than those of liquids or solids, often expressed in g/L.

Example: Air in a room expands to fill the entire space, regardless of the room's shape.

Characteristic Properties of Gases

Key Identifying Features

• Expands to fill its container

• Readily flows

• Is compressible

• Diffusion within it occurs rapidly

• Assumes both volume and shape of its container

Non-characteristic properties: Does not flow, is virtually incompressible, does not expand to fill its container, diffusion occurs extremely slowly.

Gas Pressure

Definition and Units

Gas pressure is defined as the ratio of force (F) to the surface area (A) over which the force is applied.

• Formula: $P = \frac{F}{A}$

• Force: $F = ma$ (mass × acceleration)

• Units: Pascal (Pa), bar, atmosphere (atm), torr, psi

Example: Atmospheric pressure is the force exerted by the weight of air above a unit area at Earth's surface.

Pressure Calculations

• Pressure increases as the area decreases for a given force.

• Pressure decreases as the area increases for a given force.

Example: A person wearing a pointed heel exerts more pressure on the floor than with a wide heel due to the smaller area.

Measuring Pressure

Barometers and Manometers

Pressure is measured using instruments such as barometers (for atmospheric pressure) and manometers (for gas samples in the lab).

• Barometer: Measures atmospheric pressure using a column of mercury.

• Manometer: Measures the pressure of a gas sample relative to atmospheric pressure.

Unit Conversion

Common pressure units and their standard values:

Pressure Measured in	Unit	Standard Pressure
bar	bar	1 bar
pascal	Pa	100,000 Pa
kilopascal	kPa	100 kPa
torr (mm Hg)	torr or mm Hg	750.01 torr
atmosphere	atm	1.01325 atm
pounds per square inch	psi	14.504 psi

Dimensional Analysis: Used to convert between units, e.g., mmHg to bar.

Example: $932.7\,\text{mbar} \times \frac{1\,\text{bar}}{1000\,\text{mbar}} \times \frac{100\,\text{kPa}}{1\,\text{bar}} = 93.27\,\text{kPa}$

Gas Laws

Fundamental Quantities

Four quantities are required to describe a gas:

• Amount of gas (n, in moles)

• Pressure (P, in bar)

• Volume (V, in L)

• Temperature (T, in K)

Gas laws describe the relationships between pairs of these properties.

Boyle's Law

Describes the relationship between pressure and volume at constant temperature and amount of gas.

• Formula: $V \propto \frac{1}{P}$ or $PV = \text{constant}$

• Equation for two states: $P_1V_1 = P_2V_2$

Example: Compressing a gas in a syringe decreases its volume as pressure increases.

Charles's Law

Describes the relationship between volume and temperature at constant pressure and amount of gas.

• Formula: $V \propto T$ (if T in Kelvin)

• Equation for two states: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Example: Heating a balloon causes it to expand as the gas molecules move faster.

Combined Gas Law

Combines Boyle's and Charles's laws to relate pressure, volume, and temperature for a fixed amount of gas.

• Formula: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

Example: Predicting the volume of a weather balloon as it rises and experiences changes in pressure and temperature.

Avogadro's Law

Relates the volume of a gas to the number of moles at constant pressure and temperature.

• Formula: $V \propto n$

• Equation for two states: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Example: Doubling the amount of gas in a container doubles its volume (at constant T and P).

Standard Temperature and Pressure (STP) and Molar Volume

Definition and Application

• STP: 273.15 K (0°C) and 1 bar

• Molar volume at STP: 22.7 L for 1 mole of gas

Example: 1 mole of any ideal gas occupies 22.7 L at STP.

Ideal Gas Law

General Equation

The ideal gas law combines Boyle's, Charles's, and Avogadro's laws into a single equation.

• Formula: $PV = nRT$

• R (gas constant): $0.08314\,\text{L·bar·mol}^{-1}\text{K}^{-1}$ or $8.314\,\text{L·kPa·mol}^{-1}\text{K}^{-1}$

Example: Calculating the volume, pressure, or temperature of a gas sample when the other variables are known.

Applications of the Ideal Gas Law

Molar Volume and Mass Calculations

• Calculate the volume of a given mass of gas at STP using molar volume.

• Determine the mass of a gas in a known volume at STP.

Example: What is the mass of argon gas in a 75.0 mL volume at STP?

Density and Molar Mass of Gases

Density Calculations

• At STP: $\text{density} = \frac{\text{molar mass}}{\text{molar volume}}$

• Any conditions: $d = \frac{PM}{RT}$

Example: Ranking gases by density under identical conditions.

Molar Mass Determination

• Using the ideal gas law: $M_m = \frac{mRT}{PV}$

• Using density: $M_m = \frac{dRT}{P}$

Example: Determining the molar mass of a gas from its mass, volume, pressure, and temperature.

Mixtures of Gases and Partial Pressures

Dalton's Law of Partial Pressures

In a mixture of gases, each gas exerts a pressure independently of the others.

• Formula: $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

• Mole fraction: $X_i = \frac{n_i}{n_{\text{total}}}$

• Partial pressure: $P_i = X_i P_{\text{total}}$

Example: Calculating the pressure of oxygen collected over water, accounting for water vapor pressure.

Kinetic Molecular Theory (KMT)

Assumptions and Implications

KMT provides a molecular-level explanation for the behavior of gases.

• Gases consist of tiny particles in constant, random motion.

• Collisions between particles and container walls are elastic.

• Average kinetic energy is proportional to temperature (in K).

Formula for average kinetic energy: $KE_{avg} = \frac{3}{2}RT$

Root mean square speed: $u_{rms} = \sqrt{\frac{3RT}{M}}$

Example: Explains why gases expand when heated (molecules move faster).

Real Gases and Deviations from Ideal Behavior

Non-Ideal Gas Behavior

Real gases deviate from ideal behavior at high pressures and low temperatures due to intermolecular forces and finite molecular volume.

• Van der Waals equation accounts for these deviations:

Formula: $(P + a\frac{n^2}{V^2})(V - nb) = nRT$

• a: corrects for intermolecular attractions

• b: corrects for finite volume of molecules

Example: Calculating the pressure of chlorine gas using van der Waals constants.

Summary Table: Common Gas Laws and Equations

Law	Relationship	Equation
Boyle's Law	P and V (T, n constant)	$P_1V_1 = P_2V_2$
Charles's Law	V and T (P, n constant)	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$
Avogadro's Law	V and n (P, T constant)	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$
Combined Gas Law	P, V, T (n constant)	$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$
Ideal Gas Law	P, V, n, T	$PV = nRT$
Dalton's Law	Partial pressures	$P_{\text{total}} = \sum P_i$
Van der Waals	Real gases	$(P + a\frac{n^2}{V^2})(V - nb) = nRT$

Additional info: These notes include all major concepts from Chapter 5 (Gases) relevant to a General Chemistry college course, including properties, measurement, laws, applications, and molecular theory. Practice problems and applications are integrated throughout to reinforce understanding.