The Gaseous State

Gases consist of widely separated molecules in rapid motion. pressuretemperaturevolume molar amount All gases near room temperatures and normal pressures show the same quantitative relationships among their physical properties of pressure, temperature, volume and molar amount.

SI unit of pressure: SI unit of pressure: pascal (Pa) Standard atmosphere: 1 atm = Pa = kPa Temperature: Temperature: absolute temperature scale, Kelvin scale K = °C T = t + 273

The volume of a sample of gas at a given temperature is found to vary inversely with the applied pressure Boyle’s law: (at fixed temperature for a given amount of gas) PV = constant

Pressure – Volume Data for 1.00g O2 at 0°C P (atm)V (L)PV

A plot of the volume of 1.000g O2 at 0°C for various pressures.

Charles’ Law volumetemperature Relationship between the volume and the temperature of a gas (Jacques Charles, Joseph Gay-Lussac) TemperatureVolume °CKml Variation of the volume of a sample of gas with temperature (p=const.)

absolute The volume of any sample of a gas varies directly with absolute temperature if the pressure is held constant. not The V is not directly proportional to the °C.

V i V i = initial volume V f V f = final volume T i T i = initial temperature T f T f = final temperature

Temperature-volume curve for an ideal gas (Charles’ law)

Gay-Lussac’s Law pressure At constant volume, the pressure of a given mass of gas temperature varies directly with the absolute temperature. Combined Gas Law

Avogadro’s Law (see stoichiometry) V = nV m n = n = number of moles V m V m = molar gas volume (volume of x gas molecules at a given temperature and pressure)

Standard temperature and pressure (STP) Temperature : 0°C = 273 K Pressure: 1 atm = kPa Molar gas volume at STP: L/mol

The Ideal Gas Law: at fixed T, n Boyle’s Law at fixed T, n Boyle’s Law at fixed P, n Charles’ Law a fixed T, P Avogadro’s Law Therefore, PV = nRT molar gas constant

The Ideal Gas Law: Ideal gas: A hypothetical gas that follows the behavior described by the equation of behavior described by the equation of state for an ideal gas. state for an ideal gas. J

Gas Mixtures: Dalton’s law of partial pressures: the total pressure of a mixture of gases that do not react is equal to the sum of the partial pressures of all the gases present. Ptotal = pA + pB + pC + …

Kinetic Theory of an Ideal Gas Postulates: 1.Gases are composed of molecules whose size is negligible compared to the distance between them. 2.Molecules move randomly in linear motion. 3.The collosions are elastic. 4.The average kinetic energy of a molecule is proportional to the K.

Graham’s law of effusion: The rate of effusion of gas molecules from a particular hole is inversely proportional to the square root of the molecular weight of the gas at constant temperature and pressure.

Real gases Van der Waals equation: „a” and „b” are constants