Gases and Gas Laws

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 pressure exerted by the atmosphere, primarily due to gases like N2, O2, Ar, CO2, Ne, He, and CH4.

• Barometer: A device invented by Torricelli to measure atmospheric pressure. At sea level, standard atmospheric pressure is the height (in mm) that mercury is pushed up a barometer tube.

Standard Pressure: 760 mmHg

• Factors affecting barometric pressure include altitude and weather conditions.

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)

• Standard Conversions:

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

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: For a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional.

• Mathematical 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: For a fixed amount of gas at constant pressure, the volume 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 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: Doubling the amount of gas (in moles) 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’, and Avogadro’s Laws to relate pressure, volume, and temperature for a fixed amount of gas.

• Combined Gas Law:

• Useful for problems involving changes in pressure, volume, and temperature.

The Ideal Gas Law generalizes these relationships for any amount of gas:

• Equation:

• Variables: = pressure (atm), = volume (L), = moles, = universal gas constant, = temperature (K)

• Value of R:

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

Worked Examples

• Example 1: A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What volume will it occupy at 38°C and 1 atm?

• Convert temperatures to Kelvin: ,

• Apply Charles’ Law:

• Example 2: 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: ,

• Apply Charles’ Law:

Summary Table: Gas Laws

Additional info: For more complex problems, the combined gas law or the ideal gas law is used, especially when more than one variable changes. Always ensure units are consistent, especially for R, which requires pressure in atm, volume in liters, and temperature in Kelvin.