The Ideal Gas Law and Kinetic Theory The mole, Avagadro’s number, Molecular mass The Ideal Gas Law Kinetic Theory of Gases

 For convenience, small masses will be expressed in atomic mass units (u) rather than kg.  1 u = x kg  When we have x atoms, we have 1 mole of atoms. A mole of a substance is Avogadro’s number of atoms of that substance.  Ex:

 All gases display similar behavior.  An ideal gas represents a hypothetical gas whose molecules have no intermolecular forces, that is they do not interact with each other and occupy no volume. At relatively low pressures and high temps many gases behave in ideal fashion.  State of gas is defined by four variables: pressure (p)- force per unit area (Pa) unit pascal is N/m 2 or atmospheres, 1 atm = 10 5 Pa volume (V)- measured in L or m 3 Temperature (T)- measured in Kelvins (K) = C+273 and number of moles (n)  Gases are discussed in terms of standard temperature and pressure (STP) which is at 273 K and 1 atm.  PV=nRT  R is the universal gas constant = 8.31 J/(molK)

 If the number of moles of a gas doesn’t change then both n and R are constants and the ideal gas law can be written as the combined gas law:  P 1 V 1 /T 1 = P 2 V 2 /T 2  Subscript 1 indicates the state before it is changed and then subscript 2 is after the change.  Ex:

 Combined efforts of Boltzmann, Maxwell, and others let to the kinetic theory of gases. This gives us an understanding of how gasses behave on a microscopic, molecular level.  5 assumptions of kinetic theory of gases:  Gases are made up of particles whose volumes are negligible compared to the container volume  Gas atoms or molecules exhibit no intermolecular attractions or repulsions  Gas particles are in continuous, random motion, undergoing collisions with other particles and container walls  Collisions between any two gas particles are elastic, meaning no energy is dissipated and KE is conserved  The average kinetic energy of gas particles is proportional to the absolute (K) temp of the gas and is the same for all gases at a given temp. As listed in the equations, the avg KE of each molecule is related to Kelvin temp T

 The equation that relates KE to the temp is:  K avg = 3/2 k b T  K b is the Boltzmann constant = 1.38 x J/K  Rarely on the AP-B exam they will ask for the root-mean square speed of each molecule. If asked, the following equation will be given:  V rsm = √(3k b T)/µ  µ is the mass of each molecule EX: