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 Torricelli to measure atmospheric pressure. At sea level, the atmosphere pushes mercury up a barometer tube to a standard height of 760 mm Hg.

Standard atmospheric pressure: 760 mm Hg

• Factors affecting barometric pressure: Changes in weather and altitude can alter atmospheric pressure. Fewer water vapor molecules in the air lead to lower atmospheric pressures.

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:

  • 1 atm = 760 mm Hg = 760 torr = 101,325 Pa = 14.7 psi

Example: Convert 49 torr to other units:

• In atmospheres:

• In mm Hg:

• In pascals:

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 is a constant for a given amount of gas at constant temperature)

• Two-state form:

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

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: 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 will also double, provided temperature and pressure remain constant.

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):

• Units: Pressure in atm, volume in liters, temperature in Kelvin, amount in moles.

Example: Calculate the number of moles of H2 gas occupying 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 to use based on the variables held constant and those that change. Sometimes, the combined or ideal gas law is used for more complex scenarios.

• 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 85°C at constant pressure. Calculate its new volume.

• Convert temperatures to Kelvin: ,

• Use Charles’ Law:

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

Summary Table: Gas Laws

Additional info: These notes cover the fundamental gas laws and their applications, which are essential for understanding the behavior of gases in chemical and physical processes. Mastery of these concepts is crucial for solving quantitative problems in general chemistry.