Gases: Properties, Laws, and Calculations

5.1 – Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of 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 surfaces around them.

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

• 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 mm Hg = 1 atm

Factors Affecting Barometric Pressure:

• Altitude (higher altitude = lower pressure)

• Weather conditions (humidity, temperature)

5.2 – Units of Pressure

Pressure can be measured in several units, and conversion between these units is common in chemistry problems.

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

• 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:

• Example: Squeezing a balloon decreases its volume, increasing the pressure inside.

5.4 – Charles’s Law

Charles’s 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:

• Example: Heating a balloon causes it to expand as the gas molecules move faster and occupy more space.

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.

• Mathematical Form:

• Example: Doubling the amount of gas (in moles) in a container doubles the volume, if temperature and pressure are constant.

5.6 – The Combined Gas Law and the Ideal Gas Law

The Combined Gas Law merges Boyle’s, Charles’s, 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:

• R (Universal Gas Constant):

• Units: Pressure in atm, Volume in L, Temperature in K, n in moles

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

• Given: , ,

• Use:

• Calculation:

5.7 – Applications and Problem Solving with Gas Laws

Gas law problems often require converting between units and applying the appropriate 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: ,

• Apply Charles’s Law:

• Calculation:

5.8 – Summary Table: Gas Laws

Additional info: For more complex problems, such as those involving chemical reactions or changes in the number of moles, always identify which variables are changing and which are held constant to select the correct law.