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.

• 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 Evangelista Torricelli to measure atmospheric pressure. It uses a column of mercury; at sea level, the atmosphere supports a column 760 mm high.

• Standard Pressure: Defined as 760 mmHg (millimeters of mercury).

Diagram description: A barometer consists of a tube filled with mercury inverted in a dish of mercury. The height of the mercury column (in mm) measures atmospheric pressure.

5.2 – Units of Pressure

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

• Common Units:

  • 1 atmosphere (atm) = 760 mmHg = 760 torr = 101,325 Pa = 14.7 psi

• Conversions: These units are often used as conversion factors in calculations.

• Example: To convert 49 torr to other units:

  • 49 torr × (1 atm / 760 torr) =

  • 49 torr × (101325 Pa / 760 torr) =

  • 49 torr = 49 mmHg (since 1 torr = 1 mmHg)

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 and volume of a fixed amount of gas are inversely proportional.

• Mathematical Form:

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

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:

• Temperature in Kelvin: Always use Kelvin for gas law calculations.

• Example: If a gas has a volume of 2.58 L at 15°C (288 K), what is its volume at 38°C (311 K)?

  • Solve for :

5.5 – Avogadro’s Law

Avogadro’s Law connects the volume of a gas to the number of moles at constant temperature and pressure.

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

• Mathematical Form:

• Example: If 0.50 mol O2 gas occupies 12.2 L at 1 atm and 25°C, how much volume would 0.33 mol O3 occupy under the same conditions?

  • Use stoichiometry to find moles of O3 produced, then apply Avogadro’s Law.

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, and temperature for a fixed amount of gas. The Ideal Gas Law further incorporates the number of moles and a constant.

• Combined Gas Law:

• Ideal Gas Law:

• Universal Gas Constant (R):

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

• Example: How many moles of H2 are present in 8.56 L at 0°C and 1.5 atm?

5.7 – Applications and Problem Solving

Gas law problems often require identifying which law to use based on the variables held constant and those that change. Sometimes, stoichiometry is involved, especially when chemical reactions produce or consume gases.

• 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.

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

  • Apply Charles’ Law:

  • Solve for :

Additional info: For more complex problems, the Combined Gas Law or stoichiometric relationships may be required, especially when the amount of gas changes due to a chemical reaction.