CHAPTER 5 GASES 5 1 PRESSURE Properties Gases

CHAPTER 5 - GASES

5. 1 PRESSURE � Properties � Gases of Gases uniformly fill any container � Gases are easily compressed � Gases mix completely with any other gas � Gases exert pressure on their surroundings

5. 1 PRESSURE � Measuring � The barometric pressure barometer � Invented by Evangelista Torricelli in 1643 � Units � mm Hg (torr) � newtons/m 2 (pascal (Pa)) � Atmospheres 760 torr = 1 atm 101, 325 Pa = 101. 3 k. Pa 1 atm = standard pressure

5. 2 THE GAS LAWS OF BOYLE, CHARLES AND AVOGADRO Boyle’s law (Robert Boyle) The product of pressure times volume is a constant, provided the temperature and number of moles remains the same � Pressure and volume are inversely related � Volume increases linearly as the pressure decreases (1/P)

5. 2 THE GAS LAWS OF BOYLE, CHARLES AND AVOGADRO Boyle’s Law Continued…… � At constant temperature, Boyle’s Law can be used to fine a new volume or pressure Boyle’s law works best at low pressures � Gases that obey Boyle’s Law are called Ideal Gases �

5. 2 THE GAS LAWS OF BOYLE, CHARLES AND AVOGADRO Charles’ Law (Jacques Charles) The volume of a gas increases linearly with temperature provided the pressure and number of moles remain constant. � Temperature proportional and volume are directly

5. 2 THE GAS LAWS OF BOYLE, CHARLES AND AVOGADRO Charles’ Law continued………. . � Temperature must be measured in degrees Kelvin �K = o. C + 273. 15 � 0 K is “absolute zero”

5. 2 THE GAS LAWS OF BOYLE, CHARLES AND AVOGADRO Avogadro’s Law (Amedeo Avogadro) For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles.

5. 3 THE COMBINED GAS LAW Combined gas law – (n remaining constant)

5. 3 THE IDEAL GAS LAW � Derived from existing laws……. �V = k/P, V = b. T and V = an � V = (k)(b)(a)(Tn/P) � Constants k, b and a are combined into the universal gas constant R and…. .

5. 3 THE IDEAL GAS LAW � Limitations � Works of the Ideal Gas Law well at low pressure and high temperatures � Most gases do not behave ideally above 1 atm � Does not work well near the condensation conditions of a gas

5. 3 THE IDEAL GAS LAW Variations of the Ideal Gas Law Density Molar Mass of a gas

5. 4 GAS STOICHIOMETRY At Standard Temperature and Pressure (STP) T = 273. 15 K (0 o. C) P = 1 atm (760 torr or 101. 3 k. Pa) 1 mole of an ideal gas occupies 22. 4 L of volume Remember……. . Density = mass/volume and

5. 5 DALTON’S LAW OF PARTIAL PRESSURE “For a mixture of gases in a container, the total pressure exerted is the sum of the pressures each gas would exert if it were alone. ” It is the total number of moles that is important, not the identity or composition of the gas particles.

5. 5 DALTON’S LAW OF PARTIAL PRESSURE

5. 5 DALTON’S LAW OF PARTIAL PRESSURE � Mole fraction � The ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture � For an ideal gas, the mole fraction (x):

5. 6 THE KINETIC MOLECULAR THEORY OF GASES KMT related to Ideal Gases � The particles are so small compared to the distanced between them that the volume of the individual particles can be assumed to be zero � The particles are in constant motion. Collisions of the particles with the walls of the container cause pressure. � Assume that the particles exert no force on each other � The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas

5. 6 THE KINETIC MOLECULAR THEORY OF GASES Explaining Observed Behavior with KMT 1. P and V (T, n = constant): As V is decreased, P increases V decrease causes a decrease in the surface area. Since P is force/area, the decrease in V causes the area to decrease, increasing the P

5. 6 THE KINETIC MOLECULAR THEORY OF GASES Explaining Observed Behavior with KMT 2. P and T (V, n = constant): As T increases, P increases The increase in T causes an increase in average kinetic energy. Molecules moving faster collide with the walls of the container more frequently and with greater force

5. 6 THE KINETIC MOLECULAR THEORY OF GASES Explaining Observed Behavior with KMT 3. V and T (P, n = constant): As T increases, V also increases Increased T creates more frequent more forceful collisions. V must increase proportionally to increase the surface area and maintain P.

5. 6 THE KINETIC MOLECULAR THEORY OF GASES Explaining Observed Behavior with KMT 4. V and n (P, T = constant): As n increases, V must increase Increasing the number of particles increases the number of collisions. This can be balanced by an increase in V to maintain constant P.

5. 6 THE KINETIC MOLECULAR THEORY OF GASES Explaining Observed Behavior with KMT 5. Dalton’s law of partial pressures P is independent of the type of gas molecule KMT states that particles are independent, and V is assumed to be zero. The identity of the molecule is therefore unimportant.

5. 6 THE KINETIC MOLECULAR THEORY OF GASES Root Mean Square Velocity � velocity of a gas in dependent on mass and temperature � velocity of gases is determined as an average �M = mass of one mole of gas particles in kg � R = 8. 31 J/K · mol

5. 6 THE KINETIC MOLECULAR THEORY OF GASES � Mean Free Path � Average distance a molecule travels between collisions � Example: O 2 at STP will travel 1 x 10 -7 m between collisions

5. 7 EFFUSION AND DIFFUSION � Effusion � Movement of a gas through a small opening into an evacuated container (vacuum) � Graham’s Law of Effusion

5. 7 EFFUSION AND DIFFUSION � Diffusion � The mixing of gases � Diffusion is complicated to describe both theoretically and mathematically EFFUSION DIFFUSION

5. 8 REAL GASES AND VAN DER WAALS EQUATION � Volume � Real gas molecules do have volume � Volume available is not 100% of the container volume �n = number of moles � b = is an empirical constant, derived from experimental results

5. 8 REAL GASES AND VAN DER WAALS EQUATION � Pressure � Real gas molecules experience attractive forces