Chapter 5: The Gaseous State Chemistry 1061: Principles of Chemistry I Andy Aspaas, Instructor

Pressure Pressure: force per unit area –Force exerted on a surface area by molecules in motion Units: 1 atmosphere = 14.7 psi 1 atmosphere = 760 mm Hg 1 atmosphere = 101,325 Pascals 1 Pascal = 1 kg/m·s 2

Boyle’s law Relates volume and pressure of a gas PV = constant P i V i =P f V f

Charles’s Law Relates volume and temperature of a gas V/T = constant V i / T i = V f / T f

Combined gas law Combines Charles’s and Boyle’s laws to give one equation (P i V i )/T i = (P f V f )/T f

Avogadro’s Law Relates volume with amount of gas Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules Volume of 1 mole of gas = V m, molar gas volume 22.4 L/mol at STP (standard temp & pressure, 0 °C and 1 atm) Nearly the same for any ideal gas!

Ideal gases An ideal gas follows the empirical gas laws exactly –A theoretical gas whose molecules have no volume of their own, and whose molecules do not interact with each other R = molar gas constant, the constant of the combined gas equation when 1 mol of gas is used V m = R x (T / P) PV = nRT R = (L· atm)/(K · mol)

Using the ideal gas law If moles gas can be calculated… –Moles  mass  density (if MW is known) –Moles  MW (if mass is given) –Etc. Stoiciometry in equations can give number of moles –Moles  Liters by ideal gas law

Law of partial pressures The sum of partial pressures (P A ) of all of the different gases in a mixture is equal to the total pressure of the mixture Related to mole fraction of a component of a mixture –Mole fraction: fraction of moles of a certain substance in a mixture of several substances –Mole fraction = (n A /n) = (P A /P) Vapor pressure of water, when collecting gases over water

Molecular speed and effusion Average molecular speed, (u) is dependent on the temperature and Molar mass of the gas u = [(3RT) / (M m )] 1/2 Effusion: process in which a gas flows through a small hole in a container –Rate of effusion is proportional to 1/ (M m ) 1/2

Real gases Ideal gas equation does not hold up, especially at high pressures –Real volume is larger than the ideal gas law predicts, since molecules themselves take up space –Actual pressure is smaller than ideal gas law predicts, since intermolecular attractions weaken collisions against the walls of the vessel

van der Waals equation V becomes V – nb P becomes P + n 2 a / V 2 van der Waals equation: (P + n 2 a / V 2 )(V – nb) = nRT a and b values for many gases are known in the literature