Gases: Pressure, Gas Laws, and the Ideal Gas Law

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 the surfaces around them.

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

• Barometer: A device invented by Evangelista Torricelli to measure atmospheric pressure. At sea level, the standard atmospheric pressure is the height of a mercury column pushed up by the atmosphere, defined as 760 mmHg.

Standard Pressure: 760 mmHg = 1 atm

Factors Affecting Barometric Pressure:

• Altitude: Higher altitudes have lower atmospheric pressure due to fewer air molecules.

• Weather: Changes in weather patterns can increase or decrease 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: 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: (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:

• General Equation: (where k is a constant at constant T and n)

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

• General Equation: (at constant P and n)

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

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 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:

• General Equation: (at constant T and P)

• Example: Doubling the amount of gas (in moles) at constant T and P doubles the volume.

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 universal constant.

• Combined Gas Law:

• Ideal Gas Law:

• Where:

  • P = pressure (atm)

  • V = volume (L)

  • n = moles of gas

  • R = universal gas constant ()

  • T = temperature (K)

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

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

• Given: V = 8.56 L, P = 1.5 atm, T = 0°C = 273 K, R = 0.0821 L·atm/mol·K

• Use:

• Calculation:

5.7 – Applications and Problem Solving with Gas Laws

Gas law problems often require identifying which law applies and converting all quantities to the correct units. Sometimes, more than one law is needed, especially when the number of moles changes (e.g., chemical reactions).

• 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: ,

• Use Charles’ Law:

• Calculation:

Note: When using ratios, units for volume and temperature must be consistent, but volume can be in any unit as long as both V1 and V2 use the same unit.

Summary Table: Gas Laws

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