Gases

Overview

This chapter covers the fundamental properties and behavior of gases, including the gas laws, the ideal gas equation, reactions involving gases, gas mixtures, kinetic molecular theory, and deviations from ideal behavior. Understanding these concepts is essential for predicting and explaining the physical and chemical properties of gases in various contexts.

10.1 Properties of Gases

Characteristics of Gases

• Shape and Volume: A gas assumes both the shape and volume of its container, unlike solids and liquids.

• Compressibility: Gases are highly compressible due to the large distances between particles.

• Particle Size: The sizes of gas particles are much smaller than those of liquids or solids.

• Density: Gas densities are typically expressed in g/L, while liquids and solids use g/mL or g/cm3.

• Mixtures: Gases form homogeneous mixtures (solutions) with one another easily.

Gas Pressure: Definition and Units

• Pressure is defined as the force applied per unit area:

• The SI unit of force is the newton (N):

• The SI unit of pressure is the pascal (Pa):

Units of Pressure Commonly Used in Chemistry

• Conversions: 1 atm = 760 Torr = 760 mm Hg = 14.7 psi

Calculation of Pressure

• Pressure exerted by a column of fluid is given by:

• h: height of the column (m)

• d: density of the fluid (kg/m3)

• g: gravitational constant ()

Measurement of Pressure

• Barometer: Instrument used to measure atmospheric pressure.

• Manometer: Device used to measure pressures other than atmospheric pressure.

• Atmospheric pressure is originally defined as the pressure that supports a column of mercury exactly 760 mm high at 0°C at sea level.

10.2 The Gas Laws

Boyle’s Law: Pressure-Volume Relationship

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

• Equation: (at constant temperature)

• For two states:

• Example: If a diver takes a breath at the surface (1.00 atm, 5.82 L) and dives to a depth where the pressure is 1.92 atm, the volume of air in his lungs is

Charles’s Law: Temperature-Volume Relationship

Charles’s Law states that the volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.

• Equation: (temperatures in kelvins)

• Example: A gas originally at 14.6 L and 25.0°C (298.15 K) is heated to 50.0°C (323.15 K):

Avogadro’s Law: Amount-Volume Relationship

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

• Equation:

• Example: 3.0 L of NO reacts with 1.5 L of O2 to produce 3.0 L of NO2 (assuming all reactants are consumed and conditions are constant).

Combined Gas Law

The combined gas law relates pressure, volume, and temperature for a fixed amount of gas.

• Equation:

10.3 The Ideal Gas Equation

Derivation and Applications

The ideal gas equation combines Boyle’s, Charles’s, and Avogadro’s laws to describe the behavior of gases.

• Equation:

• P: pressure (atm, Pa, etc.)

• V: volume (L, m3, etc.)

• n: number of moles

• R: gas constant (varies by units)

• T: temperature (K)

• Standard Temperature and Pressure (STP): 0°C (273.15 K) and 1 atm. At STP, 1 mole of an ideal gas occupies 22.4 L.

• Example: Calculate the volume of 1 mole of gas at room temperature (25°C, 298.15 K) and 1 atm:

Density of a Gas

• Density () can be calculated using the ideal gas law:

• P: pressure

• M: molar mass

• R: gas constant

• T: temperature

• Example: CO2 at 25°C and 1 atm has a density of

10.4 Reactions with Gaseous Reactants and Products

Stoichiometry Involving Gases

• Volumes of gases in reactions can be related using balanced equations and the ideal gas law.

• Example: For the reaction , 65.8 mL CO reacts with 32.9 mL O2 to produce 65.8 mL CO2 (at constant T and P).

Calculating Required Volume or Amount

• Use stoichiometry and the ideal gas law to determine the volume or moles of reactants/products.

• Example: 1 kg Na2O2 reacts with CO2 to produce O2. Calculate moles and volume using molar mass and .

10.5 Gas Mixtures

Dalton’s Law of Partial Pressures

• The total pressure exerted by a mixture of gases is the sum of the partial pressures of each component:

• Each partial pressure is calculated using

Mole Fractions

• The mole fraction () of a component is the ratio of its moles to the total moles in the mixture:

• The partial pressure of a component is

Vapor Pressure of Water

• Example: If 525 mL H2 is collected over water at 25°C and 0.967 atm, subtract vapor pressure of water (0.0313 atm) to find the pressure of H2 and calculate mass using .

10.6 The Kinetic Molecular Theory of Gases

Assumptions and Applications

• Gases consist of particles separated by large distances.

• Particles are in constant, random motion and collide elastically.

• No attractive or repulsive forces between particles.

• Average kinetic energy is proportional to temperature:

• Explains compressibility, pressure, and temperature relationships.

Molecular Speed

• Root-mean-square (rms) speed ():

• Example: Helium atoms move 3.316 times faster than CO2 molecules at the same temperature.

Diffusion and Effusion

• Diffusion: Mixing of gases due to random motion.

• Effusion: Escape of gas through a small hole.

• Graham’s Law: Rate of effusion is inversely proportional to the square root of molar mass:

10.7 Deviation from Ideal Behavior

Factors Causing Deviation

• At high pressures, gas molecules are close together; volume of molecules becomes significant.

• At low temperatures, intermolecular forces become significant.

The van der Waals Equation

• Accounts for non-ideal behavior by correcting for molecular volume and intermolecular forces:

• a: corrects for intermolecular attractions

• b: corrects for molecular volume

• Compressibility Factor (Z): Measures deviation from ideal behavior:

• For an ideal gas, at all pressures and temperatures.

Additional info: These notes are based on textbook slides for General Chemistry, Chapter 10 (Gases), and are suitable for college-level exam preparation.