5 Postulates of Kinetic Theory 1) Spherical molecules in constant, random straight-line motion 2) “Elastic” collisions 3) Point masses 4) No interactions 5) Avg. KE of gas molecules  Temperature

Random, straight-line motion? The gas particles move in straight lines between collisions. Recall: straight-line motion implies that no forces are acting on the particle.

Total KE is conserved. Total KE before collision = Total KE after collision. BUT KE may be TRANSFERRED! Elastic Collisions

Kinetic energy may be transferred between particles.

Inelastic Collision Kinetic Energy is NOT conserved!

Point Mass The volume of the gas molecule itself is tiny compared to the distance between gas molecules. In other words, the distance between the molecules is more important than their actual size. We say the volume of each molecule is insignificant; but they need to be a point so we can locate them in space (give them coordinates).

Temperature of a gas T gas  KE avg So all gases at the same T have the same average kinetic energy. Recall that KE = ½ mv 2.

At the same temperature, which of the following gases diffuses most rapidly? He Ne Ar Kr Xe Lightest is fastest!

At the same temperature, which of the following gases diffuses most slowly? He Ne Ar Kr Xe Heaviest is slowest!

For gases at the same Temperature KE = ½ mv 2 Lighter gas particles have higher average speeds than heavier gas particles at the same temperature.

Ideal Gas Gas that obeys all 5 assumptions of the kinetic theory all of the time. It doesn’t exist. It’s a model.

Real Gas Most real gases obey the kinetic theory most of the time.

Which assumptions of the kinetic theory hold up? 1. Spherical molecules in random, straight-line motion 2. “Elastic” collisions

Which assumptions of the kinetic theory break down? 1. Point masses 2. No interactions

When do the assumptions of the kinetic theory break down? When the gas molecules are close to each other.

When are the gas molecules close to each other? At high pressure & low temperature.

When are the gas molecules far apart from each other? At low pressure & high temperature.

How do the gas molecules act when they are far apart from each other? Good!

Real Gases Molecules are always attracted to one another, even if just weakly. Molecules take up space.

What are the properties of gases? 1. Have mass 2. Take the shape & volume of their container 3. Compressible 4. Flow 5. Diffuse 6. Exert Pressure

Pressure Force/Area

Pressure results from? Collisions of the gas molecules with the walls of the container.

With a Barometer! P = D Hg  g  h but since D Hg & g don’t change, we just report  h. How do you measure air pressure?

How do you measure the pressure of a confined gas? With a manometer! Attach gas bulb hereTo vacuum pump Closed-ended manometer A closed ended manometer:  h is directly proportional to the pressure of the confined gas. P gas = D Hg  g  h but we just say  h most of the time.

How do you measure the pressure of a confined gas? With a manometer! An open ended manometer:  h tells you how far away the gas pressure is from the air pressure. So you also need a barometer to measure P atm. AAAAAAAA P gas > P atm P gas = P atm +  h P gas < P atm P gas = P atm -  h

Pressure depends on? (microscopically) # of impacts per unit time and force of each impact

Pressure depends on? (macroscopically) # of gas molecules per unit volume And temperature

Pressure Units 1 atm = 760 torr = 760 mm Hg = kPa = 101,325 Pa = 14.7 lb / in 2 or psi

Temperature A measure of the avg. kinetic energy of the particles of a substance.

4 variables needed to completely describe a gas- phase system? 1.Temperature 2.Pressure 3.Volume 4.# of moles

Can change size: balloons or cylinders with pistons Elastic containers

Walls are fixed. Size does not change. Rigid Containers

STP Standard Temperature & Pressure 1 atm or kPa or 760 torr 0  C or 273K

Boyle’s Law For a fixed mass and temperature, the pressure-volume product is a constant.

Boyle’s Law PV = k where k = a constant Constant T, n

Boyle’s Law P 1 V 1 = P 2 V 2

Graph of Boyle’s Law Hyperbola – it’s an inverse relationship!

Graph of Boyle’s Law, Pressure vs. Volume

Double the pressure Volume goes to ½ the original volume

Triple the pressure Volume goes to 1/3 the original volume

Halve the pressure Volume goes to 2 X the original volume

Quadruple the pressure Volume goes to 1/4 of the original volume

What does the graph of a direct relationship look like?

Which temperature scale has a direct relationship to molecular velocity? Kelvin: 0 K means 0 speed.

Which graph shows the relationship between average KE and Kelvin temperature? The top graph!

Graph of Volume vs. Kelvin Temperature It’s a direct relationship.

Math expression of Volume & Kelvin Temperature V 1 /T 1 = V 2 /T 2 Charles’ Law Constant P, n

What happens to the volume when the Kelvin temperature is doubled? The volume doubles!

What happens to the volume when the Kelvin temperature is tripled? The volume triples!

What happens to the volume when the Kelvin temperature is halved? The volume is halved!

What happens to the Kelvin temperature when the volume is halved? It’s halved!

Graph of Pressure vs. Kelvin Temperature It’s a direct relationship. Constant V, n

Math expression for pressure & temperature. P 1 /T 1 = P 2 /T 2 Gay-Lussac’s Law

What happens to the pressure when the Kelvin temperature is doubled? The pressure is doubled.

What happens to the pressure when the Kelvin temperature is halved? The pressure is halved.

What happens to the pressure when the Kelvin temperature is tripled? The pressure is tripled.

What happens to the Kelvin temperature when the pressure is doubled? The Kelvin temperature is doubled.

Combined Gas Law For constant n: P 1 V 1 = P 2 V 2 T1T1 T2T2 If they do NOT mention a variable, it’s constant. Constant variables are the same on both sides, so you can neglect them.

V = kn The volume of a gas is directly proportional to the # of moles. At STP, k = 22.4 liters/mole Avogadro’s Law Constant T, P

What is another way to state Avogadro’s Law? Equal volumes of gases at the same temperature & pressure have equal numbers of molecules.

These 2 boxes have the same: a)Massc) # of molecules b)Densityd) # of atoms HeN2N2

Ideal Gas Law Equation of state for a gas. Relates the macroscopic variables that describe the system. PV = nRT R = gas law constant. In US, we use R = Liter  atm mole  K

Ideal Gas Law units Governed by R. If R = L  atm then mole  K P in atm V in liters T in Kelvins n in moles PV = nRT

moles & mass From Table T: # of moles = given mass gram-formula mass

Ideal Gas Law Extension #1 Use it to find molar mass, M PV = nRT = RT mass M Rearrange: M = massRT PV

Ideal Gas Law Extension #2 Use it to find the density of a gas: PV = nRT = mRT where m = mass M Density = m/V so MP = D or M = DRT RTP

Density of a gas at STP Only at STP: Density of a gas = Molar Mass (grams/mol) 22.4 (Liters/mol)

Vapor Gas phase of a substance that is normally a liquid at room temperature (298  C).

How do you measure vapor pressure? Closed container, at equilibrium (both liquid & gas phases present) Manometer!

Vapor pressure depends on? Temperature of the liquid phase ONLY! BOTH phases MUST be present for it to be a vapor. If no liquid is present, it’s a gas.

Handy result: since vapor pressure only depends on the temperature of the liquid phase … It can be tabulated! You don’t have to measure it every time you do an experiment!

What is Dalton’s Law of Partial Pressures? P tot = P 1 + P 2 + P 3 + P 4 + …

Gas Collection over Water The test tube was full of water at the beginning. As the reaction proceeds, the gas displaces the water. There is also some water vapor up there. When the water levels inside and outside line up, then the gas pressure + the water vapor pressure is equal to the air pressure!

Gas Collection over Water P inside = P atm when levels align N2N2 N 2 (g) + H 2 O(g) = P gas P atm = P N2 + P H2O But since it’s water vapor, we can look up P H2O in a table. P N2 = P atm – P H2O You need a barometer to measure P atm.

Dry volume of a gas at STP mLs of a gas is collected over water at 23  C. P atm = torr. Find the volume of the dry gas at STP. 1.Look up the vapor pressure of water at 23  C. It’s 21.1 torr. 2.Find the pressure of the gas alone. P gas = P atm - P H2O = = torr 3.Use combined gas law to find volume of the gas at STP. V 2 = V 1 X P X T P T Correction ratios!

Diffusion Spontaneous mixing of two substances caused by their random motion. The two gases move through each other.

Effusion Process by which gas particles pass through a tiny opening.

Graham’s Law of Effusion The rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. Another way to find the molar mass of a substance!

Graham’s Law of Effusion KE 1 = ½ m 1 v 1 2 and KE 2 = ½ m 2 v 2 2 At the same temperature, these two gases have the same average KE! ½ m 1 v 1 2 = ½ m 2 v 2 2 m 1 / m 2 = v 2 2 / v 1 2 Take the square root of both sides.

Graham’s Law of Effusion Estimate the molar mass of a gas that effuses at 1.6 times the effusion rate of CO 2. = 1.6 Square both sides! m CO2 /m unk = 2.56 or 44/x = 2.56 X = 17 Graham’s Law – general. Stick in the labels for this problem