Chapter 14 Behavior of Gases

I KnowFuzzy Need to Learn I will learn to List and explain the properties of a gas and explain how the kinetic molecular theory accounts for each property. 2. Describe the relationship among temperature, pressure, and volume of a gas and use the combined gas law to solve problems. 3. Compare and contrast real and ideal gases. 4. Relate the total pressure of a mixture of gases to the partial pressures of the component gases. 5. Explain how molar mass of a gas effects the diffusion rate.

Daily Planner ______ Day 1—Properties of Gases; Gas Laws- Boyle’s ______ Day 2—Gas Laws– Charles’, Gay-Lussac’s, Combined Gas Laws-PTV; Practice problems pp #8,10,12,15-17 ______ Day 3—pp #8,10,12,15-17 due; Psuedo Quiz ______ Day 4— Quiz ______ Day 5— Ideal Gas Law; Worksheet ______ Day 6 – Dalton’s Law and Graham’s Law; pp. 434,436 #32-38 ______ Day 7— Quiz #2; p. 434, 436 # due ______ Day 8—Review ______ Day 9—Test

Behavior of Gases vs. Kinetic Theory What happens on the molecular level when you put more air into a container? adding air (gas)  adds molecules  more collisions  more pressure

Behavior of Gases vs. Kinetic Theory What happens on the molecular level when use an aerosol can? removing 1/2 particles of gas  lowers collisions  lower pressure by 1/2

The Effect of Changing the Size of the Container What happens on the molecular level when the volume of the container is decrease? the more gas is compressed  more collisions  more pressure So if volume decreases: Pressure increases V  P 

Gas Laws P T V

Boyle's Law: Pressure-Volume Changes Robert Boyle in 1662 states: "that for a given mass of gas at constant temperature, the volume of a gas varies inversely with pressure.“ P ↓ V ↑

Boyle’s Law Ex. A 30 L helium balloon is at 100 kPa of pressure. What is the volume if the pressure decreases to 25 kPa? Will the volume increase or decrease? P ↓ V ? P ↓ V ↑ This is an inverse relationship.

Charles’ Law: Temperature-Volume Jacques Charles, 1787, states: "volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant." T ↑ V ↑

Charles’ Law Ex. A 1.0 L sample of gas at 300 K is increased to 600 K. What is the new volume? Will the volume increase or decrease? T ↑ V ? T ↑ V ↑ 1.0 L | 600 K | = | 300 K | 1.0 L | 600 K | = 2 L | 300 K |

Why use the Kelvin scale? It shows the correct ratio. 300 K to 900 K is tripled 27 o C to 627 o C is not *William Thompson, aka Lord Kelvin, noticed 0 K by using Charles' lab work 0 K --> no volume --> no K.E.

Gay-Lussac: Temperature-Pressure What happens to the pressure when temperature is increased? increase temperature --> more molecules moving --> more collisions --> more pressure T ↑ P ↑ Ex. aerosol can in a fire Joseph Gay-Lussac ( ) notice when temperature increased, pressure increases.

Gay-Lussac’s Law Ex. The gas left in a used aerosol can at a pressure of 100 kPa at 27 o C. What it is thrown in a fire, what is the pressure if the temperature reaches 927 o C? Will the pressure increase or decrease? T ↑ P ? 27 o C = 300 K927 o C = 1200K T ↑ P ↑ 100 kPa | 1200 K | = 400 kPa | 300 K |

Psuedo Quiz 1.What is the effect of adding more molecules of gas to a container? Why? 2.What is the effect of removing molecules from a container? Why? 3.How is temperature affected by increasing the pressure? 4.What law explains the effect temperature and pressure?

Psuedo Quiz 5.How is pressure affected by decreasing the volume? 6. What law explains the effect of pressure and volume? 7. How is temperature affected by decreasing the volume? 8. What law explains the effect of temperature and volume?

1.What is the effect of adding more molecules of gas to a container? Why? More pressure; more collision 2.What is the effect of removing molecules from a container? Why? Less pressure; less collision 3.How is temperature affected by increasing the pressure? Temperature increases 4.What law explains the effect temperature and pressure? Gay-Lussac 5.How is pressure affected by decreasing the volume? Pressure increases 6.What law explains the effect of pressure and volume? Boyle’s 7.How is temperature affected by decreasing the volume? Temperature decreases 8.What law explains the effect of temperature and volume? Charles’

Combined Gas Law: P T V Ex. A 30.0 L balloon at 40 o C and 150 kPa. What is the volume of the balloon at STP? Sometimes the volume is adjusted by the pressure and the temperature. We are going to use the logical approach of P T V and two bridges

Combined Gas Law: P T V Ex. A 30.0 L balloon at 40 o C and 150 kPa. What is the volume of the balloon at STP? What do you know? 40 o C = 313 K STP = 273 K and kPa P --> 150 kPa to kPa P ↓ V ? T --> 313 K to 273 KT ↓ V ?

Combined Gas Law: P T V Ex. A 30.0 L balloon at 40 o C and 150 kPa. What is the volume of the balloon at STP? P --> 150 kPa to kPa P ↓ V ↑ T --> 313 K to 273 KT ↓ V ↓ 30.0 L | 273 K | 150 kPa | = 38.7 L | 313 K | kPa |

Combined Gas Law: P T V A 5.0 L air sample has a pressure of 107 kPa at a temperature of -50 o C. If the temperature is raised to 102 o C and the volume expands to 7.0 L, what will the new pressure be? What do you know?

1. The volume of a sample of gas is 0.5 L at 25 o C and 155 kPa. Calculate the volume of the sample at STP. (STP = 0 o C and kPa)

2. The volume of a sample of gas is 300 mL at 293 K and 98.6 kPa. Calculate the volume at STP.

Homework pp #8,10,12,15-17 due tomorrow

Ideal Gas Law: PV = nRT When you are concerned about the amount of gas --> mol PV = nRT P = pressure (kPa, mm Hg, atm) V = volume (L) n = moles R = constant depending on P (8.31 kPa L/mol K) (62.4 mm L/mol K) ( atm L/mol K) T = temperature (K)

Ideal Gas Law: PV = nRT R?What is R for 1 mole of gas at STP? PV = nRT PV/nT = R R = kPa (22.4L) 1 mol (273 K) R = 8.31 kPa L/mol K If you use P = 760 mm Hg, R = 62.4 mm L/mol K P = 1 atm R = atm L/mol K

Ex. of PV = nRT A steel cylinder with a volume of 20,000 mL is filled with N 2 with a pressure of 20,000 kPa at 27 o C. How many moles of N 2 are in the cylinder? Hey z man PV = nRT PV/RT = n n = 20,000 kPa(20.0 L) 8.31kPa*L/mol*K(300K) n = 160 mol

Real vs. Ideal Gases Ideal gases make too assumptions: 1) no volume 2) molecules are not attracted to one another Real gases have 1) finite volume 2) attracted to one another especially at low temps Real Gas Equation: [P + an 2 ] [V – nb] = nRT V 2 Ugly!!!

QUIZ tomorrow

Dalton’s Law

Dalton's Law of Partial Pressures At constant temperature and volume, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases. P total = P 1 + P 2 + P Ex. P air = P Nitrogen + P Oxygen + P Carbon Dioxide + P other gases kPa = kPa kPa +.04 kPa +.95 kPa

Dalton’s Law Ex. A balloon of helium and methane has a pressure is kPa. If the pressure of He is 100 kPa, what is the pressure of methane? kPa kPa = 1.2 kPa

Diffusion and Graham's Law What is diffusion? tendency of molecules to move toward areas of lower concentration until the concentration is uniform What is effusion? gas escaping through a tiny hole in a container of gas

Graham's Law of effusion The rate of effusion of a gas is inversely proportional to the square root of its molar mass. rate A = √ molar mass B rate B √ molar mass A *lighter molecules move faster

Graham's Law of effusion Ex. Which molecule diffuses faster NH 3 or HCl? HCl = 36 g/mol NH 3 = 17 g/mol √36 = 1.5 NH 3 is 1.5 times faster than HCl √17

Homework p # due tomorrow #8, 10, 12, Review Sheet Thursday Test Friday

Ch. 14 Test has only 7 problems Know the names of the Gas Laws: V.P. Boyle Charles watches T.V. Gay-Lussac needs T.P. Dalton’s Partial Pressure 7 Problems: 1.Boyle 2.Charles 3.Gay-Lussac 4.Combined Gas Laws 5.PV = nRT 6.Dalton’s Partial Pressure 7.Effusion

Avogadro's Hypothesis Equal volumes of gases at the same temperature and pressure contain equal number of particles. At STP, 1 mole of any gas is 22.4 L Ex. Determine the volume, in liters, occupied by 14.0 g of nitrogen gas at STP. 14 g N 2 x | 1 mol | x | 22.4 L | = 11.2 L | 28 g | | 1 mol |