The Gas Laws

1. A gas is composed of particles molecules or atoms – hard spheres far enough apart- ignore volume Empty space The Kinetic Theory of Gases Makes three descriptions of gas particles

2. Particles are in constant random motion. Move in straight lines until they bounce off each other or the walls. 3. Elastic collisions

8 Elastic vs. Inelastic Collisions 8 v1v1 elastic collision inelastic collision POW v2v2 v3v3 v4v4

Kinetic Energy and Temperature Temperature : – Average kinetic energy of the molecules of a substance. Higher temperature faster molecules. At absolute zero (0 K) all molecular motion would stop.

Kinetic Molecular Theory Postulates Evidence 1. Gases are tiny molecules in mostly empty space. The compressibility of gases. 2. There are no attractive forces between molecules. Gases do not clump. 3. The molecules move in constant, rapid, random, straight-line motion. Gases mix rapidly. 4. The molecules collide classically with container walls and one another. Gases exert pressure that does not diminish over time. 5. The average kinetic energy of the molecules is proportional to the Kelvin temperature of the sample. Charles’ Law

Characteristics of Gases Gases expand to fill any container. – random motion, no attraction Gases are fluids (like liquids). – no attraction Gases have very low densities. – no volume = lots of empty space Courtesy Christy Johannesson

Characteristics of Gases Gases can be compressed. no volume = lots of empty space Gases undergo diffusion & effusion. –r–random motion Courtesy Christy Johannesson

Kinetic Molecular Theory Ideal gases… – have no volume. – have elastic collisions. – are in constant, random, straight-line motion. – don’t attract or repel each other. – have an avg. KE directly related to Kelvin temperature Courtesy Christy Johannesson

Real Gases Particles in a REAL gas… – have their own volume – attract each other And are most ideal… – at low pressures – at high temperatures – in nonpolar atoms/molecules Courtesy Christy Johannesson

Properties of Gases V = volume of the gas (liters, L) T = temperature (Kelvin, K) P = pressure (atmospheres, atm) n = amount (moles, mol) R = gas constant (R = L atm / (mol K PV = nRT Gas properties can be modeled using math. Model depends on:

Kinetic theory of gases and … Compressibility of Gases Boyle’s Law P  collision rate with wall Collision rate  number density Number density  1/V P  1/V Charles’ Law P  collision rate with wall Collision rate  average kinetic energy Average kinetic energy  T P  TP  T

Kinetic theory of gases and … Avogadro’s Law P  collision rate with wall Collision rate  number density Number density  n ( or moles) P  nP  n Dalton’s Law of Partial Pressures Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas P total =  P i

Ideal Gas Law Equation

PV/T = K Comparison for a fixed amount of gas (Real gas) Combination of all gas laws Combined Gas Law

Molar Volume Timberlake, Chemistry 7 th Edition, page mol of a STP has a volume of 22.4 L 273 K n He = 1 mole (4.0 g) V He = 22.4 L P = 1 atm 273 K n N = 1 mole (28.0 g) V N = 22.4 L P = 1 atm K n O = 1 mole (32.0 g) V O = 22.4 L P = 1 atm 2 2

Avogadro’s Hypothesis N2N2 H2H2 Ar CH 4 At the same temperature and pressure, equal volumes of different gases contain the same number of molecules. Each balloon holds 1.0 L of gas at 20 o C and 1 atm pressure. Each contains mol or 2.69 x molecules of gas.

Pressure collisions of molecules with the walls of a container force/unit area SI units = Newton/meter 2 = 1 Pascal (Pa)

Pressure KEY UNITS AT SEA LEVEL kPa (kilopascal) or 101,325 Pa 1 atm 760 mm Hg 760 torr 14.7 psi Courtesy Christy Johannesson Sea level

Barometer- measures atmospheric pressure Zumdahl, Zumdahl, DeCoste, World of Chemistry  2002, page 401 Empty space (a vacuum) Hg Weight of the mercury in the column Weight of the atmosphere (atmospheric pressure)

Manometer –measures contained gas pressure U-tube Manometer Courtesy Christy Johannesson

Manometer PbPb PaPa 750 mm Hg P a =

lower pressure Manometer PaPa height 750 mm Hg 130 mm lower pressure 620 mm Hg P a = h = -

880 mm Hg higher pressure higher pressure Manometer PaPa height 750 mm Hg 130 mm P a = h = +

B. Graham’s Law Diffusion Diffusion – Spreading of gas molecules throughout a container until evenly distributed. Effusion Effusion – Passing of gas molecules through a tiny opening in a container

B. Graham’s Law KE = ½mv 2 Speed of diffusion/effusion Speed of diffusion/effusion – Kinetic energy is determined by the temperature of the gas. – At the same temp & KE, heavier molecules move more slowly. – Larger m  smaller v because…

B. Graham’s Law Graham’s Law Graham’s Law – Rate of diffusion of a gas is inversely related to the square root of its molar mass.

Determine the relative rate of diffusion for krypton and bromine. Kr diffuses times faster than Br 2. B. Graham’s Law The first gas is “Gas A” and the second gas is “Gas B”. Relative rate mean find the ratio “v A /v B ”.

A molecule of oxygen gas has an average speed of 12.3 m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions? B. Graham’s Law Put the gas with the unknown speed as “Gas A”.

An unknown gas diffuses 4.0 times faster than O 2. Find its molar mass. B. Graham’s Law The first gas is “Gas A” and the second gas is “Gas B”. The ratio “v A /v B ” is 4.0. Square both sides to get rid of the square root sign.

Gas Law Calculations Ideal Gas Law PV = nRT Ideal Gas Law PV = nRT Dalton’s Law Partial Pressures P T = P A + P B Dalton’s Law Partial Pressures P T = P A + P B Charles’ Law Charles’ Law T 1 = T 2 V 1 = V 2 Boyle’s Law Boyle’s Law P 1 V 1 = P 2 V 2 Gay-Lussac T 1 = T 2 P 1 = P 2 Combined Combined T 1 = T 2 P 1 V 1 = P 2 V 2 Avogadro’s Law Avogadro’s Law Add or remove gas Manometer Manometer Big = small + height R = L atm / mol K 1 atm = 760 mm Hg = kPa Bernoulli’s Principle Bernoulli’s Principle Fast moving fluids… create low pressure Density Density T 1 D 1 = T 2 D 2 P 1 = P 2 Graham’s Law Graham’s Law diffusion vs. effusion