General Chemistry: Chapter 6 – Gases (Study Notes)

Gases and Their Properties

Introduction to Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container. The study of gases involves understanding their physical properties, behavior under various conditions, and the laws that govern these behaviors.

• Key Properties: Pressure, volume, temperature, and amount (in moles).

• Applications: Atmospheric phenomena, respiration, industrial processes, and more.

Gas Pressure

Definition and Origin of Pressure

Pressure is defined as the force exerted per unit area by gas molecules as they collide with the surfaces around them.

• Formula: $P = \frac{\text{force}}{\text{area}}$

• Gas molecules are in constant motion, and their collisions with container walls create pressure.

• Example: Just as a ball exerts a force when it bounces against a wall, a gas particle exerts a force when it collides with a surface.

Atmospheric Pressure and Its Effects

Atmospheric pressure is the pressure exerted by the weight of air in Earth's atmosphere. It varies with altitude and weather conditions.

• High-pressure regions are usually associated with clear weather; low-pressure regions with unstable weather.

• Pressure decreases with increasing altitude due to fewer gas particles in a given volume.

Pressure and Particle Density

The pressure exerted by a gas depends on the number of particles in a given volume.

• Higher density of gas particles results in higher pressure.

• Lower density results in lower pressure.

Pressure Imbalance in the Ear

A difference in pressure across the eardrum membrane can cause pain as the membrane is pushed in or out.

Measuring Gas Pressure

The Barometer

A barometer is an instrument used to measure atmospheric pressure. It consists of an evacuated glass tube submerged in mercury.

• Atmospheric pressure pushes mercury upward into the tube.

• Standard atmospheric pressure supports a column of mercury about 760 mm high.

Common Pressure Units

Unit	Symbol	Average Air Pressure at Sea Level
Pascals	Pa	101325 Pa
Atmospheres	atm	1 atm
Millimeters of mercury	mmHg	760 mmHg
Torr	torr	760 torr
Pounds per square inch	psi	14.7 psi
Inches of mercury	inHg	29.92 inHg

The Manometer

A manometer measures the pressure of a gas trapped in a container. It is a U-shaped tube partially filled with liquid, connected to the gas sample on one side and open to the air on the other.

• The difference in liquid levels indicates the pressure difference between the gas and the atmosphere.

Blood Pressure

Blood pressure is the force within arteries that drives circulation. It is measured using a sphygmomanometer.

Condition	Systolic (mmHg)	Diastolic (mmHg)
Hypotension	<100	<60
Normal	100-119	60-79
Prehypertension	120-139	80-89
Hypertension Stage 1	140-159	90-99
Hypertension Stage 2	>160	>100

Simple Gas Laws

Boyle’s Law: Pressure and Volume

Boyle’s Law states that the pressure of a gas is inversely proportional to its volume at constant temperature and amount.

• Equation: $P_1 V_1 = P_2 V_2$

• As pressure increases, volume decreases by the same factor.

• Graph of P vs V is a curve; P vs 1/V is a straight line.

• Example: Diving – For every 10 m of depth, pressure increases by 1 atm. If a diver ascends quickly, the volume of air in the lungs expands, potentially causing injury.

Charles’s Law: Volume and Temperature

Charles’s Law states that the volume of a fixed amount of gas at constant pressure increases linearly with increasing temperature (in kelvins).

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

• Temperature must be in kelvins: $T(K) = T(°C) + 273$

• At absolute zero (0 K or -273.15°C), the volume extrapolates to zero.

• Example: A balloon expands when moved from ice water to boiling water due to increased kinetic energy of gas particles.

Avogadro’s Law: Volume and Amount

Avogadro’s Law states that the volume of a gas is directly proportional to the number of moles of gas at constant temperature and pressure.

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

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

Ideal Gas Law

The relationships described by Boyle’s, Charles’s, and Avogadro’s laws can be combined into the Ideal Gas Law.

• Equation: $PV = nRT$

• R is the gas constant (0.08206 L·atm/mol·K or 8.314 J/mol·K).

• Allows calculation of any one variable if the other three are known.

Standard Conditions and Molar Volume

Standard Temperature and Pressure (STP) is defined as 0°C (273 K) and 1 atm. The molar volume of a gas at STP is 22.4 L per mole.

• At STP, 1 mole of any ideal gas occupies 22.4 L.

• The identity of the gas does not affect the volume at STP.

Density of Gases

Density is the ratio of mass to volume, typically expressed in g/L for gases.

• Equation: $\text{Density} = \frac{\text{molar mass}}{\text{molar volume}}$

• At STP, density is directly proportional to molar mass.

• Example: Helium (4 g/mol) has a lower density than nitrogen (28 g/mol) at STP, so helium balloons float.

Mixtures of Gases and Partial Pressures

Mixtures of Gases

Many gas samples are mixtures, such as air, which contains nitrogen, oxygen, argon, carbon dioxide, and trace gases.

• Mixtures can be treated as a single gas for calculations of total pressure, volume, and temperature.

Partial Pressure and Dalton’s Law

The pressure due to any individual component in a gas mixture is its partial pressure.

• Equation: $P_i = \frac{n_i RT}{V}$

• The total pressure is the sum of the partial pressures: $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

• Dalton’s Law: Gases behave independently; total pressure is the sum of partial pressures.

Mole Fraction

The mole fraction is the ratio of the number of moles of a component to the total number of moles in the mixture.

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

• Partial pressure of a component: $P_i = \text{mole fraction} \times P_{\text{total}}$

• For example, nitrogen is 78% of air; its partial pressure is $0.78 \times 1.00$ atm = 0.78 atm.

Collecting Gases Over Water

When gases are collected by displacement of water, the collected gas contains water vapor. The partial pressure of water vapor depends only on temperature and can be found in tables.

• Equation: $P_{\text{total}} = P_{\text{dry gas}} + P_{\text{water vapor}}$

Gases in Chemical Reactions

Stoichiometry with Gases

In reactions involving gases, quantities are often specified in terms of volume at a given temperature and pressure. The ideal gas law is used to relate moles and volume.

• Equation: $n = \frac{PV}{RT}$

• At STP, use 1 mol = 22.4 L for conversions.

• Example: Calculating grams of water formed from a given volume of hydrogen gas at STP.

Kinetic Molecular Theory

Basic Postulates

The kinetic molecular theory models a gas as a collection of particles in constant motion.

• The size of gas molecules is negligibly small compared to the distance between them.

• The average kinetic energy of a particle is proportional to the temperature in kelvins.

• Collisions between particles and with container walls are completely elastic (no energy loss).

Nature of Pressure

Pressure results from gas particles colliding with the walls of the container.

• Equation: $P = \frac{F}{A}$

Explaining Gas Laws with Kinetic Theory

• Boyle’s Law: Decreasing volume increases collision frequency, raising pressure.

• Charles’s Law: Increasing temperature increases particle speed and kinetic energy, requiring a larger volume to maintain constant pressure.

• Avogadro’s Law: Increasing the number of particles increases collisions; volume must increase to keep pressure constant.

• Dalton’s Law: Particles of different gases behave independently; total pressure is the sum of partial pressures.

Molecular Velocities and Temperature

Average Kinetic Energy and Velocity

The average kinetic energy of gas molecules depends on their mass and velocity.

• Equation: $KE_{\text{avg}} = \frac{1}{2} N_A m u^2$

• At the same temperature, lighter particles have higher average velocities than heavier ones.

• Root Mean Square Velocity: $u_{\text{rms}} = \sqrt{\frac{3RT}{M}}$

Mean Free Path

The average distance a molecule travels between collisions is called the mean free path. It decreases as pressure increases.

Diffusion and Effusion

Definitions

• Diffusion: The process of molecules spreading from high to low concentration.

• Effusion: The process by which molecules escape through a small hole into a vacuum.

The rates of diffusion and effusion are inversely proportional to the square root of the molar mass.

• Graham’s Law of Effusion: $\frac{\text{rate}_1}{\text{rate}_2} = \sqrt{\frac{M_2}{M_1}}$

Real Gases and Deviations from Ideal Behavior

Limitations of the Ideal Gas Law

At high pressures and low temperatures, real gases deviate from ideal behavior due to molecular volume and intermolecular attractions.

• Real gas molecules occupy space and experience attractions.

Van der Waals Equation

Johannes van der Waals modified the ideal gas equation to account for molecular volume and intermolecular forces.

• Equation: $\left[P + a \left(\frac{n}{V}\right)^2 \right] \left[V - nb \right] = nRT$

• a corrects for intermolecular attractions; b corrects for particle volume.

Behavior of Real Gases

• At low pressures, intermolecular attractions are most significant (PV/RT lower than ideal).

• At high pressures, molecular volume is most significant (PV/RT higher than ideal).

Additional info: Some conceptual questions and diagrams were referenced in the original material. For full mastery, students should practice applying these laws to real-world and exam problems.