Gas Laws and Properties Quiz

Gases and the Kinetic Molecular Theory

• Gases, unlike liquids and solids, have volumes that change significantly with pressure and temperature.
• Gas volume expands when heated and shrinks when cooled; this change is much greater than that of liquids and solids.
• Gases flow freely and have relatively low densities; gas density increases when cooled.
• Gases form solutions in any proportions and are freely miscible with each other.

Application of the Gas Laws: Breathing

• For air to move in and out of the lungs, the pressure inside the lungs must change, forcing the lungs to change volume.
• Inhalation involves expanding the lungs; decreasing pressure in the lungs causes air to flow in.
• Exhalation involves shrinking the lungs; increasing pressure in the lungs forces air out.

11: Gases and the Kinetic Molecular Theory

• Sections 11.1-11.6 discuss various aspects of gases and their behavior, from physical states to real-gas deviations.

The Three States of Matter

• Gases: particles are far apart, move freely, filling the available volume.
• Liquids: particles are close together but can move around each other.
• Solids: particles are close together in a fixed, regular arrangement and do not move around freely.

An Overview of the Physical States of Matter

• Gas volume changes significantly with pressure.
• Solid and liquid volumes are not greatly affected by pressure.
• Gases expand when heated and shrink when cooled.
• Volume change for gases is significantly greater than for liquids and solids (50-100 times).
• Gases flow easily and have low densities.
• Gas density increases as the gas cools.
• Gases mix in any proportions.
• Gases are miscible with each other.

Gas Pressure

• Atmospheric pressure arises from the force exerted by atmospheric gases on Earth's surface.
• Atmospheric pressure decreases with altitude.
• Pressure is defined as force over area.

A Mercury Barometer

• A barometer measures atmospheric pressure.
• At sea level, the column of Hg exerts the same pressure on the Hg surface as the atmosphere does.
• Atmospheric pressure is often measured in units of mmHg, torr, atm, Pa, kPa, etc.

Common Units of Pressure

• Common units for pressure include pascals (Pa), kilopascals (kPa), atmospheres (atm), millimeters of mercury (mmHg), torr, and pounds per square inch (psi).

The Gas Laws

• Gas laws describe the physical behavior of gases through pressure (P), temperature (T), volume (V), and amount (n).
• Three gas laws look at the effect of one variable on another while keeping the other two constant.
• Ideal gases exhibit linear relationships among variables.

Boyle's Law

• At constant temperature, the volume of a fixed amount of gas is inversely proportional to the external pressure.
• Pressure and volume are inversely proportional (PV = constant).

Charles's Law

• At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature.
• Volume and temperature are directly proportional (V/T = constant).

Avogadro's Law

• At constant temperature and pressure, equal volumes of any ideal gas contain equal numbers of particles (moles).
• Volume and amount are directly proportional (V/n = constant).

Gas Behavior at Standard Conditions

• Standard Temperature and Pressure (STP) is defined as 0 °C and 1 atm (760 torr).
• The standard molar volume of an ideal gas at STP is 22.4 L/mol.

Gay-Lussac's Law

• At constant volume, the pressure of a fixed amount of gas is directly proportional to its absolute temperature.

The Ideal Gas Law

• The ideal gas law (PV = nRT) relates pressure (P), volume (V), amount (n), and temperature (T) of an ideal gas.
• The gas constant (R) depends on the units used.
• For one mole of a gas at STP, R = 0.0821 L·atm/mol·K or 8.314 J/mol·K.

Individual Gas Laws as Special Cases

• Boyle's, Charles', and Avogadro's Laws are special cases of the ideal gas law.

Application of the Gas Laws: Breathing

• Boyle's law explains breathing mechanics.
• Changing lung volume changes pressure, causing air to flow in or out.

Sample Problem 1

• Provides an example of applying the ideal gas law principles to calculate helium mass increase to create a blimp.

The Ideal Gas Law and Gas Density

• Gas density (d) is related to molar mass (M), pressure (P), and temperature (T) by the ideal gas law.

The Ideal Gas Law and Molar Mass

• The ideal gas law can be used to calculate molar mass.

Mixtures of Gases

• Gases mix homogeneously in any proportion.
• Dalton's law of partial pressures states that the total pressure in a mixture is the sum of the partial pressures of the component gases.

Air Composition

• Percentage composition of dry air by volume is approximately 21% O2, 78% N2, and 1% Ar.
• Calculating the average molar mass of dry air.

The Ideal Gas Law and Stoichiometry

• The ideal gas law combines to relate gas amounts in chemical reactions.

Sample Problem 2

• An example of using gas laws for stoichiometry problems

Kinetic-Molecular Theory

• Describes gas behavior from a microscopic standpoint.
• Five postulates cover the behavior of gas particles.
• Kinetic energy is the total energy of motion in a system of particles.

Molecular Speed

• Each gas particle has a molecular speed.
• The most probable speed of gas particles increases with temperature.
• The average kinetic energy (Ek) and temperature (T) are related (Ek = c × T).

Molar Mass and Molecular Speed

• The most probable molecular speed increases when molar mass decreases (lighter molecules are faster).
• Gases with low molar masses exhibit faster speeds because a lighter molecule needs less energy to reach a given velocity.

Molecular View of the Gas Laws

• A visualization of the kinetic molecular theory and gas laws, explaining how changes in volume (Boyle's), temperature (Charles',), amount (Avogadro's), or gas identity (Dalton's) affect a gas sample.

Kinetic Energy and Gas Behavior

• All gases at the same temperature share the same average kinetic energy.
• Kinetic energy of gas particles is proportional to the absolute temperature of the gas; the average speed of the particles differs according to their molar mass.
• Temperature measures average kinetic energy.

Graham's Law of Effusion

• Effusion is the escape of a gas through a small opening into a vacuum.
• Diffusion is the mixing of gases due to random motion.
• Rate of effusion is inversely proportional to the square root of its molar mass.

Real Gases: Deviations from Ideal Behavior

• Ideal gas models do not account for the volume of gas particles or their inter-particle attractive and repulsive forces.
• Real gas behavior deviates from ideal gas behavior most substantially at low temperatures and high pressures.

Molar Volume of Some Common Gases

• Molar volume data for several common gases at STP.
• Comparison reveals how different gases exhibit varying conditions under STP.

Deviations With Increasing External Pressure

• Deviations from ideal gas behavior are apparent when using PV/RT values; higher external pressures lead to an increase from ideal PV/RT.
• Effect of inter-particle attractions and particle volume leads to non-ideal gas behavior.

Effect of Interparticle Attractions

• At moderate pressures, interparticle attractions between gas particles lower the force of collisions with the container walls.
• Lowering the force decreases the gas pressure because PV/RT < 1.

Effect of Particle Volume

• At very high pressures, the free volume between gas particles is less than the container volume, so interparticle volume becomes significant resulting in PV/RT > 1.

Van der Waals Equation

• Corrects the ideal gas law to account for particle volume and interparticle attractions (using constants 'a' and 'b').

Van der Waals Constants

• Compilation of 'a' and 'b' constants for several common gases. These constants are used in the van der Waals equation.