Gases and Pressure - Lecture Review

Pressure (P) is defined as the force per unit area exerted on a surface.
- Formula: P = \frac{F}{A} where:
- P = pressure (Pa)
- F = force (N)
- A = area (m²)
The SI unit for pressure is the Pascal (Pa).
Pressure is measured using devices like barometers.
- Example: A person with a mass of 51 kg exerts a force of 500 N on the ground due to gravitational pull (computed as 51 \text{ kg} \times 9.8 \text{ m/s}^2 ).
- Thus, the pressure exerted by this person on a surface area of 325 cm² is calculated as: \frac{500 \text{ N}}{325 \text{ cm}^2} = 1.5 \text{ N/cm}^2 .

The first barometer invented by Evangelista Torricelli in the early 1600s.
- Demonstrated that mercury rises to a height of 30 in. (760 mm) when the tube is inverted into mercury.

Pressure can be measured in various units:
- Millimeters of mercury (mm Hg): 1 mm Hg = 1 torr.
- Atmospheres (atm): Standard atmospheric pressure at sea level = 760 mm Hg = 101.325 kPa.
- Pascal (Pa): 1 Pa = 1 N/m². Note that 1 atm corresponds to 101325 Pa.

Definition: The total pressure of a gas mixture equals the sum of the partial pressures of each gas in the mixture: P{total} = P1 + P2 + … + Pn .
The individual pressure of each gas (the partial pressure) is independent of the others.
Application: When gases are collected over water, the vapor pressure must be considered. The formula used is: P{atm} = P{gas} + P_{water} .

Scenario: Oxygen collected from potassium chlorate decomposition at a barometric pressure of 731.0 torr and water vapor pressure of 17.5 torr at 20.0°C.
Solution: To find the partial pressure of oxygen,
- P{gas} = P{atm} - P_{water} = 731.0 ext{ torr} - 17.5 ext{ torr} = 713.5 ext{ torr} .

Postulates:
- Gases consist of large numbers of small particles (molecules) that are in constant, random motion.
- The volume of the gas molecules is negligible compared to the volume of their container.
- Attractive forces between molecules are negligible.
- Gas particles undergo elastic collisions with one another and the container walls.
- The average kinetic energy of gas particles is directly proportional to the absolute temperature (in Kelvin).

Relationships between volume, pressure, and temperature of gases: Boyle’s Law, Charles’s Law, Gay-Lussac’s Law, and the Combined Gas Law.

Boyle’s Law states that the volume of a fixed mass of gas varies inversely with its pressure at constant temperature.
- Mathematically expressed as: PV = k .
- Alternative form: P1V1 = P2V2 .
Example: An oxygen sample with initial conditions V1 = 150.0 ext{ mL}, P1 = 0.947 ext{ atm} will have a final volume V2 at pressure P2 = 0.987 ext{ atm} .

Charles’s Law states that the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature.
- It can be defined mathematically as: V = kT or \frac{V1}{T1} = \frac{V2}{T2} .
Example: Gas volume changes from 752 mL at 25°C to volume V_2 at 50°C, with known values for temperature in Kelvin.

Gay-Lussac’s Law states that the pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature.
- Mathematically, it can be written as: \frac{P1}{T1} = \frac{P2}{T2} .

The combined gas law expresses the relationship between pressure, volume, and temperature when conditions change: \frac{P1V1}{T1} = \frac{P2V2}{T2} .

The ideal gas law combines relationships between pressure, volume, temperature, and number of moles: PV = nRT , where:
- R = ideal gas constant (0.0821 \text{L atm/(K mol)} ).

Implications from the gas laws relate to real-world applications, including the behavior of gases under various conditions and their applications in various fields from meteorology to chemical engineering.

At standard temperature and pressure (STP), one mole of an ideal gas occupies 22.4 L.
Conversion factors can be applied to calculate gas masses and volumes using molar volume.

States that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.
- V = kn , where k is proportionality constant and n is the number of moles.

The coefficients of gases in balanced chemical equations can be interpreted in terms of volume ratios when the reactions occur at the same temperature and pressure.

Diffusion: The process of gas molecules spreading to fill their container due to random motion.
Effusion: Movement of gas molecules through a tiny opening.

The rates of effusion of gases are inversely proportional to the square roots of their molar masses: \frac{RateA}{RateB} = \sqrt{\frac{MB}{MA}} .
Example: This law can be used to compare the effusion rates of hydrogen and oxygen gases, with calculations showing that hydrogen effuses faster due to its lower molar mass.