Chapter 10: Gases – Properties, Laws, and Calculations

Gases

Properties of Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container. Unlike solids and liquids, gases have neither a fixed shape nor a fixed volume.

• Compressibility: Gases can be compressed easily due to the large spaces between particles.

• Low Density: The density of gases is much lower than that of solids or liquids.

• Expansion: Gases expand to fill the volume of their container.

• Fluidity: Gas particles move freely and can flow.

• Diffusion: Gases mix evenly and completely when combined.

• Example: Air in a balloon expands to fill the entire balloon.

Pressure

Pressure is a key property of gases, defined as the force exerted by gas particles per unit area on the walls of their container.

• Definition: Pressure ($P$) is the result of collisions of gas molecules with the surfaces of their container.

• Units: Common units include atmospheres (atm), millimeters of mercury (mm Hg), torr, and pascals (Pa).

• Conversions:

  • 1 atm = 760 mm Hg = 760 torr

  • 1 atm = 101,325 Pa

• Variables Affecting Pressure: Temperature, volume, and the number of gas particles all influence pressure.

• Example: Increasing the temperature of a gas in a sealed container increases its pressure.

Empirical Gas Laws

Empirical gas laws describe the relationships between pressure, volume, temperature, and amount of gas under specific conditions.

• Boyle's Law: At constant temperature, the pressure and volume of a gas are inversely related. $P_1V_1 = P_2V_2$ Example: Compressing a syringe decreases its volume and increases the pressure inside.

• Charles' Law: At constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin). $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ Example: A hot air balloon expands as the air inside is heated.

• Gay-Lussac's Law: At constant volume, the pressure of a gas is directly proportional to its temperature (in Kelvin). $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ Example: A sealed aerosol can may burst if heated.

• Combined Gas Law: Combines Boyle's, Charles', and Gay-Lussac's laws for a fixed amount of gas. $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ Example: Calculating the final pressure of a gas when both temperature and volume change.

• Avogadro's Law: At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles. $\frac{V_1}{n_1} = \frac{V_2}{n_2}$ Example: Doubling the amount of gas in a container doubles its volume.

• Calculations: Use the above equations to solve for unknown variables in gas law problems.

Ideal Gas Law

The ideal gas law combines all the empirical gas laws into a single equation, describing the behavior of an ideal gas.

• Basic Postulates (Assumptions):

  • Gas particles have negligible volume compared to the container.

  • No intermolecular forces between gas particles.

  • Collisions between particles and container walls are perfectly elastic.

• Ideal Gas Equation: $PV = nRT$ Where:

  • $P$ = pressure

  • $V$ = volume

  • $n$ = number of moles

  • $R$ = ideal gas constant

  • $T$ = temperature (Kelvin)

• R – The Ideal Gas Constant:

  • $R = 0.0821$ L·atm/(mol·K)

  • $R = 8.314$ J/(mol·K)

• Calculations: The ideal gas law can be used to determine any one variable if the others are known.

• Example: Calculate the volume occupied by 2 moles of an ideal gas at 1 atm and 273 K.

Dalton’s Law of Partial Pressures

Dalton’s Law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas.

• Equation: $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

• Example: In a container with oxygen and nitrogen, the total pressure is the sum of the pressures from each gas.

Absolute Zero

Absolute zero is the theoretical temperature at which a gas would have zero volume and all molecular motion would cease.

• Definition: Absolute zero is 0 Kelvin ($0\,K$), equivalent to $-273.15\,^{\circ}\text{C}$.

• Significance: It is the lowest possible temperature, and is the basis for the Kelvin temperature scale.

• Example: At absolute zero, the pressure and volume of an ideal gas would be zero.