Gas Laws and Properties of Gases: Study Notes for General Chemistry

Pressure and Its Measurement

Definition and SI Unit

Pressure is defined as the force exerted per unit area by gas molecules as they collide with the surfaces of their container. The SI unit for pressure is the Pascal (Pa), named after Blaise Pascal.

• Pressure (P): $P = \frac{F}{A}$, where F is force (in Newtons) and A is area (in m2).

• 1 Pa = 1 N/m2

Example: If the same amount of gas is transferred from a 5.0 L container to a 10.0 L container, the pressure will decrease (assuming temperature and amount of gas are constant).

Pressure Unit Conversions

Other common units for pressure include atmospheres (atm), millimeters of mercury (mmHg), and torr. These units can be converted as follows:

Unit Name	Pressure Value
Atmosphere (atm)	1 atm = 101,325 Pa
Millimeter of Mercury (mmHg)	1 atm = 760 mmHg
Torr	1 atm = 760 torr
Kilopascal (kPa)	1 atm = 101.325 kPa
Pounds per square inch (psi)	1 atm = 14.7 psi

Example: Convert 24.9 inHg to mmHg and atm.

Mole Fraction and Partial Pressure

Mole Fraction (X)

The mole fraction (X) of a component in a mixture is the ratio of the number of moles of that component to the total number of moles in the mixture.

• Formula: $X = \frac{n_{component}}{n_{total}}$

• Mole fraction is a unitless quantity.

Example: Calculate the mole fraction of dichloromethane in a mixture with 25.0 g CH2Cl2 and 125 g H2O.

1. Convert all masses to moles.

2. Place the moles of the component of interest in the numerator and total moles in the denominator.

Law of Partial Pressures (Dalton's Law)

The partial pressure of a gas in a mixture is the pressure it would exert if it occupied the container alone. The total pressure is the sum of the partial pressures of all gases present.

• Formula: $P_{total} = P_{gas1} + P_{gas2} + P_{gas3} + \ldots$

• Partial pressure can also be calculated using mole fraction: $P_{gas} = X_{gas} \times P_{total}$

Example: If neon exerts 1.85 atm and nitrogen exerts 500 torr, the total pressure is the sum (after converting units if necessary).

Using Moles to Determine Partial Pressure

If gases behave ideally, the partial pressure of each can be calculated using the Ideal Gas Law:

• Formula: $P_{gas} = \frac{nRT}{V}$

Example: Calculate the partial pressure of helium if 12.0 g He and 20.0 g O2 are placed in a 5.0 L cylinder at 30°C.

Ideal Gas Law

Definition and Formula

The Ideal Gas Law relates the pressure, volume, temperature, and amount (in moles) of a gas:

• Formula: $PV = nRT$

• P = pressure (atm), V = volume (L), n = moles, R = gas constant, T = temperature (K)

Example: A 500 mL container at 600 mmHg contains 23.9 g N2 at 50°C. Use the correct units for the Ideal Gas Law.

Gas Constant (R)

The gas constant R has different values depending on the units used:

R Value	Conversion Factor	Units
0.08206	1 L·atm	mol-1·K-1
8.314	1 J	mol-1·K-1

Example: How many moles of NH3 are in a 25.0 L tank at 190°C and 5.20 atm?

Gas Law Derivations and Applications

Combined Gas Law

The Combined Gas Law combines Boyle's, Charles's, and Gay-Lussac's Laws to relate pressure, volume, and temperature:

• Formula: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

This law is used when the amount of gas is constant but pressure, volume, and temperature change.

Example: If a gas occupies 8.30 L at 202°C, what temperature is needed to decrease the volume to 5.25 L at constant pressure?

Direct and Inverse Relationships

By rearranging the Ideal Gas Law, we can establish the following relationships:

• P & V: Inversely proportional (Boyle's Law)

• P & T: Directly proportional (Gay-Lussac's Law)

• V & T: Directly proportional (Charles's Law)

• V & n: Directly proportional (Avogadro's Law)

Example: If the number of moles is tripled at constant pressure, the volume will triple.

Chemistry Gas Laws

Boyle's Law

States that the volume of a gas is inversely proportional to its pressure at constant temperature and amount:

• Formula: $P_1V_1 = P_2V_2$

Example: If the volume of a container increases, the pressure decreases.

Charles's Law

States that the volume of a gas is directly proportional to its temperature (in Kelvin) at constant pressure and amount:

• Formula: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Example: Heating a gas in a flexible container increases its volume.

Gay-Lussac's Law (Amontons's Law)

States that the pressure of a gas is directly proportional to its temperature (in Kelvin) at constant volume and amount:

• Formula: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

Example: Heating a sealed can increases the pressure inside.

Avogadro's Law

States that the volume of a gas is directly proportional to the number of moles at constant pressure and temperature:

• Formula: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

Example: Adding more gas to a balloon increases its volume.

Practice Problems and Applications

• Calculating mass, volume, or pressure of gases using the Ideal Gas Law and its derived forms.

• Determining mole fractions and partial pressures in gas mixtures.

• Applying gas laws to real-world scenarios, such as changes in pressure with altitude or temperature.

Example: A 10.0 L cylinder with 3.00 atm pressure—if the volume doubles, the pressure will halve (Boyle's Law).

Additional info: These notes cover the fundamental gas laws, pressure units, and calculations relevant to a General Chemistry course, including worked examples and practice problems for exam preparation.