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, 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, etc.) that make up the atmosphere.

• Barometer: A device used to measure atmospheric pressure, invented by Italian physicist Evangelista Torricelli. 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 = 1 atm

Factors Affecting Barometric Pressure: Changes in weather, altitude, and the amount of water vapor in the air can alter atmospheric pressure.

5.2 – Units of Pressure

Pressure can be measured in several different 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 atmospheres, mm Hg, and pascals.

• 49 torr × (1 atm / 760 torr) = 0.064 atm

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

• 49 torr × (101,325 Pa / 760 torr) = 6,500 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, so as P increases, V decreases.

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 temperature increases.

• Note: Temperature must always be 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: 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’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:

• Where:

  • P = pressure (atm)

  • V = volume (L)

  • n = number of moles

  • R = universal gas constant ()

  • T = temperature (K)

• Units: It is important to use the correct units for each variable to match the 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 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 its new volume.

• Unit Consistency: When using ratios, units for volume and temperature must be consistent, but do not need to be in liters or Kelvin unless required by the equation.

Summary Table: Gas Laws

Additional info: These notes cover the foundational 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 further study in thermodynamics, chemical kinetics, and equilibrium.