CHAPTER 12 GASES AND THE KINETIC MOLECULAR THEORY 1 Comparison of Solids Liquids and Gases temperature changes have little effect on gases but large effect on pressure changes have large effect on gases but little effect on liquids liquids and solids and solids Composition of the Atmosphere and Some Common Properties 2 of Gases gases can be compressed gases exert pressure on their surroundings gases can expand without limit gases diffuse into each other i e they are miscible diffuse into each other gases can be described in terms of their volume V temperature T pressure P and the number of molecules moles represented by n of gas present g M n m where Mm molar mass Pressure pressure force per unit area 1 atm 760 mmHg 760 torr Boyle s Law The Pressure Volume Relationship maintains constant temperature and number of moles volume is inversely proportional to pressure P 1 V as one goes up the other goes down assumes number of moles n and temperature T Boyle s Law remain constant P1V1 P2V2 Charles Law The Volume Temperature Relationship maintains constant pressure and number of moles volume is directly proportional to the absolute temperature note that all gas calculations must be done in Kelvin V T as one goes up the other goes up as well Charles Law assumes number of moles n and pressure P remain constant V V 1 T 2 T 3 4 5 6 Standard Temperature and Pressure all gases behave identically at the same temperature and pressure standard pressure 1 00000 atm 760 torr 760 mmHg standard temperature 273 15 K 0 00 oC other standards 1 mol and 22 4 L Gay Lussac s Law assumes number of moles n and volume V remain constant note that all gas calculations must be done in Kelvin 7 The Combined Gas Law Equation combines Boyle s Law Charles Law and Gay Lussac s Law if the number of moles of the gas n remains constant Combined Gas Law note that all gas calculations must be done in Kelvin assumes number of moles n remains constant 8 Avogadro s Law and the Standard Molar Volume keep in mind that STP includes 1 mol and 22 4 L maintains constant temperature and pressure volume is directly proportional to number of moles assumes temperature T and pressure P remain 1 2 P 1 T 1 P 2 T 2 k P V T P1V 1 T1 P2V 2 T2 V n Avogadro s Law constant V 1 n 1 V 2 n 2 9 Summary of the Gas Laws The Ideal Gas Equation the ideal gas constant R can have different values due to different units R 8 134 J mol K R 8 134 kg m2 s2 K mol R 1 987 cal K mol Ideal Gas Law variables can have any units PV nRT n must be in moles and T must be in Kelvin all other 10 Determination of Molecular Weights and Molecular Formulas of Gaseous Substances empirical formula x n molecular formula where n molar mass empirical mass note that this n is not the same as the n in the previous equations 11 Dalton s Law of Partial Pressures Dalton s Law the sum of the partial pressures of those gases the total pressure exerted by a mixture of ideal gases is Ptotal PA PB PC mole fraction represented by XA a unitless quantity essentially a percentage X A PA Ptota l or PA XA x Ptotal Raoult s Law vapor pressure temperature increases pressure is the number of collisions that the gas molecules have with the side of the container a function of temperature vapor pressure increases as so there is more vapor pressure in a sealed container of boiling water more dots than there is in a sealed container of ice water fewer dots 12 Mass Volume Relationships in Reactions Involving Gases 1 mole of an ideal gas occupies 22 4 liters at standard conditions 1 mol Mm g 6 022 x 1023 molecules 22 4 L 13 The Kinetic Molecular Theory gas particles have the same exact velocity before and after colliding kinetic energy with themselves and the sides of the container the average kinetic energies of different gases are equal at a given temperature KE T where T is absolute temperature the energy a body possesses by virtue of its motion gas particles move faster at a higher temperature than they do at a KE 1 2 mv2 lower temperature relating the Kinetic Molecular Theory to the other gas laws Boyle s Law P 1 V as V increases molecular collisions with container walls decrease and P decreases Dalton s Law Ptotal PA PB PC gases have few intermolecular attractions so their pressures are independent of each other Charles Law V T an increase in temperature raises the molecular velocities thus the V increases to keep the P constant 14 Diffusion and Effusion of Gases see lecture outline 15 Deviations from Ideal Gas Behavior real gases behave ideally at ordinary temperatures and pressures at low temperatures and high pressures real gases do not behave ideally For the Test be able to name the law and tell how each variable is effected based on various information provided in a question be able to draw intermolecular forces