Gases: Properties, Laws, and Calculations – Study Notes for General Biology

Properties and Behavior of Gases

Introduction to Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container. Understanding the properties and behavior of gases is essential in biology, chemistry, and environmental science.

• Gases exert pressure on the walls of their container due to the constant motion of their molecules.

• Pressure (P) is defined as force per unit area: Pressure = Force / Area.

• The Earth's atmosphere exerts pressure on its surface, known as atmospheric pressure.

Measuring Atmospheric Pressure

Barometer

Atmospheric pressure is commonly measured using a barometer, an instrument invented by Torricelli in 1643.

• Standard atmospheric pressure is defined as the pressure that supports a column of mercury (Hg) 760 mm high at 0°C at sea level.

• Units of pressure include: mm Hg (torr), atm (atmosphere), and Pascal (Pa).

Gas Laws

Standard Temperature and Pressure (STP)

• STP is defined as 0°C (273.15 K) and 1 atm pressure.

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

Boyle's Law

Describes the relationship between pressure and volume at constant temperature.

• Formula: $P_1V_1 = P_2V_2$

• As pressure increases, volume decreases (inverse relationship).

• Example: Compressing a gas in a syringe decreases its volume.

Charles's Law

Describes the relationship between volume and temperature at constant pressure.

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

• As temperature increases, volume increases (direct relationship).

• Example: A balloon expands when heated.

Combined Gas Law

Combines Boyle's and Charles's laws to relate pressure, volume, and temperature.

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

• Used when the amount of gas is constant but conditions change.

Ideal Gas Law

Relates pressure, volume, temperature, and amount of gas (in moles).

• Formula: $PV = nRT$

• P = pressure (atm), V = volume (L), n = moles, R = gas constant (0.08206 L·atm/mol·K), T = temperature (K).

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

Gas Density and Molar Mass

• If the density (d) of a gas is known, the molar mass (M) can be calculated from the ideal gas law:

$d = \frac{MP}{RT}$

• Gas densities depend on temperature and pressure.

Gas Stoichiometry

Gas stoichiometry involves using the ideal gas law to relate the volumes of gases involved in chemical reactions.

• Balanced chemical equations are used to relate mole ratios.

• Example: Calculating the volume of hydrogen gas produced from the reaction of aluminum with hydrochloric acid.

Dalton's Law of Partial Pressures

In a mixture of gases, each gas exerts its own pressure, called partial pressure. The total pressure is the sum of the partial pressures.

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

• Each gas behaves independently in a mixture.

Collecting Gases Over Water

• When collecting gases over water, the total pressure is the sum of the gas pressure and the vapor pressure of water.

• Formula: $P_{\text{total}} = P_{\text{gas}} + P_{\text{H}_2O}$

• Vapor pressure increases with temperature.

Mole Fraction

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

• Formula: $\chi_A = \frac{n_A}{n_{\text{total}}}$

• The sum of all mole fractions in a mixture is 1.

• Mole fraction can also be defined as the ratio of the partial pressure of a component to the total pressure.

• Formula: $\chi_A = \frac{P_A}{P_{\text{total}}}$

Graham's Law of Effusion

Effusion is the process by which gas particles pass through a tiny opening. Graham's law states that the rate of effusion is inversely proportional to the square root of the molar mass.

• Formula: $\text{Rate of effusion} \propto \frac{1}{\sqrt{M}}$

• Lighter gases effuse and diffuse faster than heavier gases.

• The rates of effusion of two gases (1 and 2) are related by:

$\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}}$

Diffusion

Diffusion is the spreading of a gas throughout a space or another gas. The rate of diffusion is also inversely proportional to the square root of the molar mass.

• Lighter gases diffuse faster than heavier gases.

• The rate of diffusion is slower than the rate of effusion for a gas.

Summary Table: Gas Laws and Relationships

Law	Relationship	Formula	Constant
Boyle's Law	P ∝ 1/V	$P_1V_1 = P_2V_2$	T, n
Charles's Law	V ∝ T	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	P, n
Combined Gas Law	Relates P, V, T	$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$	n
Ideal Gas Law	Relates P, V, n, T	$PV = nRT$	R
Dalton's Law	Total pressure = sum of partial pressures	$P_{\text{total}} = \sum P_i$	—

Applications and Examples

• Calculating the mass, volume, or pressure of a gas sample under various conditions using the gas laws.

• Determining the molar mass of an unknown gas from density or other measurements.

• Solving stoichiometry problems involving gases produced or consumed in chemical reactions.

• Calculating partial pressures and mole fractions in gas mixtures.

• Predicting the rates of effusion and diffusion for different gases.

Additional info: These notes are based on lecture slides and textbook content relevant to General Biology and introductory Chemistry, focusing on the physical properties and mathematical relationships governing gases.