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Chapter 5 Lecture - Gases

Chapter 5 Lecture: Gases

Characteristics of Gases

  • Conforms to the shape of the container and fills it completely.

  • Particles are very far apart and move randomly.

  • Important aspects of gases:

    • Gas volume is significantly affected by pressure.

    • Gas volume is significantly affected by temperature.

    • Gases flow freely, meaning they have very low viscosity.

    • Gases have relatively low densities, typically measured in units like g/L.

    • Gases form a homogeneous solution (mixture) in any proportion with other gases.

Gas Pressure

  • Definition: Gas pressure is the force exerted by the collisions of gas molecules with the walls of their container.

  • Formula: Pressure is defined as force per unit area: P = \frac{\text{force}}{\text{area}}

  • Measuring Gas Pressure:

    • Barometer: Used to measure atmospheric pressure.

    • Manometer: Used to measure the pressure of a gas in an experimental setup.

  • Units of Pressure:

    • Pascal (Pa): The derived unit in the SI system. 1 \text{ Pa} = 1 \text{ N/m}^2 (Newton per square meter).

    • Standard atmosphere (atm): Represents the average atmospheric pressure measured at sea level at 0^\circ\text{C}.

    • 1 \text{ atm} = 101.325 \text{ kPa} = 101,325 \text{ Pa}

    • Millimeter of mercury (mmHg): Often referred to as "torr" when temperatures are other than 0^\circ\text{C}.

    • 1 \text{ atm} = 760 \text{ mmHg} = 760 \text{ torr} (these are exact quantities by definition).

    • Bar: Another common unit of pressure.

    • 1 \text{ bar} = 100 \text{ kPa} = 100,000 \text{ Pa}

    • Pounds per square inch (psi): Often used in engineering applications.

    • 14.7 \text{ psi} = 1 \text{ atm}

Gas Laws and Their Foundations

  • Four Variables to Describe Gases: These variables are interdependent.

    • Pressure (P): Measurements are typically in mmHg or torr; calculations are usually done in atmospheres (atm).

    • Temperature (T): Measurements are usually in degrees Celsius (^\circ\text{C}); calculations must be done in Kelvin (K).

    • Volume (V): Measurements may be in milliliters (mL); calculations are commonly done in liters (L).

    • Amount (n): Measurements are often given in grams (g); calculations are performed using moles (mol).

  • Gas Laws: These are empirical relationships that express the effect of one variable on another while holding the other two variables constant.

  • Ideal Gases: The gas laws describe the behavior of theoretical

1. Boyle's Law (Pressure-Volume Relationship)

  • Statement: At constant temperature (T) and amount of gas (n), the volume (V) of a gas is inversely proportional to its pressure (P).

  • Observations: As pressure increases, volume decreases.

  • Formula: P1V1=P2V2

2. Charles's Law (Volume-Temperature Relationship)

  • Statement: At constant pressure (P) and amount of gas (n), the volume (V) of a gas is directly proportional to its absolute temperature (T).

  • Observations: As temperature increases, volume increases.

  • Formula: \frac{V1}{T1}=\frac{V2}{T2}

3. Avogadro's Law (Volume-Amount Relationship)

  • Statement: At constant temperature (T) and pressure (P), the volume (V) of a gas is directly proportional to the number of moles (n) of the gas.

  • Observations: As the amount of gas increases, volume increases.

  • Formula: \frac{V1}{n1}=\frac{V2}{n2}

4. Gay-Lussac's Law (Pressure-Temperature Relationship)

  • Statement: At constant volume (V) and amount of gas (n), the pressure (P) of a gas is directly proportional to its absolute temperature (T).

  • Observations: As temperature increases, pressure increases.

  • Formula: \frac{P1}{T1}=\frac{P2}{T2}

5. Combined Gas Law

  • Statement: This law combines Boyle's, Charles's, and Gay-Lussac's laws, relating pressure, volume, and temperature for a fixed amount of gas.

  • Conditions: Amount of gas (n) is constant.

  • Formula: \frac{P1\cdot V1}{T1}=\frac{P2\cdot V2}{T2}

6. Ideal Gas Law

  • Statement: Integrates the relationships among pressure, volume, temperature, and the amount of gas into a single equation.

  • Formula: PV = nRT

    • Where R is the ideal gas constant. The value of R depends on the units of pressure and volume.

    • Commonly used value: R = 0.08206 \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}} (when P is in