Preludes to the Ideal Gas Equation Pressure (P) inversely proportional with Volume (V) at constant Temperature Boyles law. Volume (V) directly proportional with Temperature (T) at constant Pressure Charles law. Pressure (p) directly proportional with Temperature (T) at constant Volume Gay-Lussacs law Relationships between three equations can be combine into single equation:- PV = nRT (Ideal gas equation) R = L atm mol -1 K -1 What is an Ideal Gas? Obey the gas equation in any pressure and temperature condition. Practically, ideal gas do not exist (does the ideal of anything really exist?) Real gas at low pressure and high temperature is nearly an ideal gas. Kinetic Theory Of Gases A gas contains large molecules that moves in random directions :- Has velocity Has momentum continuous collisions that exerts forces per unit area is called pressure. Assumptions A container with volume V contains a very large number (N) of identical molecules, each of mass m. Volume = V Mass of each molecule = m N=number of molecules V Assumptions The size of each molecule is small compared with the average distance between them and the dimensions of the container. Assumptions The molecules are in constant motion. The molecules undergo perfectly elastic collisions with each other and also with the wall of the container. Assumptions The container walls are perfectly rigid and do not move as a result of the collisions. Daltons Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P1P1 P total = P2P2 P3P3 PnPn Daltons Law Blood Gases and Dalton Avogadros Principle Equal volumes of gases contain equal numbers of moles at constant temp & pressure V n Root Mean Square (Rms) Speed Of Gas Molecule PV = nRTKE = m u 2 KE= N A (1/2 mu 2 ) N A is the number of particles in a mole PV = 2/3 KE n PV = RT n KE = 3/2 RT u rms = u 2 U 2 = 3RT N A m u 2 = u rms = 3RT N A m u rms = 3RT M (mass of a mole in kg) Root Mean square velocity Vrms = Molecular Kinetic Energy (Average Translational Kinetic Energy) Each molecules of gas has a true speed of its own due to moving randomly. We use V rms to determine kinetic energies of all those molecules, which is a kind of an average value Hence = m o where m o = mass of molecule = square of the V rms Effusion and Diffusion Effusion passage of a gas through a tiny opening Diffusion mixing of gases Effusion Rates Rate of effusion for gas 1 = M 2 Rate of effusion for gas 2 M 1 Rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. So the more mass a gas has, the slower it effuses. Comparison Gas Molecules Move in three ways Translation Rotation Vibration Examples Internal Energy Principle of equipartition of energy Any amount of energy absorb by the molecule of gas will be distributed equally between every translational and rotational degree of freedom of the molecule Internal energy of ideal gas Definition : Internal energy of a gas U is equal to the total amount of average kinetic energy and potential energy which contains in any gasses.