Gas Laws Lecture

Kinetic Molecular Theory of Gases 1) Gases consist of large numbers of tiny particles that are far apart relative to their size 2) Collisions between gas particles and between particles and container walls are elastic – they result in no net loss of kinetic energy

3) Gas particles are in continuous, rapid, random motion 3) Gas particles are in continuous, rapid, random motion. They therefore possess kinetic energy, which is energy in motion. 4) There are no forces of attraction or repulsion between gas particles 5) The average kinetic energy of gas particles depends on the temperature of the gas

In Theory . . . Theories are great things, especially when they are true . . . The Kinetic Molecular Theory is mostly true In the “real world” there are attractions between particles in gases when the particles get close enough and have low kinetic energy Theory truest for noble gases Theory less true for water vapor

Properties of Gases Expansion Fluidity Gases have no definite volume, they expand to fill whatever space is available Fluidity Because there are no attractions between particles, the particles can slide past each other (flow). This is why gases have no definite shape.

Low Density Compressibility Gas particles are “far apart,” so there is a lot of empty space and therefore low density. The density of a material as a gas is typically 1/1000 of its liquid or solid state. Compressibility Because gas particles are naturally far apart, it is possible to push them closer together. This is called compression

Diffusion Diffusion is the spontaneous mixing of two substances caused by their random motion. The net result will appear to be the movement from areas of high concentration to areas of low concentration. The rate of diffusion depends on 1) their speed 2) their diameters 3) the attractive forces between them

Effusion Effusion is the movement of gas particles through tiny openings Gortex works by effusion

Units of Measure for Gases Temperature – average kinetic energy of a sample (Kelvins, K = C + 273) Pressure – how much the particles are pressing on each other and the walls of a container measures in – atmospheres (atm), millimeters of mercury (mm Hg), or pascals (Pa) 1 atm = 760 mm Hg = 101.325 kPa (1013.25 Pa) Volume – amount of space (L)

Boyle’s Law Pressure and Volume are inversely proportional P1V1 = P2V2 A 50 mL gas sample at 110 kPa, what is the new pressure if it is compressed to 35 mL? (50 mL)(110 kPa) = (35 mL)P2 P2 = 157.14 kPa

Charles’ Law Temperature and Volume are directly proportional Temperature must be in °K (°C + 273) V1/T1 = V2/T2 A 250 mL gas sample at 25 °C, what is the new temperature if it is compressed to 175 mL? (250 mL)/(298 K) = (175 mL)/T2 T2 =208.6 °K

Gay-Lussac’s Law Temperature and Pressure are directly proportional Temperature must be in °K (°C + 273) P1/T1 = P2/T2 A gas sample is at 61 °C and .79 atm, what is the new pressure if the temperature changes to 117 °C? (.79 atm)/(334 K) = P2 /(390 K) P2 = .92 atm

Combined Gas Law Combines previous three laws Temperature must be in °K (°C + 273) P1V1/T1 = P2 V2/T2 A 315 mL gas sample is at 12 °C and .98 atm, what is the new pressure if the temperature changes to 47 °C and the volume to 415 mL? (.98 atm)(315 mL)/(285 K) = P2(415 mL)/(320 K) P2 = .84 atm

Ideal Gas Law Shows relationship between moles, pressure, temperature, and volume PV=nRT Temperature must be in °K (°C + 273) n = moles R = constant (.0821 atm L /mol °K) What is the volume of a 2.5 mole sample of oxygen at 2.1 atm and 78 °C? (2.1atm)V = (2.5 mol)(.0821 atm L/mol °K)(351 °K) V = 34.31 L