Gases: Properties, Laws, and Calculations

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 on the Earth's surface.

• Barometer: A device invented by Torricelli to measure atmospheric pressure. At sea level, standard atmospheric pressure is defined as the pressure that 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, and conversion between these units is often required in gas law calculations.

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

• Standard Conversions:

• These units are interchangeable using the above conversion factors.

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: At constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume.

• Mathematical Form: (where k is a constant for a given amount of gas at constant T)

• Two-State Form:

• Example: Squeezing a balloon decreases its volume, so pressure increases.

5.4 – Charles’ Law

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

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

• Mathematical Form:

• Two-State Form:

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

• Note: Temperature must always be in Kelvin for gas law calculations.

Example Calculation: A gas at 15°C (288 K) and 2.58 L is heated to 38°C (311 K) at constant pressure. What is the new volume?

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: At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas present.

• Mathematical Form:

• Two-State Form:

• Example: If you double the amount of gas (in moles), the volume also doubles (at constant T and P).

Example Calculation: If 12.2 L of O2 at 0.50 mol is converted to O3 at the same T and P, what is the volume of O3?

• First, calculate moles of O3 produced:

• Then,

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, temperature, and moles of a gas.

• Combined Gas Law:

• Ideal Gas Law:

• R (Universal Gas Constant):

• All variables must be in specific units: P in atm, V in L, n in mol, T in K.

Example Calculation: How many moles of H2 are present 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 converting between units and applying the correct law based on the variables held constant.

• 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 the new volume.

• Convert temperatures to Kelvin: 5°C = 278 K, 86°C = 359 K

Note: When using the gas constant R, ensure all units are compatible (e.g., volume in liters, pressure in atm, temperature in Kelvin).

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 in your textbook or lecture notes.