Science Reviewer 4th quarter

Expansion: Gases expand to fill any container due to random motion and no attractive forces between molecules.
Fluids: Gases are classified as fluids (like liquids) because they flow easily.
FluidsDensity: Gases have very low densities, as they occupy lots of empty space with no fixed volume.
Compressibility: Gases can be compressed due to the abundance of empty space.
Diffusion & Effusion: Gases undergo diffusion and effusion due to constant random motion of particles.

Diffusion: Gradual mixing of molecules of different gases (e.g., HCl and NH3 meeting in a tube).
- HCl (heavier) and NH3 (lighter) diffuse from opposite ends of a tube and meet to form NH4Cl closer to the HCl end.
Effusion: Movement of gas molecules through a small hole into an empty container.

Governs the effusion and diffusion of gas molecules.
Formula: The rate of effusion is inversely proportional to the square root of its molar mass:
- v ext{ (velocity)} ext{ varies with } M ext{ (molar mass)}
- The average KE of gas molecules is given by:
  KE = rac{1}{2} mv^2
Key Points:
- Molecules effuse through holes in a rubber balloon at a rate proportional to temperature and inversely proportional to molar mass.
- Example: Helium (He) effuses more rapidly than O2 at the same temperature.

Problem J: Compare H2 and O2 effusion rates at the same temperature and pressure:
- Given gases: H2, O2
- Apply Graham's Law to find:
- Hydrogen effuses 3.98 times faster than oxygen.

Pressure Definition: Pressure is the force exerted per unit area.
- ext{Pressure} = rac{ ext{force}}{ ext{area}}
Measurement Instruments:
- Barometer: Measures atmospheric pressure (e.g., mercury barometer).
- Manometer: Measures pressure of contained gas.
Key Pressure Units at Sea Level:
- 101.325 kPa,
- 1 atm,
- 760 mm Hg,
- 760 torr,
- 14.7 psi.

Relationship: Pressure and volume are inversely related at constant temperature.
- PV = K
- P_1V_1 = P_2V_2
- Exemplar:
- Increasing the pressure from 1.0 atm to 2.0 atm while volume decreases from 1.0 L to 0.5 L.

Relationship: Volume of a gas varies directly with absolute temperature at constant pressure.
- V/T = K
- V_1/T_1 = V_2/T_2
- Example: A heated balloon expands as temperature increases, following Charles’s Law.
- Temperature Conversion: Ensure temperatures are in Kelvin when applying the laws: K = C + 273

Relationship: Pressure and temperature (in Kelvin) are directly related at constant volume.
- P/T = K
- P_1/T_1 = P_2/T_2
- Application: Pressure cookers function faster due to higher pressures resulting in higher temperatures.

Formula: Combines Boyle's, Charles's, and Gay-Lussac's Laws:
- P_1V_1/T_1 = P_2V_2/T_2
Simplifies evaluations regarding simultaneous changes in pressure, volume, and temperature of a contained gas under constant moles.
You can derive individual laws from it by holding one variable constant.

Molar Relationship: Volume is directly related to the amount of gas (number of moles) at constant temperature and pressure.
- V ext{ varies with } n
- V_1/n_1 = V_2/n_2
- Example: Doubling the number of moles of gas in a flexible container doubles the volume.

Equation: Describes the state of an ideal gas mixed with pressure, volume, and temperature.
- PV = nRT
- Where R is the gas constant.
- At STP, 1 mole of an ideal gas occupies 22.414 L.

Definition: The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each gas in the mixture.
- P_{total} = P_1 + P_2 + P_3 + …
- Useful for calculating pressures in gas mixtures using the mole fraction:
- P_i = X_i P_{total}

Temperature increase in an enclosed gas increases pressure (if volume constant).
Combined gas law explains relationships among pressure, volume, and temperature.
Volume increases with increased temperature at constant pressure.
Volume inversely decreases with increased pressure at constant temperature.