KINETIC THEORY & the GAS LAWS

Kinetic Molecular Theory Based on idea that particles of matter are always in motion Relates the phase of matter to the heat (energy) content of the particles and the forces that act between them

Five assumptions of the kinetic molecular theory of gases. 1. Most of the volume of a gas is empty space. 2. There are NO forces of attraction or repulsion between gas particles. 3. Gas particles are in continuous rapid, random motion and therefore have kinetic energy. 4. Collisions between particles and the walls of the container are elastic. (no energy is lost) 5. All gases at a given temperature have the same kinetic energy. (KE = ½ mv2) temperature & speed direct mass & speed inverse

Real Gases vs. Ideal Gases Ideal gases obey all 5 assumptions Ideal gases don’t exist always some deviation (BUT real gases obey their mathematical laws very closely) Some gases come close to ideal behavior He, Ne, Ar, Xe, Rn H2, O2, N2 Most gases behave ideally at high T and low P

The KMT explains the physical properties of gases. Fluidity: particles flow or slide easily past each other Low Density small mass, large volume Expansion: fill the container; gases have NO definite shape or volume Compressibility: under pressure, gas particles can be easily crowded closer together (decreasing the volume)

physical properties of gases. The KMT explains the physical properties of gases. Diffusion: spontaneous mixing due to random motion; spread from areas of high to low concentration Perfume spreading across the room Effusion: process by which gas particles move through a tiny opening Gas escaping from a hole in a container

Pressure depends on force and area. Pressure: force per unit area SI unit = pascal (Pa) Barometer- used to measure atmospheric pressure The pressure of gases in a closed container is measured by a manometer Force is unchanged, as mass and acceleration due to gravity are unchanged As area decreases, pressure increases

At sea level (normal), it has a value of: 1. 1 atm (atmosphere) Atmospheric Pressure (air pressure): the pressure exerted by all the gas particles in the atmosphere; varies with elevation At sea level (normal), it has a value of: 1. 1 atm (atmosphere) 2. 760 mm Hg (= 760 torr) 3. 101.3 kPa 4. 14.7 psi STP: Standard Temperature and Pressure Standard P = 1 atm Standard T = 0°C = 273 K

Measuring Pressure The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century. The device was called a “barometer” Baro = weight Meter = measure The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high. 9

NO negative temperatures on the Kelvin scale! 0o C = 273 K Kelvin = C + 273 °C = Kelvin – 273 NO negative temperatures on the Kelvin scale! Absolute zero = 0 K = -273oC Never been reached. No molecular motion at this temperature is predicted. STP: Standard Temperature and Pressure Standard P = 1 atm Standard T = 0°C = 273 K

GAS LAWS

Graham’s Law of Effusion (Diffusion) Graham’s Law proves to be an inverse proportion between velocity and molar mass. Graham’s Law states: The effusion rates of gases at the same temp. and pressure are inversely proportional to the square roots of their molar masses. vA = √ MB vB √ MA This means that heavier gases travel slower than lighter gases and vice versa 13

Diffusion Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. 14

Effusion Effusion: describes the passage of gas into an evacuated chamber. 15

Ptotal = pp1 + pp2 + … ppn Dalton’s Law of Partial Pressures A. The total pressure in a closed container is the sum of all of the individual partial pressure (pp) of all the gases in the container Ptotal = pp1 + pp2 + … ppn

B. Gases collected by Water Displacement: Due to water displacement, some of the water evaporates and mixes with the other gas(es) There is a known amount of water vapor per temperature (vapor pressure of water) ***Table A-8 (p. 859) Subtract the water vapor pressure from the total pressure P (total) = P(atm) = P(gas) + P (water) …..or P (gas) = P(atm) – P(water)

I. Combined Gas Law

#32 Combined Gas Law P1V1 = P2V2 T1 T2 This law expresses all variables with a constant number of moles. Why are moles constant? Gases usually undergo changes in T, V and P, not the amount of moles. Text Page 375 24

VI. Combined Gas Laws P1V1 = P2V2 Boyles’ Law: P and V are inversely proportional Assumes constant T P1V1 = P2V2 1=initial 2=final

ROBERT BOYLE

V1/T1 = V2/T2 Charles’ Law: T and V are directly proportional Assumes constant P Form of Thermal Expansion: a substance expands in volume as it is heated V1/T1 = V2/T2

JACQUES CHARLES

Gay-Lussac’s Law: P and T are directly proportional Assumes constant V P1 / T1 = P2 /T2

Joseph-Louis Gay-Lussac

IX. Density & Gases Density D=m/v ΔV: ↑V…↓D ΔP: ↑P… ↓V … ↑D ΔT: ↑T… ↑V…↓D Mass of a gas can be calculated using the density equation

I. Measuring and comparing the Volumes of reacting gases OBSERVATIONS OF GAY-LUSSAC Early 1800’s Gay-Lussac noticed gas volume relationships at a constant temperature and pressure. Hydrogen gas + oxygen gas  water vapor @ constant T and P 2L + 1L  2L 2Volumes + 1 Volume  2 Volumes 45

Hydrogen gas + Chlorine gas  Hydrogen chloride 1L + 1L  2L 1 Volume + 1 Volume  2 Volumes Hydrogen chloride + ammonia  ammonium chloride 1 L + 1L  1L 1 Volume + 1Volume  1 Volume Gay – Lussac noticed small whole number ratios, however, couldn’t explain why the ratio’s occurred. 46

Gay-Lussac’s Law of Combining Volumes : At a constant T and P, the volumes of R and P can be expressed as small whole number ratios. 47

II. Avogadro’s Law An explanation of Gay-Lussac’s Observations Equal volumes of gases (refer to H2 and Cl2) under the same constant conditions of T and P, contain the same number of molecules. 1 mol O2 gas 1mol H2 gas 1 Volume 1 Volume Mass = 32.00 g Mass = 2.02 g 10 molecules 10 molecules 48

Avogadro also proved a direct relationship existed between volume and number of moles (particles) k = Volume n Direct Proportion H2 (g) + Cl2 (g)  2HCl (g) 1 L 1L 2 L Volume 1mol 1 mol 2 mol Moles = n Regardless of mass, 1 mol of any gas at the same T and P, will occupy the same volume. 22.4 L of space = Standard Molar Volume = 1 mol @ STP 49

Diatmoic Molecules Gay-Lussac’s work was explained by Avogadro (1811) H2 (g) + Cl2 (g)  2HCl (g) 1 Volume + 1 Volume  2 Volumes 1L + 1L  2L The simplest ratio, due to charge, for HCl is 1:1 +1, -1 Therefore, Avogadro concluded that hydrogen gas and chlorine gas must be DIATOMIC. The ratio at which certain gases combine supports the existence of diatomic molecules a. Molecules of active gaseous elements are diatomic H2, N2, O2, F2, Cl2, Br2, I2 b. Molecules of noble gases are monatomic   This proved John Dalton to be incorrect. Remember, Dalton said that single atoms and combined atoms do not exist. This proved Gay-Lussac to be correct – This is why Gay-Lussac noticed whole number ratios 50

III. Molar Volume of a gas Standard Molar Volume is… the volume occupied by 1 mole of any gas at STP @ 22.4 L/mol containing the same number of molecules 1 mol O2 gas 1mol H2 gas Volume = 22.4 L Volume = 22.4 L Mass = 32.00 g Mass = 2.02 g 10 molecules 10 molecules 51

Standard Molar Volume Equal volumes of all gases at the same temperature and pressure contain the same number of molecules. - Amedeo Avogadro Density at STP = Mass of one mole / 22.4 L 52

Summary Many conclusions can be made at this point 2.02 g + 70.90  36.46 x 2 Mass H2 (g) + Cl2 (g)  2HCl (g) 1 L 1L 2 L Volume 1mol 1 mol 2 mol Moles = n 1 particle 1 particle 2particles Particles 22.4 L 22.4 L 44.8 L Standard Molar V

Iv. Ideal Gas Law The ideal gas law is a mathematical relationship that helps describe gas behavior. The variables needed include: P, V, T, #moles (n) 54

Derivation of the Ideal Gas Law Shows how the Ideal Gas Law forms. V α n V α T T α P V α 1/P Avogadro Charles’ Gay-Lussac Boyle’s Direct Direct Direct Inverse _____________________________________________________ ______________________________________________________ 55

The Ideal Gas Law states… The volume of a gas varies directly with n and the Kelvin Temperature and inversely with Pressure. The ideal gas law is a combination of all of the separate gas laws Ideal Gas law : PV = nRT 56

V. The Ideal Gas Law Constant = R The value for R is dependent upon Pressure. Prove the derivation of R for 1 mol of a gas @STP R = (1 atm) (22.41410 L) (1 mole) (273.15 K ) R = ______________________ R can also be equal to other values – Calculate with different standard pressure units. 57

Ideal Gas Law in terms of Density n = mol m = mass (g) M = Molar mass (g/mol) D = Density m/V PV = nRT Substitute variables…. m/M = n so …….. PV = mRT so……. M = mRT M PV so…. M = DRT P D = MP RT 58

Vi. Gas Stoichiometry These calculations involve past knowledge and should NOT be difficult at this point in Chemistry. Remember: Coefficients in a balanced chemical equation represent mole ratio’s, volume ratio’s and particle ratio’s. Review Mole Bridge!!! 59

PV = nRT X. Ideal Gas Law…quantifies gas in terms of moles R (ideal gas constant) = 8.314 n = number of moles Deviations from Ideal occur at High P & Low T (system forced to a liquid)

Molar Volume…the volume of one mole of ANY gas at STP (standard temperature and pressure)… 22.4 L …at STP: ALL gases: 1. occupy the same space (22.4 L) 2. have the same # of molecules (6.022x1023)