Section 5 – Gases

Introduction to Gases

Gases are a fundamental state of matter, though relatively few substances exist as gases under typical conditions. Their properties and behavior are crucial in chemistry and everyday life, especially in the Earth's atmosphere.

• Atmosphere: The layer of gases surrounding Earth, essential for supporting life and protecting from harmful radiation.

• Pressure: All gases exert pressure on their surroundings due to the force exerted by gas molecules as they strike surfaces.

• Atmospheric Pressure: The pressure exerted by the mixture of gases in the atmosphere (mainly N2, O2, Ar, CO2, Ne, HCl, etc.).

• Barometer: A device invented by Evangelista Torricelli to measure atmospheric pressure.

Standard atmospheric pressure: 760 mmHg

Factors Affecting Atmospheric Pressure

• Altitude: Atmospheric pressure decreases as altitude increases because there is less air above.

• Weather (Humidity): More water vapor molecules in the air (higher humidity) result in lower atmospheric pressure, as water vapor is less dense than dry air.

Units of Pressure

Pressure can be measured in several units, and conversion between them is often necessary in chemical calculations.

• Common units: atm (atmosphere), mmHg (millimeters of mercury), torr, Pa (pascal), psi (pounds per square inch).

Conversion between units is essential for solving gas law problems.

Gas Laws Leading to the Ideal Gas Law

Several empirical gas laws describe the relationships between pressure, volume, temperature, and amount of gas. These laws are combined to form the Ideal Gas Law.

Boyle's Law

Describes the inverse relationship between pressure and volume at constant temperature.

• Formula: (at constant T)

• Application: If the volume of a gas decreases, its pressure increases, and vice versa.

• Example: Compressing a balloon decreases its volume and increases its pressure.

Charles's Law

Describes the direct relationship between volume and temperature at constant pressure.

• Formula: (T in Kelvin, at constant P)

• Application: Heating a balloon increases its volume.

• Example: A gas at 15°C and 1 atm has a volume of 2.58 L. When heated to 38°C, its volume increases to 2.79 L.

Avogadro's Law

Relates the volume of a gas to the number of moles at constant temperature and pressure.

• Formula: (at constant T, P)

• Application: Adding more moles of gas increases the volume.

• Example: 12.2 L of O2 gas contains 0.50 mol. If the amount is increased to 0.80 mol, the volume increases to 8.1 L.

The Combined Gas Law and the Ideal Gas Law

By combining Boyle's, Charles's, and Avogadro's laws, we obtain the Combined Gas Law and the Ideal Gas Law, which relate all four variables: pressure, volume, temperature, and moles.

• Combined Gas Law:

• Ideal Gas Law:

• R (Universal Gas Constant):

These laws allow calculation of any one variable if the others are known.

Example Calculations

• Finding moles of hydrogen gas: Given volume, temperature, and pressure, use .

• Finding volume of nitrogen gas: Given moles, pressure, and temperature, use .

• Combined Gas Law application: Used when conditions change (e.g., pressure and temperature both change), to find new volume or pressure.

Standard Temperature and Pressure (STP)

STP is a reference condition for gases: 0°C (273 K) and 1 atm pressure. At STP, 1 mole of an ideal gas occupies 22.4 L.

Summary Table: Key Gas Laws

Additional info:

• All temperatures in gas law calculations must be in Kelvin.

• Gas law problems often require conversion between units (e.g., Celsius to Kelvin, mmHg to atm).

• Real gases deviate from ideal behavior at high pressures and low temperatures, but the Ideal Gas Law is a good approximation under most conditions.