 Properties of Gases  Gases uniformly fill any container  Gases are easily compressed  Gases mix completely with any other gas  Gases exert pressure on their surroundings

 Measuring barometric pressure  The barometer  Invented by Evangelista Torricelli in 1643  Units  mm Hg (torr) 760 torr = 1 atm  newtons/m 2 (pascal (Pa)) 101,325 Pa = 1 atm 101,325 Pa = kPa  Atmospheres 1 atm = standard pressure

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)

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

Charles’ Law (Jacques Charles) The volume of a gas increases linearly with temperature provided the pressure and number of moles remain constant.  Temperature and volume are directly proportional

Charles’ Law continued………..  Temperature must be measured in degrees Kelvin  K = o C  0 K is “absolute zero”

Avogadro’s Law (Amedeo Avogadro) For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles.

Combined gas law – (n remaining constant)

 Derived from existing laws…….  V = k/P, V = bT and V = an  V = (k)(b)(a)(Tn/P)  Constants k, b and a are combined into the universal gas constant R and…..

 Limitations of the Ideal Gas Law  Works 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

Variations of the Ideal Gas Law Density Molar Mass of a gas

At Standard Temperature and Pressure (STP) T = K (0 o C) P = 1 atm (760 torr or kPa) 1 mole of an ideal gas occupies 22.4 L of volume Remember…….. Density = mass/volume and moles (n)= grams/molar mass

“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.

 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):

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

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

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

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.

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.

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.

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

 Mean Free Path  Average distance a molecule travels between collisions  Example: O 2 at STP will travel 1 x m between collisions

 Effusion  Movement of a gas through a small opening into an evacuated container (vacuum)  Graham’s Law of Effusion

 Diffusion  The mixing of gases  Diffusion is complicated to describe both theoretically and mathematically EFFUSIONDIFFUSION

 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

 Pressure  Real gas molecules experience attractive forces