Ch. 12 Behavior of Gases

Gases Gases expand to fill its container, unlike solids or liquids Easily compressible: measure of how much the volume of matter decreases under pressure

Variables that describe a gas Pressure (P) – Measured in kilopascals, kPa – Pressure and number of molecules are directly related  increase molecules = increase pressure – Gases naturally move from areas of high pressure to low pressure, due to the available space to move into

Gas Pressure - collision of gas molecules with the walls of the container

Variables that describe a gas Volume (V) – Measured in Liters, L – Volume and pressure are inversely related As volume decreases, the pressure increases Smaller container = less room for movement, therefore molecules hit sides of container more often

B. Volume Reduce volume - ↑ pressure Increase volume - ↓ pressure Ex: piston in a car II. Factors Affecting Gas Pressure

Variables that describe a gas Temperature (T) – Measured in Kelvin, K – The temperature and pressure are directly related Increase in temp = increase in pressure Volume must be held constant Molecules hit the walls harder (due to increase in K.E.) and more frequently.  Think about a tire in hot weather…

Variables that describe a gas Amount – Measured in moles, mol – Moles and pressure are directly related Increase in # of moles = increase in pressure Ex: Inflating a balloon is adding more molecules. Temperature must remain constant

II. Factors Affecting Gas Pressure A. Amount of Gas Add gas - ↑ pressure Remove gas - ↓ pressure Ex: pumping up a tire adding air to a balloon aerosol cans

Gas Pressure (Cont.) -- 3 ways to measure pressure: » atm (atmosphere) » mm Hg » kPa (kilopascals) U-tube Manometer

III. Variables that describe a gas VariablesUnits Pressure (P) –kPa, mm Hg, atm Volume (V) – L, mL, cm 3 Temp (T) –°C, K (convert to Kelvin) K = °C Mole (n) - mol

How pressure units are related: 1 atm = 760 mm Hg = kPa How can we make these into conversion factors? 1 atm101.3 kPa 760 mm Hg 1 atm

Guided Problem: 1. Convert 385 mm Hg to kPa 385 mm Hg 2. Convert 33.7 kPa to atm 33.7 kPa x kPa = 51.3 kPa 760 mm Hg x =.33 atm kPa 1 atm

Standard Temperature and Pressure Standard pressure – 1 atm, 760 mmHg, or101.3 kPa Standard temp. – 0° C or 273K STP

Gas Laws Describe how gases behave Change can be calculated Know the math and the theory!!

Boyle’s Law (1662) Gas pressure is inversely related to volume (as volume increases, pressure decreases) Temperature is constant P 1 V 1 = P 2 V 2

10. The pressure on 2.50 L of anesthetic gas changes from 105 kPa to 40.5 kPa. What will be the new volume if the temp remains constant? P 1 = 105 kPa P 2 = 40.5 kPa V 1 = 2.5 L V 2 = ? P 1 × V 1 = P 2 × V 2 (105) (2.5) = (40.5)(V 2 ) = 40.5 (V 2 ) 6.48 L = V 2 Example Problems pg 335 # 10 &11

11. A gas with a volume of 4.00L at a pressure of 205 kPa is allowed to expand to a volume of 12.0L. What is the pressure in the container if the temp remains constant? P 1 = 205 kPa P 2 = ? V 1 = 4.0 LV 2 = 12.0 L P 1 × V 1 = P 2 × V 2 (205) (4.0) = (P 2 )(12) 820 = (P 2 ) L = P 2 Example Problems pg 335 # 10 &11

Charles’s Law (1787)

Example Problems pg. 337 # 12 & If a sample of gas occupies 6.80 L at 325°C, what will be its volume at 25°C if the pressure does not change? V 1 = 6.8LV 2 = ? T 1 = 325°C = 598 K T 2 = 25°C = 298 K 6.8 = V × V 2 = V 2 = 3.39 L

13. Exactly 5.00 L of air at -50.0°C is warmed to 100.0°C. What is the new volume if the pressure remains constant? V 1 = 5.0L V 2 = ? T 1 = -50°C = 223 K T 2 = 100°C = 373 K 5 = V (223) V 2 = V 2 = 8.36 L Example Problems pg. 337 # 12 & 13

Gay-Lussac’s Law (1802)

Example Problems 1. The gas left in a used aerosol can is at a pressure of 103 kPa at 25°C. If this can is thrown onto a fire, what is the pressure of the gas when its temperature reaches 928°C? P 1 = 103 kPaP 2 = ? T 1 = 25°C = 298 K T 2 = 928°C = 1201 K 103 = P × P 2 = 123,703 P 2 = 415 kPa

Example Problem pg. 338 # A gas has a pressure of 6.58 kPa at 539 K. What will be the pressure at 211 K if the volume does not change? P 1 = 6.58 kPaP 2 = ? T 1 = 539 K T 2 = 211 K 6.58 = P × P 2 = P 2 = 2.58 kPa

Combined Gas Law

How to remember each Law! P V T Gay-Lussac Boyles Charles Cartesian Divers Balloon and flask Demo Fizz Keepers

Ex: 3.0 L of Hydrogen gas has a pressure of 1.5 atm at 20 o C. What would the volume be if the pressure increased to 2.5 atm at 30 o C?

Ideal Gas Law

A gas behaves “ideally” if it conforms to the gas laws – Gases do not usually do this – Real gases only behave this way at: 1.High temps (molecules move fast) 2.Low pressure (molecules are far apart) This is because gases will stay a gas under these conditions – Molecules are not next to each other very long so attractive forces can’t play a role b/c molecules are moving too fast – Ideal Gases do no exist because: 1.Molecules do take up space 2.There are attractive forces between molecules otherwise no liquid would form. (Molecules slow down to become liquids)

E. Ideal Gas Law You don’t need to memorize this value! You can calculate the # of n of gas at standard values for P, V, and T PV Tn = R (1 atm)(22.4L) (273K)(1 mol) = R UNIVERSAL GAS CONSTANT R= atm∙L/mol∙K

E. Ideal Gas Law P= pressure in atm V = volume in liters n = number of moles R= atm∙L/mol∙K T = temperature in Kelvin PV=nRT

E. Example Problems 1. At what temperature will 5.00g of Cl 2 exert a pressure of 900 mm Hg at a volume of 750 mL? 2. Find the number of grams of CO 2 that exert a pressure of 785 mm Hg at a volume of 32.5 L and a temperature of 32 degrees Celsius. 3. What volume will 454 g of H 2 occupy at 1.05 atm and 25°C.

Ex: What volume will 2.0 mol of N 2 occupy at 720 torr and 20 o C?

Dalton’s Law of Partial Pressures Used for mixture of gases in a container If you know the P exerted by each gas in a mixture, you can calculate the total gas pressure It is particularly useful in calculating pressure of gases collected over water. P total = P 1 + P 2 + P 3 … *P1 represents the “partial pressure” or the contribution by the gas

F. Dalton’s Partial Pressure Law The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P total = P 1 + P 2 + P

F. Dalton’s Law Example problem: 1. Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen (P O 2 ) if the total pressure is kPa. And the partial pressures of nitrogen, carbon dioxide, and other gases are kPa, kPa, and 0.94 kPa. P O 2 = P total – (P N 2 + P CO 2 + P others ) = kPa – (79.10 kPa kPa kPa) = kPa

F. Dalton’s Law 2. A container holds three gases : oxygen, carbon dioxide, and helium. The partial pressures of the three gases are 2.00 atm, 3.00 atm, and 4.00 atm respectively. What is the total pressure of the container? 3. A gas mixture contains oxygen, nitrogen and carbon dioxide. The total pressure is 50.0 kPa. If the carbon dioxide has a partial pressure of 21 kPa and the nitrogen has a partial pressure of 15 kPa, what is the partial pressure of the oxygen? 4. A container contains two gases – helium and argon, at a total pressure of 4.00 atm. Calculate the partial pressure of helium if the partial pressure of the argon is 1.5 atm.

Graham’s Law of Effusion

A. Graham’s Law Diffusion Diffusion – The tendency of molecules to move toward areas of lower concentration. Ex: air leaving tire when valve is opened Effusion Effusion – Passing of gas molecules through a tiny opening in a container

A. Graham’s Law Which one is Diffusion and which one is Effusion? Diffusion Effusion Tiny opening