Boyle's Law relates pressure and volume inversely when temperature is constant. This fundamental concept in gas behavior underpins many practical applications in chemistry and physics.

Charles' Law shows that at constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin. This relationship is essential for understanding thermal expansion in gases.

Standard temperature is defined as 273 K (0°C) and is commonly used in gas law calculations at STP. Knowledge of these standard conditions is crucial in achieving consistent and accurate results.

At standard temperature and pressure, one mole of an ideal gas occupies 22.4 liters. This molar volume is a key constant used in various stoichiometric and analytical calculations involving gases.

The pressure of a gas is the result of collisions between gas particles and the walls of its container. These impacts transfer momentum and generate force per unit area, which is observed as pressure.

The Ideal Gas Law is expressed as PV = nRT, linking pressure, volume, number of moles, and temperature with the gas constant R. This equation is central to solving many gas-related problems.

According to Boyle's Law, pressure and volume are inversely proportional at a constant temperature. Thus, a reduction in volume results in an increase in pressure.

Raising the temperature of a gas increases the average kinetic energy of its particles, since temperature is directly related to molecular motion. This results in faster-moving molecules.

Adding more particles to a fixed volume increases the frequency of collisions with the container walls, thereby raising the pressure. This concept is rooted in the kinetic molecular theory of gases.

Gases tend to behave ideally when the effects of intermolecular forces and molecular volumes are minimized, which is typically achieved at low pressure and high temperature. These conditions allow the gas molecules to move independently.

Dalton's Law outlines that the total pressure of a gas mixture is the sum of the pressures each gas would exert if it occupied the entire volume alone. This principle is vital when working with mixtures of gases.

Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. This means lighter gases will diffuse faster than heavier gases under similar conditions.

The Ideal Gas Law assumes that gas particles have negligible volume and do not attract each other. These simplifications can lead to inaccuracies when dealing with real gases, especially under high-pressure or low-temperature conditions.

Avogadro's Law states that at the same temperature and pressure, equal volumes of gases contain an equal number of moles. This concept is fundamental for calculations involving gas volumes and moles.

Boyle's Law focuses on the relationship between pressure and volume when temperature is held constant. Maintaining a constant temperature ensures the inverse proportionality between these two variables.

Using the Ideal Gas Law V = nRT/P, calculate V = (1 × 0.0821 × 300) / 2.0 ≈ 12.315 L, which rounds to 12.3 L. This problem reinforces the application of the Ideal Gas Law in quantitative reasoning.

The mole fraction is calculated by dividing the partial pressure of oxygen by the total pressure. Here, 150 torr / 760 torr ≈ 0.20, meaning oxygen makes up about 20% of the gas mixture.

Applying the combined gas law, (P1V1/T1) = (P2V2/T2) leads to P2 = 1.00 atm × (2.00 L/1.00 L) × (546 K/273 K) = 4 atm. This problem demonstrates how simultaneous changes in volume and temperature influence pressure.

Graham's Law indicates that the rate of diffusion is inversely proportional to the square root of the molar mass. Thus, rA/rB = √(32/4) = √8, which is approximately 2.83, meaning Gas A diffuses nearly 2.83 times faster than Gas B.

The Van der Waals equation modifies the Ideal Gas Law by incorporating correction factors to account for intermolecular forces and the finite size of gas molecules. These adjustments help predict real gas behavior under non-ideal conditions.