Chapter 14 The Behavior of Gases Chemistry Honors

Chapter 14 The Behavior of Gases Chemistry Honors 1

Beans beans the royal fruit the more you eat the more you toot 2

Section 14. 1 The Properties of Gases u. OBJECTIVES: • Describe the properties of gas particles. 3

Section 14. 1 The Properties of Gases u. OBJECTIVES: • Explain how the kinetic energy of gas particles relates to Kelvin temperature. 4

THREE STATES OF MATTER 5

Kinetic Theory Revisited 1. Gases consist of hard, spherical particles (usually molecules or atoms) 2. Small- so the individual volume is considered to be insignificant 3. Large empty space between them 4. Easily compressed and expanded 5. No attractive or repulsive forces 6. Move rapidly in constant motion 6

Kinetic Theory Revisited u. Recall: that the average kinetic energy of a collection of gas particles is directly proportional to the Kelvin temperature of the gas. 7

We can measure gases in 4 ways: Measurement Amount of gas (n) Unit Moles Volume (V) Liters (L) Temperature (T) K Pressure (P) atm, k. Pa, Torr, mm Hg, 8

1. Amount of Gas u. When we inflate a balloon, we are adding gas molecules. u. Increasing the number of gas particles increases the number of collisions • thus, the pressure increases u If temp. is constant- doubling the number of particles doubles pressure

Pressure and the number of molecules are directly related u More molecules means more collisions. u Fewer molecules means fewer collisions. u Gases naturally move from areas of high pressure to low pressure because there is empty space to move in too- spray can is example.

Common use? u. Aerosol (spray) cans • gas moves from higher pressure to lower pressure • a propellant forces the product out • whipped cream, hair spray, paint u. Fig. 14. 5, p. 416 11

2. Volume of Gas u. In a smaller container, molecules have less room to move. u. Hit the sides of the container more often. u. As volume decreases, pressure increases. (think of a syringe)

3. Temperature of Gas u. Raising the temperature of a gas increases the pressure, if the volume is held constant. u. The molecules hit the walls harder, and more frequently! u. The only way to increase the volume at constant pressure is to increase the temperature.

Result? u. Figure 14. 7, p. 417 u. Think of tire pressure • measured when “cold” 14

Pressure (P) The force per unit area on a surface 15

Pressure is caused by gas particles slamming into the container’s walls. 16

Section 14. 2 The Gas Laws u. OBJECTIVES: • State: a) Boyle’s Law, b) Charles’s Law, c) Gay-Lussac’s Law, and d) the Combined Gas Law. 17

Robert Boyle (1627 -1691) "From a knowledge of His work, we shall know Him" One of the founders of the Royal Society in 1660, Robert Boyle was sometimes called 'the son of the Earl of Cork and the father of chemistry. ' Although he spent most of his life in Britain, Robert was born at Lismore Castle in Co. Waterford Ireland, the youngest of fourteen children. Robert was born into a world in which theories of Aristotle and the beliefs of alchemy were paramount. He made many great contributions in both physics and chemistry, and we particularly remember him when we learn Boyle's Law, which state that at constant temperature, the volume of a gas is inversely proportional to the pressure applied to it. (V x p = constant) 18

Section 14. 2 The Gas Laws u. OBJECTIVES: • Apply the gas laws to problems involving: a) the temperature, b) the volume, and c) the pressure of a contained gas. 19

The Gas Laws u. These will describe HOW gases behave. u. Can be predicted by theory. u. Amount of change can be calculated with mathematical equations.

1. Boyle’s Law u. At a constant temperature, gas pressure and volume are inversely related. • As one goes up the other goes down u. Formula to use: P 1 x V 1= P 2 x V 2

Boyle’s Law A bicycle pump is a good example of Boyle’s law. As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire. 22

A gas occupies a volume of 0. 458 L at a pressure of 1. 01 k. Pa and temperature of 295 Kelvin. Although the temperature stays the same, the volume is increased to 0. 477 L. What is the new pressure? 0. 970 k. Pa 23

Examples u. A balloon is filled with 25 L of air at 1. 0 atm pressure. If the pressure is changed to 1. 5 atm what is the new volume? P 1 V 1 = P 2 V 2 1. 0 atm x 25 L = 1. 5 atm x V 2 1 atm x 25 L 1. 5 atm = 16. 7 L

u. A balloon is filled with 73 L of air at 1. 3 atm pressure. What pressure is needed to change the volume to 43 L? P 1 V 1 = P 2 V 2 1. 3 atm x 73 L = P 2 x 43 L 1. 3 atm x 73 L 43 L = 2. 21 atm 25

2. Charles’s Law u. The volume of a gas is directly proportional to the Kelvin temperature, if the pressure is held constant. u. Formula u If to use: V 1/T 1 = V 2/T 2 one temperature goes up, the volume goes up!

Charles’s original balloon Warm air is less dense than cooler air Modern long-distance balloon 27

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What will be the volume of a gas sample at 309 K if its volume at 215 K is 3. 42 L? Assume that pressure is constant. 4. 92 L 29

Examples u What is the temperature of a gas expanded from 2. 5 L at 25 ºC to 4. 1 L at constant pressure? V 1 T 1 = V 2 T 2 2. 5 L = 4. 1 L 298 K T 2 Temperature must be in K T 2 = 488. 7 K or 215. 7 °C

u. What is the final volume of a gas that starts at 8. 3 L and 17 ºC, and is heated to 96 ºC? V 2 = 10. 6 L 31

3. Gay-Lussac’s Law u. The temperature and the pressure of a gas are directly related, at constant volume. u. Formula to use: P 1/T 1 = P 2/T 2 u. If one temperature goes up, the pressure goes up!

Gay-Lussac’s Law: Pressure and Temperature u When a gas is heated at constant volume, the pressure increases. 33

A balloon with a pressure of 0. 900 atm is heated from 105 K to 155 K. If volume is held constant, what is the new pressure? 1. 33 atm 34

Examples u What is the pressure inside a 0. 250 L can of deodorant that starts at 25 ºC and 1. 2 atm if the temperature is raised to 100 ºC? P 2 = 1. 5 atm u At what temperature will the can be above have a pressure of 2. 2 atm? T 2 = 546. 3 K

4. Combined Gas Law u. The Combined Gas Law deals with the situation where only the number of molecules stays constant. u. Formula: (P 1 x V 1)/T 1= (P 2 x V 2)/T 2 u. This lets us figure out one thing when two of the others change.

Combined Gas Law u The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! No, it’s not related to R 2 D 2 37

Combined Gas Law If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! P 1 V 1 T 1 P 2 V 2 = T 2 Boyle’s Law Charles’ Law Gay-Lussac’s Law 38

Combined Gas Law Problem A sample of helium gas has a volume of 0. 180 L, a pressure of 0. 800 atm and a temperature of 29°C. What is the new temperature(K) of the gas at a volume of. 090 L and a pressure of 3. 20 atm? Set up Data Table P 1 = 0. 800 atm V 1 =. 180 L T 1 = 302 K P 2 = 3. 20 atm V 2=. 090 L T 2 = ? ? 39

Calculation P 1 = 0. 800 atm P 2 = 3. 20 atm P 1 V 1 T 1 = P 2 V 2 T 2 V 1 =. 180 L V 2=. 090 L T 1 = 302 K T 2 = ? ? P 1 V 1 T 2 = P 2 V 2 T 1 P 1 V 1 T 2 = 3. 20 atm x. 090 L x 302 K = 604 K 0. 800 atm x. 180 L 40

The gas in a 0. 010 L container has a pressure of 1. 39 atmospheres. When the gas is transferred to a 0. 017 L container at the same temperature, what is the pressure of the gas? 0. 818 atm 41

Example u. A 15 L cylinder of gas at 4. 8 atm pressure and 25 ºC is heated to 75 ºC and compressed to 17 atm. What is the new volume? V 2 = 4. 9 L

u. If 6. 2 L of gas at 723 mm Hg and 21 ºC is compressed to 2. 2 L at 4117 mm Hg, what is the final temperature of the gas? T 2 = 594 K or 321 °C 43

u The combined gas law contains all the other gas laws! u If the temperature remains constant. . . P 1 x V 1 = P 2 x V 2 T 1 Boyle’s Law T 2

u The combined gas law contains all the other gas laws! u If the pressure remains constant. . . P 1 x V 1 T 1 = P 2 x V 2 T 2 Charles’s Law

u The combined gas law contains all the other gas laws! u If the volume remains constant. . . P 1 x V 1 T 1 = P 2 x V 2 T 2 Gay-Lussac’s Law

Tips for Gas Law Problems u u 1) Determine which gas law you need • Pressure and volume = Boyle’s • Temperature and volume = Charles’ • Temperature and Pressure = Gay-Lussac’s • Temperature, pressure, and volume = Combined 2) Identify your variables. Be sure you put the proper numbers together 3) Change all variables into the correct units • Temperature must be K • Pressure units must match • Volume units must match 4) Put numbers into the gas law equation and solve 47

And now, we pause for this commercial message from STP OK, so it’s really not THIS kind of STP… STP in chemistry stands for Standard Temperature and Pressure Standard Pressure = 1 atm (or an equivalent) Standard Temperature = 0 deg C (273 K) STP allows us to compare amounts of gases between different pressures and temperatures 48

STP Standard Temperature and Pressure: 0°C and 1 atm 49

Section 14. 3 Ideal Gases u. OBJECTIVES: • Distinguish between ideal and real gases. 50

Ideal Gases u. We are going to assume the gases behave “ideally”- obeys the Gas Laws under all temp. and pres. u. An ideal gas does not really exist, but it makes the math easier and is a close approximation. u. Particles have no volume. u. No attractive forces.

Ideal Gases u. There are no gases for which this is true; however, u. Real gases behave this way at high temperature and low pressure.

5. The Ideal Gas Law u Equation: Px. V=nx. Rx. T u Pressure times Volume equals the number of moles times the Ideal Gas Constant (R) times the temperature in Kelvin. u This time R does not depend on anything, it is really constant u R = 8. 31 (L x k. Pa) / (mol x K) or u 0. 0821 (L x atm) / (mol x K)

Ideal Gas Law The mother of all gas laws. It includes everything! PV = n. RT 54

PV = n. RT P = pressure (atm) V = volume (L) n = moles (mol) R = Gas Constant T = Temperature (Kelvin) 55

Using PV = n. RT P = Pressure V = Volume T = Temperature N = number of moles R is a constant, called the Ideal Gas Constant. Depending what your pressure unit is determines which of the 3 gas constants you need to use. R = 8. 314 L • k. Pa Mol • K R = 62. 4 L • mm Hg Mol • K R =. 0821 L • k. Pa Mol • K 56

The Ideal Gas Law u. We now have a new way to count moles (amount of matter), by measuring T, P, and V. We aren’t restricted to STP conditions n= Px. V Rx. T

If the pressure exerted by a gas at 0. 00°C in a volume of 0. 0010 L is 5. 00 atm, how many moles of gas are present? 2. 2 x -4 10 moles 58

Examples u. How many moles of air are there in a 2. 0 L bottle at 19 ºC and 747 mm Hg? n = Px. V Rx. T n = 747 mm. Hg x 2 L 62. 4 L mm. Hg x 292 K mole K =. 0820 moles air

u. What is the pressure exerted by 1. 8 g of H 2 gas in a 4. 3 L balloon at 27 ºC? P = 5. 10 You have to get moles from the 1. 8 g of H 2 by multiplying by the molar mass of H 2 60

Ideal Gases don’t exist u. Molecules do take up space u. There attractive forces uotherwise there would be no liquids formed

Real Gases behave like Ideal Gases. . . u When the molecules are far apart u The molecules do not take up as big a percentage of the space u We can ignore their volume. u This is at low pressure

Real Gases behave like Ideal gases when. . . u. When molecules are moving fast • = high temperature u. Collisions are harder and faster. u. Molecules are not next to each other very long. u. Attractive forces can’t play a role.

Section 14. 4 Gas Molecules: Mixtures and Movements u. OBJECTIVES: • Calculate: a) moles, b) masses, and c) volumes of gases at STP. 65

Avagadro’s Hypothesis Equal volumes of gas (at same T and P) contain the same amount of particles 66

23 10 1 mole = 6. 02 x particles 1 mole = 22. 4 L Only works at same T and P 67

6. Dalton’s Law of Partial Pressures u. The total pressure inside a container is equal to the partial pressure due to each gas. u. The partial pressure is the contribution by that gas. PTotal = P 1 + P 2 + P 3

u We can find out the pressure in the fourth container. u By adding up the pressure in the first 3. 2 atm + 1 atm + 3 atm = 6 atm

A balloon contains O 2 and N 2 gas. If the partial pressure of the O 2 is 0. 75 atm and the partial pressure of the N 2 is 0. 55 atm, what is the total pressure of the balloon? 1. 30 atm 70

Table of Vapor Pressures for Water 3. 56 k. Pa 1. 40 k. Pa 5. 65 k. Pa 31. 2 k. Pa 71

u What Examples is the total pressure in a balloon filled with air if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg? Ptotal = 170 mm Hg + 620 mm Hg Ptotal = 790 mm Hg

In a second balloon the total pressure is 1. 3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mm Hg? First: Convert 720 mm Hg to atm 720 mm Hg x 1 atm =. 95 atm 760 mm Hg PTotal = 1. 3 -. 95 PTotal =. 35 atm 73

Diffusion u. Molecules moving from areas of high concentration to low concentration. u. Example: perfume molecules spreading across the room. u Effusion: Gas escaping through a tiny hole in a container. u Depends on the speed of the molecule.

Graham’s Law u. Heavier molecules move slower at the same temp. (by Square root) u Heavier molecules effuse and diffuse slower u. Helium effuses and diffuses faster than air - escapes from balloon.