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, acting as a waste receptacle for exhaust gases, and shielding 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) that make up the atmosphere.

• Barometer: A device invented by Italian physicist Evangelista Torricelli to measure atmospheric pressure. At sea level, the atmosphere pushes mercury up a barometer tube to a height of 760 mm Hg, which is defined as standard atmospheric pressure.

Standard Pressure: 760 mm Hg

• 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 necessary in gas law calculations.

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

• Conversion Factors:

• Example: To convert 49 torr to other units:

All these values represent the same pressure, just in different units.

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:

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

5.4 – Charles’ Law

Charles’ Law describes the relationship between 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 temperature (in Kelvin).

• Mathematical Form:

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

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

5.5 – Avogadro’s Law

Avogadro’s Law relates 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:

• Example: If you double the amount of gas (in moles), the volume will also double, provided temperature and pressure remain constant.

5.6 – The Combined Gas Law and the Ideal Gas Law

The Combined Gas Law combines 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 and a universal constant.

• Combined Gas Law:

• Ideal Gas Law:

• Where:

  • = pressure (atm)

  • = volume (L)

  • = number of moles

  • = universal gas constant ()

  • = temperature (K)

• Units: Always use the correct units for ; pressure in atm, volume in L, temperature in K, and amount in mol.

Example Problem (Ideal Gas Law):

A sample of H2 gas occupies a volume of 8.56 L at 0°C and a pressure of 1.5 atm. How many moles of hydrogen are present?

Example Problem (Combined Gas Law):

A sample of methane gas with a volume of 38 mL at 5°C is heated to 85°C at constant pressure. Calculate its new volume.

• Convert temperatures to Kelvin: ,

• Apply Charles’ Law:

Summary Table: Gas Laws

Key Takeaways:

• Always use Kelvin for temperature in gas law calculations.

• Be careful with units; convert as necessary to match the gas constant .

• Understand which law applies to a given problem based on what variables are held constant.

Additional info: For more advanced topics, such as Dalton’s Law of Partial Pressures, the Kinetic Molecular Theory, and real gas behavior, see subsequent sections in your textbook or lecture notes.