Kinetic Molecular Theory Matter is composed of tiny particles (atoms, molecules or ions) with definite and characteristic sizes that never change. The particles are in constant random motion, that is they possess kinetic energy. E k = 1 / 2 mv 2 The particles interact with each other through attractive and repulsive forces (electrostatic interactions), that is the possess potential energy. U = mgh The velocity of the particles increases as the temperature is increased therefore the average kinetic energy of all the particles in a system depends on the temperature. The particles in a system transfer energy form one to another during collisions yet no net energy is lost from the system. The energy of the system is conserved but the energy of the individual particles is continually changing.

Properties of Gases  DIFFUSION Diffusion is the ability of two or more gases to mix spontaneously until a uniform mixture is formed. Example: A person wearing a lot of perfume walks into an enclosed room, eventually in time, the entire room will smell like the perfume.   EFFUSION Effusion is the ability of gas particles to pass through a small opening or membrane from a container of higher pressure to a container of lower pressure. The lighter the gas, the faster it moves. The General Rule is: The lighter the gas, the faster it moves. Graham’s Law of Effusion: Rate of effusion of gas A = √ (molar mass B / molar mass A) Rate of effusion of gas B The rate of effusion of a gas is inversely proportional to the square root of the molar mass of that gas.

PRESSURE A physical property of matter that describes the force particles have on a surface. Pressure is the force per unit area, P = F/A Pressure can be measured in: atmosphere (atm)atmosphere (atm) millimeters of mercury (mmHg)millimeters of mercury (mmHg) (torr) after Torricelli, the inventor of the mercury barometer (1643)(torr) after Torricelli, the inventor of the mercury barometer (1643) pounds per square inch (psi)pounds per square inch (psi) 1 atm = 760 mmHg = 760 torr = psi

TEMPERATURE A physical property of matter that determines the direction of heat flow. Measured on three scales. Fahrenheit o F Celsius o CFahrenheit o F Celsius o C Kelvin KKelvin K o F = (1.8 o C) + 32 o C = ( o F - 32)/1.8 o F = (1.8 o C) + 32 o C = ( o F - 32)/1.8 K = o C K = o C

EMPIRICAL GAS LAWS Boyle’s Law P 1 V 1 = P 2 V 2 Charles’ LawV 1 / T 1 = V 2 / T 2 Guy-Lussac’s LawP 1 / T 1 = P 2 / T 2 Avogadro’s LawV 1 / n 1 = V 2 / n 2 Combined Gas Law P 1 V 1 / T 1 = P 2 V 2 / T 2 Ideal Gas Law PV = nRT P = pressure (atm)V = volume (L) n = chemical amount (mol)T = Temperature (K) R = ideal gas constant = L-atm / mol-K

Empirical Gas Laws 1. At 25 o C, a sample of N 2 gas under a pressure of 689 mmHg occupies 124 mL in a piston-cylinder arrangement before compression. If the gas is compressed to 75% of its original volume, what must be the new pressure (in atm) at 25 o C? First make a list of the measurements made: P 1 =689 mmHgV 1 = 124 mL P 2 = ?V 2 = 75% V1 From the variables, choose the appropriate equation, in this case Boyle’s Law: P 1 V 1 =P 2 V 2 (689 mmHg) (124 mL) = P 2 (0.75 x 124 mL) Solve for P 2 : P 2 = (689mmHg) (124 mL) / (93 mL) = 919 mmHg Now convert to atm: 1.21 atm 919 mmHg (1 atm / 760 mmHg) = 1.21 atm

Empirical Gas Laws 2. The gas in a Helium filled ball at 25 o C exerts a volume of 4.2 L. If the ball is placed in a freezer and the volume decreases to 1/8 of its original value, what is the temperature inside the ball? First make a list of the measurements made: V 1 =4.2 atmT 1 = 25 o Cc = V 2 = 1/8 P 1 T 2 = ? From the variables, choose the appropriate equation, in this case Charles’ Law: V 1 /T 1 =V 2 /T 2 (V 1 ) / (298 K) = (1/8 V 1 ) / T 2 Solve for T 2 : T 2 = [(298 K) (1/8 V 1 )] / (V 1 ) = 298 / 8 = 37.3 K or -235 o C 3. A balloon containing 6.50 grams of NH 3 has a volume of L at a temperature of 20.0 o C and a pressure of torr. What would be the pressure of NH 3 if the volume decreased to 2.50 L without a change in temperature? Pressure of NH 3 = 2.84 x 10 3 torr.

COMBINED GAS LAW A gas occupies a volume of 720 mL at 37 o C and 640 mmHg pressure. Calculate the volume the gas would occupy at 273 K and 1 atm. P 1 V 1 / T 1 = P 2 V 2 / T 2 rearranged to solve for V 2 is: V 2 = P 1 V 1 T 2 / P 2 T 1 V 2 = (640 mmHg)(720 mL) (273 K) / (760 mmHg) (310 K) V 2 = 534 mL

COMBINED GAS LAW A gas occupies a volume of 720 mL at 37 o C and 640 mmHg pressure. –Calculate the pressure if the temperature is increased to 1000 o C & the volume expands to 900 mL. –Calculate the temperature if the pressure is decreased to 10 torr & the volume is reduced to 500 mL. P 2 = 2.1 x 10 3 mmHg T 2 = 3.4 K or -270 o C

Avogadro’s Hypothesis Avogadro pictured the moving molecule as occupying a small portion of the larger space apparently occupied by the gas. Thus the “volume” of the gas is related to the spacing between particles and not to the particle size itself. Imagine 3 balloons each filled with a different gas (He, Ar, & Xe). These gases are listed in increasing particle size, with Xe being the largest atom. According to Avogadro’s Hypothesis, the balloon filled with one mole of He will occupy that same volume as a balloon filled with one mole of Xe. V  nSo for a gas, the “volume” and the moles are directly related. V  n

Avogadro’s Hypothesis A sample of N 2 gas at 3.0 atm and 20.0 o C is known to occupy a volume of 1.43 L. What volume would a mole sample of NH 3 gas occupy at the same pressure and temperature? First calculate the number of moles of nitrogen gas: PV = nRT where P = 3.0 atm, V = 1.43 L, R = L-atm/mol-K, and T = 20.0 o C = 293K n = PV / RT = (3.0 atm x 1.43L) / (0.082 L-atm/mol-K x 293K) = moles of N2N2 So since the moles of N2 N2 is mol and the moles of ammonia is mol according to Avogadro’s hypothesis the volume of NH 3 at that pressure and that temperature is 1.43 L, the same!!!

DALTON’S LAW OF PARTIAL PRESSURES If there is more than one gas present in a container, each gas contributes to the total pressure of the mixture. P total = P gas A + P gas B + P gas C … If the total pressure of a system was 2.5 atm, what is the partial pressure of carbon monoxide if the gas mixture also contained 0.4 atm O 2 and 1.48 atm of N 2 ? P T - P O2 - P N2 = P CO 2.5 atm atm atm = 0.62 atm

PRACTICE PROBLEM # 20a 1. You prepared carbon dioxide by adding aqueous HCl to marble chips, calcium carbonate. According to your calculations, you should obtain 79.4 mL of carbon dioxide at 0 o C and 760 mmHg. How many milliliters of gas would you obtain at 27 o C at the same pressure? 2. Divers working from a North Sea drilling platform experiences pressures of 50 atm at a depth of 5.0 x 10 2 m. If a balloon is inflated to a volume of 5.0 L (the volume of a lung) at that depth at a water temperature of 4.0 o C, what would the volume of the balloon be on the surface (1.0 atm) at a temperature of 11 o C? 3. What volume would 5.30 L of H 2 gas at 0 o C and 760 mmHg occupy if the temperature was increased to 70 o F and the pressure to 830 torr? 4. The pressure gauge reads 125 psi on a m 3 compressed air tank when the gas is at 33.0 o C. To what volume will the contents of the tank expand if they are released to an atmospheric pressure of 751 torr and a temperature of 13 o C? 5. A gas has a volume of mL at atm. What will be its pressure (in torr) if the volume is changed to L? 87.3 mL 256 L 5.23 L m torr

PRACTICE PROBLEM # 20a 6. Which of the following statements is false? a) If the Celsius temperature is doubled, the pressure of a fixed volume of gas would double. b) All collisions between gas molecules are perfectly elastic (no energy is lost) according to KMT. c) The volume of gas is inversely proportional to the temperature of gas present (P constant) d) Gases are capable of being greatly compressed. 7. Which of the following statements are true? a) In a large container of O 2 gas the pressure exerted by the oxygen will be greater at the bottom of the container. b) Of the three states of matter, gases are the most compact and the most mobile. c) The formula of ozone is 3 O 2. d) Molecules of O 2 gas and H 2 gas at the same temperature will have the same average kinetic energies and the same average velocities. C D

GROUP STUDY PROBLEMS 1. A sample of O 2 gas initially at 0 o C and 1.0 atm is transferred from a 2-L container to a 1-L container at constant temperature. a) What effect does this change have on the average kinetic energy of the gas molecules? b) What effect does the total number of collisions of O 2 molecules with the container walls in a unit time? 2. At constant pressure, a student needed to decrease a volume of 155 mL of Ne gas by 32.0%. To what temperature, (in o C), must the gas be cooled if the initial temperature was 21 o C? 3. A sample of CO 2 gas has a volume of L at a pressure of 789 torr and a temperature of 30 o C. What will be the temperature if the pressure was increased to 900 torr & the volume decreased to 95.0 L? F 2 gas, which is dangerously reactive, is shipped in steel containers of 30.0 L capacity, at a pressure of 10.0 atm at 26.0 o C. What should be the volume of the tank if the pressure is increased to torr & the temperature is 43.0 o C?