1 Chapter 14 Gases Pioneer High School Ms. Julia V. Bermudez

2 u OBJECTIVES: Explain pressure and volume are related

3 u OBJECTIVES: To calculate the volume and pressure of a sample of gas before and after a change.

Boyle’s Law u In 1662, Robert Boyle first confirmed the relationship between the pressure and the volume of a gas using a vacuum pump.

Boyle’s Law u The gas particles in the cylinder apply pressure on the balloon.

6 Boyle’s Law u As the gas particles in the cylinder are removed the pressure on the balloon decreases.

7 Boyle’s Law u ….And thus the volume of the balloon Increases!

Boyle’s Law u Boyle’s Law can be considered an inverse law. u Why? As one variable increases the other variable will decrease And vice versa

Boyle’s Law u As the volume gets smaller the molecules have less room to move. u The molecules will hit the sides more often, causing more pressure As Volume goes Pressure goes

Boyle’s Law u In a larger container, molecules have more room to move. u Hit the sides of the container less often. As Volume goes Pressure goes

Boyle’s Law In order for this law to work: Must a constant temperature This means the temperature of the gas does not change!

12 Examples Using Boyle’s Law we can predict the change in pressure or volume of a gas at constant temperature. Formula to use: P 1 V 1 = P 2 V 2 P 1 = Pressure (start) V 1 = Volume (start) P 2 = Pressure (end) V 2 = Volume (end)

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? Example #1

14 Example #2 u A sample of He gas in a balloon is compressed from 4.0 L to 2.5 L at a constant T. If the pressure of the gas at 4.0 L is 210 kPa, what will the pressure be at 2.5 L?

15 Practice Problems Pg. 422 # 1-4

16 Gases u OBJECTIVES: Understand the Kelvin scale of temperature

17 Gases u OBJECTIVES: Convert values of temperature between Celsius and Kelvin.

18 Kelvin Scale u What causes tires to appear low on air on a cold day? u The relationship between temperature and volume can help explain this anomaly.

19 Kelvin Scale u In 1787 Jacques Charles studied the relationship between volume and temperature. u He noticed as temperature increases for a gas so does the volume when pressure was held constant.

20 Kelvin Scale Gas particles move inside a balloon and collide with the sides creating the volume of the balloon.

21 Kelvin Scale As the temperature increases the kinetic energy of the gas also increase. The gas molecules collide with the sides more frequently and with greater force.

22 Kelvin Scale …..Thus the volume of the balloon will also increase.

23 Kelvin Scale u The graph of Volume vs. Temp. is a straight line. u Charles predicted the temp. at which volume is 0 L.

24 Kelvin Scale u He extrapolated (continued) the line and described the theoretical temperature at which matter stops moving. u This is called Absolute Zero… (- 273 o C or 0 K)

25 Kelvin Scale u You can convert between different temperatures by using a simple equation: K = o C o C = K - 273

26 Kelvin Scale Convert the following temperatures: o C = ______ K K = ______ o C K = ______ o C o C = ______ K o C = ______ K

27 HOMEWORK u Pg 448 # 88 a&c, 90, 107 a&c CLASSWORK u Prelab for Absolute Zero Title Purpose Procedure (in your own words) Data Table

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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

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

39 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.

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 = 8.31 (L x kPa) / (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 D = =

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.

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

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

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

8. Graham’s Law u The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. u Kinetic energy = 1/2 mv 2 u m is the mass v is the velocity. 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