I - Chapter 12 Gases Revisited “Ideal gas” - An ideal gas is one that behaves like our mental picture predicts.

Section 1 Gases Revisited

What are the characteristics of an “Ideal” Gas? 1) How big are gas molecules? Gas molecules are tiny and insignificant compared to the space between them. Because of this different gases will usually behave the same.

What are the characteristics of an “Ideal” Gas? 1) How big are gas molecules? The volume that a sample of gas occupies depends on how many molecules are in the sample. …not on how big the molecules are.

What are the characteristics of an “Ideal” Gas? 2) How do the molecules move? Molecules move in a straight line until they run into one another where they can transfer kinetic energy to one another. We don’t notice this since they’re not colliding with us.

What are the characteristics of an “Ideal” Gas? 2) How do the molecules move? Collisions are “elastic” Elastic means that no energy is lost during the collision. So molecules can exchange energy with each other, but the temperature should remain the same.

What are the characteristics of an “Ideal” Gas? 2) How do the molecules move? Their motion and collisions create pressure to hold up the gas. The more molecules or faster they move should make pressure get higher?

What are the characteristics of an “Ideal” Gas? 2) How do the molecules move? Their motion and collisions create pressure to hold up the gas. The volume the gas takes up will depend on the number of molecules in the sample and their speed.

What are the characteristics of an “Ideal” Gas? 3) Are there intermolecular sticky forces like in liquids and solids? Gases appear to have little or no sticky forces holding molecules together. They might if we could get them close together.

What are the characteristics of an “Ideal” Gas? 3) Are there intermolecular sticky forces like in liquids and solids? For this reason gases made of large “sticky” molecules act just like gases made from little molecules (CO2 vs. H2 ) Because of this different gases will usually behave the same.

What are the characteristics of an “Ideal” Gas? 4) How are gases with small molecules different from gases with big molecules? Recall that at the same temperature, two different samples will have molecules with the same “average kinetic energy”?

What are the characteristics of an “Ideal” Gas? 4) How are gases with small molecules different from gases with big molecules? (KE = ½ mv2) Energy is a function of speed (velocity - V) and mass – m

What are the characteristics of an “Ideal” Gas? 4) How are gases with small molecules different from gases with big molecules? …so small molecules have to move faster to make up for their lower mass.

What are the characteristics of an “Ideal” Gas? 4) How are gases with small molecules different from gases with big molecules? Large molecules move slow so their kinetic energy will be the same as that of the smaller molecules

Why does a helium balloon deflate faster than an air balloon? Here’s an example to illustrate this: Effusion – Escape of a gas through a pin hole Why does a helium balloon deflate faster than an air balloon?

Which molecules will find the hole the quickest? Here’s an example to illustrate this: Effusion – Escape of a gas through a pin hole Which molecules will find the hole the quickest?

Helium molecules move faster, will find the hole sooner. Here’s an example to illustrate this: Effusion – Escape of a gas through a pin hole Helium molecules move faster, will find the hole sooner.

Test Your Understanding He (4g) NH3 (17g) O2 (32g) The following are trick questions: 1. If each sample above contained 1 mole of molecules, which sample should occupy the largest volume? All have the same volume, Why?

Test Your Understanding He (4g) NH3 (17g) O2 (32g) The following are trick questions: 2. As molecules collide over time, what should happen to the pressure inside each balloon? It would stay the same, Why?

Test Your Understanding He (4g) NH3 (17g) O2 (32g) The following are trick questions: 3. Which sample will have the strongest IM sticky forces? None, Why?

Try these regents questions:

Try these regents questions:

Try these regents questions:

Section 2A The gas laws

Section II - THE GAS LAWS: Math relationships between Pressure, volume and temperature for ideal gases Click here to try this online simulation

Pressure vs. Volume (Boyle’s law) More pressure Smaller volume The Volume of a gas is inversely proportional to its pressure, If temperature is kept constant… (the same)

This means that when one increases, the other decreases by a proportional quantity.

Ex: If pressure is doubled, volume becomes one-half Or If volume is doubled, pressure becomes one-half

Lets use our Kinetic molecular theory to explain why: (molecules confined to smaller space collide more, and create more pressure)

Lets measure the volume as pressure increases Pressure vs. Volume (Boyle’s law) Ex: A sample of a gas is confined to a closed container with a movable piston Lets measure the volume as pressure increases

Lets measure the volume as pressure increases Notice as pressure increases, volume decreases Press Vol Trial 1 50 kPa 6 liters Trial 2 100 kPa 3 liters Trial 3 150 kPa 2 liters

Lets measure the volume as pressure increases Notice: P x V always = 300 k Press Vol Trial 1 50 kPa 6 liters Trial 2 100 kPa 3 liters Trial 3 150 kPa 2 liters x = 300 x = 300 x = 300

Lets measure the volume as pressure increases P x V is a constant The symbol for a constant is “k” k Press Vol Trial 1 50 kPa 6 liters Trial 2 100 kPa 3 liters Trial 3 150 kPa 2 liters x = 300 x = 300 x = 300

Lets measure the volume as pressure increases Ex: If pressure is reduced to 25, what is the new volume? P x V = 300 25 x ? = 300

Lets measure the volume as pressure increases Since P x V is a constant then P1 x V1 = P2 x V2 = P3 x V3 etc.

So now we have a formula for these types of problems: P1 x V1 = P2 x V2 Lets use the initial values: 50 x 6 = P2 x V2 And our new value for Pressure: 50 x 6 = 25 x V2 And solve for the new volume:

So now we have a formula for these types of problems: P1 x V1 = P2 x V2 50 x 6 = 25 x V2 25 25 12 liter = V2

Pressure vs. Volume (Boyle’s law) Ex: A sample of a gas is confined to a closed container with a movable piston Pressure Volume k 1 50 6 300 2 100 3 300 3 150 2 etc. Graph the values: This an hyperbola: It shows an inverse relationship

Try one: P1= Show work here: P1V1 = P2V2 V1 = P2 = At a pressure of 240 kPa the gas above occupies a volume of 25 liters. Calculate the new volume when the pressure drops to 100 kPa. P1= 240 kPa Show work here: P1V1 = P2V2 V1 = 25 L P2 = 100 kPa

THE GAS LAWS: Math relationships between Pressure, volume and temperature for ideal gases Volume vs. Temperature (Charles law) The Volume of a gas is directly proportional to Kelvin temperature (as long as pressure is kept the same!) As temperature increases, volume increases Why? (Molecules move faster, push out …and volume expands)

THE GAS LAWS: Math relationships between Pressure, volume and temperature for ideal gases Volume vs. Temperature (Charles law) Volume / Temperature k 200 mL 100 kelvins 2 600 mL 300 kelvins 2 100 mL 50 kelvins 2 Notice V ÷ T = 2 So V/T = k Equation: V1 V2 T1 T2 =

THE GAS LAWS: Math relationships between Pressure, volume and temperature for ideal gases V1 V2 T1 T2 = A different gas has a volume of 1.0 liter at 200 Kelvin's. If temperature is reduced to 50 K, what is the new volume? Substitute values and solve: 1.0 L = V2 200 K 50 K (1.0 L)(50 K) = (200 K )V2 (1.0 L)(50 K) = V2 (200 K) V2 = 0.25 L

THE GAS LAWS: Math relationships between Pressure, volume and temperature for ideal gases Graphing:

Where is absolute zero Kelvin? Cool a gas until its molecules stop moving Absolute zero is the temperature at which gas molecules would stop moving. -273.14oC 0 50 100 150 200 250 300 Kelvins

Do these Practice problems A 150. mL sample of a gas at standard pressure (1 atm) is compressed to 125 mL. What is its new pressure? A 150 ml sample of a gas at standard temp (00C) is heated to 250C. What is its new volume? Show work here: P1V1 = P2V2 1.2 atm Show work here: V1 = V2 T1 T2 Don’t forget: 0 o C + 273 = 163 ml 25 o C + 273 =

Pressure vs. Temperature (Gay-Lussac’s law) pressure is directly proportional to Kelvin Temp. As Kelvin temp increases, pressure increases P/T=K P1 = P2 T1 T2 (KMT: faster molecules collide more, increase pressure) Ex: an “empty” 0.5 liter aerosol can at 250C is heated to 8000C. What is the final pressure inside the can? P1 = 1 atm T1 = 250C + 273 = 298 K P2 = ? T2 = 800 + 273 = 1073 K P1 = P2 T1 T2 P2 = 3.6 atm (1 atm) = P2 (298 K) (1074 K)

Combined laws (Three equations in one!) P V and T P1V1 = P2V2 T1 T2 Ex: 100 mL of a gas at STP has its temp increased to 546 K while its pressure is increased to 2 atmospheres. What is the new volume? (1 atm)(100 mL) = (2 atm) V2 (273 K) (546 K) (1 atm)(100 mL) (546 K) = (273 K)(2 atm) V2 (1 atm)(100 mL) (546 K) = V2 100 mL = V2 (273 K)(2 atm) Why didn’t the volume change?

Three equations in one. If variables are P1V1 = P2V2 P1V1 = P2V2 Held constant: T1 T2 Boyles law P1V1 = P2V2 V1 = V2 Charles T1 T2 T1 T2 P1V1 = P2V2 P1 = P2 etc. T1 T2 T1 T2

The PTV Card will help you check Keeping Temp constant Volume increases If pressure decreases

P T V P T V PTV Card Volume increases If pressure Temperature Keeping pressure constant

P T V P T V PTV Card Keeping volume constant If Temperature decreases pressure decreases

Do these Practice problems: P T V 3. A 200 mL aerosol can contains gas under pressure at room temperature (270C). If its initial pressure is 500 kpa. What pressure will the gas exert when its temperature is increased to 627 0C?

P T V 4) A 5.0 Liter He balloon is released and rises into the air. The temperature decreases from 300 k to 250 k, while the pressure decreases from 100 kpa to 50 kpa. What is the final volume of the balloon? P T V

Learning Check Describe the molecules in an ideal gas. In terms of the kinetic theory, explain why gas pressure increases while its volume decreases? Why do aerosol containers contain the label “do not incinerate? For the graph below estimate the value of the k constant.

Section 2B Other stuff

Are our Assumptions about ideal gases always true?: Molecules act like they have no volume (far apart relative to their small size) Assumption 2- Molecules have no attraction for each other (they move so fast, the weak forces are not noticeable)

Are our Assumptions about ideal gases always true?: Gases will act most ideal when the molecules are Far apart ….. (at low pressure) Moving fast …. (at high temperature) Also, Small molecules like H2 and He are more ideal (Must move faster to make up for their tiny size)

Gases will begin to deviate when molecules are Close together….. (as pressure increases) Moving slow…. (as temperature decreases)

sticky forces attract molecules Deviations- Gases will Deviate (they won’t behave according to the gas laws) when molecules are… Moving slowly (at low temperature) sticky forces attract molecules The Deviant

When molecules are Close together (at high pressure) larger molecules’ size interfere with each other The Deviant Large molecules deviate more than small ones. Ex: CO2 (mass = 44) moves slower, and has stronger sticky forces, than He or H2

Where are deviations apparent? Examples: Air cools as it rises up (its cold on mountain tops?) Why? Kilimanjaro in Africa

Where are deviations apparent? As air rises, the pressure on it decreases. It expands (As P decreases, V increases) Sticky forces slow molecules down as they move away from each other so Temp decreases. Kilimanjaro in Africa

Gases can be liquefied at Low temperatures and high pressures Gas liquefaction: Gases can be liquefied at Low temperatures and high pressures Push Molecules close together, and Cool them so they move slow …can now stick together and liquefy What state is liquid propane gas?

Questions

Partial Pressures In a mixture of gases, each gas produces its own part of the total pressure (Each molecule own pressure!) Ex: 2 moles of O2 gas are mixed with 1 mole of H2 gas. If the total pressure is 100 kpa, how much pressure does each gas exert? Since 2/3rds of the molecules are O2 and 1/3rd are H2 The oxygen will produce 2/3rds of the pressure 2 x (100 kpa) = 67 kpa 3 and hydrogen 1/3 rd of the pressure: 1 x (100 kpa) = 33 kpa

H2 O2 AVOGADRO’S HYPOTHESIS Equal volumes of gases, at the same temperature and Pressure Must have equal numbers of molecules Or Two gas samples with equal number of molecules Under same conditions of Temp and Press Will occupy equal volumes 1 liter 250C 1 atmosphere Ex: Two balloons one with hydrogen, the other with oxygen both occupy 1 liter at the same temp and pressure. If the hydrogen balloon contains 0.25 moles of gas, how much oxygen gas is contained in the other balloon? H2 O2 0.25 moles Duh…