1 Chapter 12 The Behavior of Gases

2 Section 12.1 The Properties of Gases u OBJECTIVES: Describe the properties of gas particles.

3 Section 12.1 The Properties of Gases u OBJECTIVES: Explain how the kinetic energy of gas particles relates to Kelvin temperature.

4 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

5 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. u Fig. 12.3, page 328

6 Variables that describe a Gas u The four variables and their common units: 1. pressure (P) in kilopascals 2. volume (V) in Liters 3. temperature (T) in Kelvin 4. number of moles (n)

7 Section 12.2 Factors Affecting Gas Pressure u OBJECTIVES: Explain how the amount of gas and the volume of the container affect gas pressure.

8 Section 12.2 Factors Affecting Gas Pressure u OBJECTIVES: Infer (conclude or decide) the effect of temperature changes on the pressure exerted by a contained gas.

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 - spray can is example.

11 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. 12.7, page 331

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 temperature at constant pressure is to increase the volume.

14 Result? u Figure 12.9, page 332 u Think of tire pressure measured when “cold”

15 Section 12.3 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.

16 Section 12.3 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.

The Gas Laws u These will describe HOW gases behave. u Can be predicted by the 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

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? 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? Examples

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 to use: V 1 /T 1 = V 2 /T 2

Examples u What is the temperature of a gas expanded from 2.5 L at 25 ºC to 4.1L at constant pressure? u What is the final volume of a gas that starts at 8.3 L and 17 ºC, and is heated to 96 ºC?

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

Examples u What is the pressure inside a L can of deodorant that starts at 25 ºC and 1.2 atm if the temperature is raised to 100 ºC? u At what temperature will the can above have a pressure of 2.2 atm?

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.

Examples 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? 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?

u The combined gas law contains all the other gas laws! u If the temperature remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Boyle’s Law

u The combined gas law contains all the other gas laws! u If the pressure remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Charles’s Law

u The combined gas law contains all the other gas laws! u If the volume remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Gay-Lussac’s Law

29 Section 12.4 Ideal Gas u OBJECTIVES: Calculate the amount of gas at any specific conditions of: a) pressure, b) volume, and c) temperature.

30 Section 12.4 Ideal Gases u OBJECTIVES: Distinguish between ideal and real gases.

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.

Ideal Gases don’t exist u Molecules do take up space u There are attractive forces u otherwise 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.

5. The Ideal Gas Law #1 u Equation: P x V = n x R x 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 = (L x atm) / (mol x K)

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 P x V R x T The Ideal Gas Law n =

Examples u How many moles of air are there in a 2.0 L bottle at 19 ºC and 747 mm Hg? u What is the pressure exerted by 1.8 g of H 2 gas in a 4.3 L balloon at 27 ºC? u Samples 12-5, 12-6 on pages 342 and 343

6. Ideal Gas Law #2 u P x V = m x R x T M u Allows LOTS of calculations! u m = mass, in grams u M = molar mass, in g/mol u Molar mass = m R T P V

Density u Density is mass divided by volume m V so, m M P V R T  = =

42 Section 12.5 Gas Molecules: Mixtures and Movements u OBJECTIVES: State a) Avogadro’s hypothesis, b) Dalton’s law, and c) Graham’s law.

43 Section 12.5 Gas Molecules: Mixtures and Movements u OBJECTIVES: Calculate: a) moles, b) masses, and c) volumes of gases at STP.

44 Section 12.5 Gas Molecules: Mixtures and Movements u OBJECTIVES: Calculate a) partial pressures, and b) rates of effusion.

Avogadro’s Hypothesis u Avogadro’s Hypothesis: Equal volumes of gases at the same temp. and pressure contain equal numbers of particles. Saying that two rooms of the same size could be filled with the same number of objects, whether they were marbles or baseballs.

7. 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. P Total = 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

Examples u What 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? u 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?

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

8. Graham’s Law u The rate of effusion is inversely proportional to the square root of the molar mass of the molecules. Rate A  Mass B Rate B  Mass A =

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. Graham’s Law