Gases and Gas Laws

5.1 – Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air in the atmosphere on the Earth's surface. It is a fundamental concept in understanding the behavior of gases under typical conditions.

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

• Pressure: The force exerted by gas molecules as they strike the surfaces around them.

• Atmospheric Pressure: The pressure exerted by the mixture of gases (mainly N2, O2, Ar, CO2, Ne, He, CH4) in the atmosphere.

• Barometer: A device used to measure atmospheric pressure, invented by Evangelista Torricelli. It typically uses a column of mercury; at sea level, the standard atmospheric pressure supports a column of mercury 760 mm high.

Standard Pressure: 760 mmHg = 1 atm

• Factors Affecting Barometric Pressure: Changes in weather and altitude can alter atmospheric pressure.

5.2 – Units of Pressure

Pressure can be measured in several units, which are often used interchangeably in chemistry problems.

• Common Units: mm Hg (millimeters of mercury), torr, atm (atmospheres), Pa (pascals), psi (pounds per square inch)

• Conversion Factors:

• These conversion factors are frequently used to convert between pressure units in calculations.

Example: Convert 49 torr to other units:

• In atm:

• In mm Hg: 49 mm Hg (since 1 torr = 1 mm Hg)

• In Pa:

5.3 – Boyle’s Law

Boyle’s Law describes the relationship between the pressure and volume of a gas at constant temperature.

• Statement: For a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional.

• Mathematical Form:

• General Equation: (where k is a constant at constant T and n)

• Example: Squeezing a balloon decreases its volume, so as P increases, V decreases.

5.4 – Charles’ Law

Charles’ Law relates the volume and temperature of a gas at constant pressure.

• Statement: For a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature (in Kelvin).

• Mathematical Form:

• General Equation: (at constant P and n)

• Example: Heating a balloon causes it to expand as the gas volume increases with temperature.

Note: Always use temperature in Kelvin for gas law calculations.

5.5 – Avogadro’s Law

Avogadro’s Law connects the volume of a gas to the number of moles present, at constant temperature and pressure.

• Statement: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules (or moles).

• Mathematical Form:

• General Equation: (at constant T and P)

• Example: Doubling the number of moles of gas in a container (at constant T and P) doubles the volume.

5.6 – The Combined Gas Law and the Ideal Gas Law

The Combined Gas Law merges Boyle’s, Charles’, and Avogadro’s Laws to relate pressure, volume, and temperature for a fixed amount of gas. The Ideal Gas Law further incorporates the number of moles.

• Combined Gas Law:

• Ideal Gas Law:

• Variables: P = pressure (atm), V = volume (L), n = moles, R = universal gas constant, T = temperature (K)

• Value of R:

Example: Calculate the number of moles of H2 gas in 8.56 L at 0°C and 1.5 atm:

5.7 – Applications and Problem Solving with Gas Laws

Gas law problems often require identifying which law applies and converting all quantities to appropriate units.

• Tip: PV = nRT problems usually involve a single situation, not a before/after scenario.

• Example: A sample of methane gas with a volume of 38 mL at 5°C is heated to 86°C at constant pressure. Calculate its new volume.

• Convert temperatures to Kelvin: ,

• Apply Charles’ Law:

• Solve for :

Note: When using the gas laws, always ensure that:

• Pressure is in atmospheres (atm)

• Volume is in liters (L)

• Temperature is in Kelvin (K)

• Moles (n) are in mol

Summary Table: Gas Laws

Additional info: For more advanced topics such as Dalton’s Law of Partial Pressures, Kinetic Molecular Theory, and Real Gases, refer to subsequent sections or chapters in your textbook.