Gases Laws Notes

Pressure Pressure- force per unit area caused by particles hitting the walls of a container Barometer- Measures atmospheric pressure Atmospheric Pressure- Results from the weight of the air- mass of air being pulled toward the center of the earth by gravity.

Manometer- Measures pressure of a gas in a container Two types – Open and Closed

Units for pressure mm Hg, torr, Pascal (Pa), Kilopascal (kPa), atmospheres (atm), pounds square inch (psi) 1 atm = 760 mm Hg = 760 torr = Pa = kPa = psi Ex: You have 28 psi. How many atm? Torr? Pascals? = 28 psi x ________ psi atm atm = 28 psi x ________ psi Pa x 10 5 Pa = 28 psi x ________ psi torr torr

Learning Check How many mmHg are 8.92atm?

Boyle’s Law -Relationship between pressure and volume (constant temp.) -Inverse proportion  P  V P 1 V 1 = P 2 V 2 Given V 1 = 1.5 L P 1 = 56 torr P 2 = 150 torr V 2 = ? V 2 = P 1 V 1 P2P2 ____ V 2 = (56 torr)(1.5 L) ____________ 150 torr V 2 = 0.56 L Ex: Consider a 1.5 L sample of CCl 2 F 2 at a pressure of 56 torr. If pressure is changed to 150 torr at constant temperature, what is the new volume?

Learning Check Boyle’s Law variables: Is Boyle’s Law an inverse or direct relationship? Boyle’s Law constants: Boyle’s Law formula:

Charles’s Law -Relationship between volume and temperature (constant pressure) -Directly proportional  V  T -Temperature in Kelvin V 1 = V 2 T 1 T 2 Given V 1 = 2.0 L T 1 = 298 K T 2 = 278 K V 2 = ? V 2 = T 2 V 1 T1T1 ______ V 2 = (278 K)(2.0 L) ____________ 298 K V 2 = 1.9 L °C = ____ K Ex: A 2.0 L sample of air is collected at 298 K and cooled to 278 K, the pressure is held constant. What is the volume?

Learning Check Charles’ Law variables: Is Charles’ Law an inverse or direct relationship? Charles’ Law constants: Charles’ Law formula:

Gay-Lussac’s Law -Relationship between pressure and temperature (constant volume) -Directly proportional  P  T -Temperature in Kelvin Given P 1 = 107 kPa T 1 = 22 °C = 295 K T 2 = 45 °C = 318 K P 2 = ? P 2 = T 2 P 1 T1T1 ______ P 2 = (318 K)(107 kPa) ______________ 295 K P 2 = 115 kPa °C = ____ K Ex: A mylar balloon is filled with helium gas to a pressure of 107 kPa when the temperature is 22 °C. If the temperature changes to is 45 °C, what will be the pressure of helium in the balloon? P 1 = P 2 T 1 T 2

Learning Check Gay-Lussac’s Law variables: Is Gay-Lussac’s Law an inverse or direct relationship? Gay-Lussac’s Law constants: Gay-Lussac’s Law formula:

Avogadro’s Law -Relationship between volume and moles (constant temperature and pressure) -Directly proportional  V  n V 1 = V 2 n 1 n 2 Given V 1 = 12.2 L n 1 = 0.50 mol n 2 = 0.50 mol O 2 V 2 = ? V 2 = n 2 V 1 n1n1 ______ V 2 = (0.33 mol)(12.2 L) ______________ 0.50 mol V 2 = 8.1 L x ________ mol O 2 mol O = 0.33 mol Ex: 12.2L sample contains 0.50 moles O 2. If O 2 is converted to O 3, what will the volume be? 3O 2  2O 3 n = # of moles

Learning Check Avogadro’s Law variables: Is Avogadro’s Law an inverse or direct relationship? Avogadro’s Law constants: Avogadro’s Law formula:

Combined Gas Law Combination of Boyle’s law, Charles’ law and Gay-Lussac’s Law Given V 1 = 3.5 L P 1 = 6.32 atm T 1 = 27 °C = 300. K V 2 = 4.7 L P 2 = 4.15 atm T 2 = ? P 1 V 1 = P 2 V 2 T 1 T 2 T 2 = P 2 V 2 T 1 _______ P1V1P1V1 T 2 = (4.15 atm)(4.7 L)(300. K) _____________________ (6.32 atm)(3.5 L) T 2 = 260 K Ex: A 3.5 L sample of Argon exerts a pressure of 6.32 atm at 27 °C. When the volume is increased to 4.7 L and the pressure is decreased to 4.15 atm, what is the final temperature?

Learning Check Combined Gas Law variables: Combined Gas Law constants: Combined Gas Law formula: A gas is heated from K to K and the volume is increased from 24.0 liters to 35.0 liters by moving a large piston within a cylinder. If the original pressure was 1.00 atm, what would the final pressure be?

Ideal Gas Law P= pressure (atm) V= volume (L) n= Mole Gas (mol) T= temperature (K) R= universal gas constant Ex: H 2 has a volume of 8.56 L at 0 o C and 1.5 atm. Calculate the moles of H 2 present. PV = nRT R = L* atm mol * K Given V= 8.56 L T = 0 o C = 273 K P = 1.5 atm n = ? R = atm L/mol K n = PV RT ____ n = (1.5 atm)(8.56 L) _______________________ ( atm L/mol K)(273 K) n = 0.57 mol

Learning Check How many moles of gas are contained in a 2.00L flask at 98.8 kPa and 25.0°C?

Dalton’s Law of Partial Pressures Partial Pressure – pressure that a gas would exert if it alone in the container. P total = P 1 + P 2 + P 3 … Ex: 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 inside the container? Given P 1 = 2.00 atm P 2 = 3.00 atm P 3 = 4.00 atm P total = ? P total = P 1 + P 2 + P 3 P total = 2.00 atm atm atm P total = 9.00 atm

A common method of collecting gas samples in the laboratory is to bubble the gas into a bottle filled with water and allow it to displace the water. When this technique is used, however, the gas collected in the bottle contains a small but significant amount of water vapor. As a result, the pressure of the gas that has displaced the liquid water is the sum of the pressure of the gas plus the vapor pressure of water at that temperature. The vapor pressures of water at various temperatures are given in Table. P Total - P vapor = P Gas

Given T = 16°C P vapor = V = 188 mL (doesn’t matter) P total = 92.3 kPa P gas = ? 92.3 kPa – 1.82 kPa = P Gas P gas = 90.5 kPa Ex: A student collects oxygen gas by water displacement at a temperature of 16°C. The total volume is 188 mL at a pressure of 92.3 kPa. What is the pressure of oxygen collected? 1.82 kPa

Given T = 17°C = 290. K P vapor = V = L P total = atm P gas = ? n gas = P Total - P vapor = P Gas 100. kPa – 1.94 kPa = P Gas P gas = 98 kPa Ex: Hydrogen gas is collected by water displacement. Total volume collected is L at a temperature of 17°C and a pressure of atm. What is the pressure of dry hydrogen gas collected? How many moles of hydrogen are present? 1.94 kPa x ________ atm kPa =100. kPa n = PV RT ____ n = (0.97 atm)(0.461 L) _______________________ ( atm L/mol K)(290. K) n = mol x ________ kPa atm = 0.97 atm

Learning Check What does it mean to collect gas over water? A sample of oxygen gas is collected over water. The total pressure is kPa. The partial pressure of the dry oxygen calculated to be kPa. What is the vapor pressure of water?

Gas Stoichiometry STP = Standard Temperature and Pressure Standard Temperature = 0 o C Standard Pressure = 1 atm Molar Volume1.00 mol gas = 22.4 L gas Ex 1: A sample of N 2 has a volume of 1.75 L at STP. How many moles of N 2 are present? x ________ L mol = mol 1.75 L or use PV = nRT

Ex 3: Calculate the volume of CO 2 produced at STP from 152g of CaCO 3. CaCO 3  CaO + CO 2 mol CaCO 3 mol CO = 34.0 L x ___________ g CaCO 3 mol CaCO g CaCO 3 x _______x __________ L mol or use PV = nRT

Ex 2: Calculate the volume of O 2 produced at 1.00 atm and 25 o C by the decomposition of 10.5g KClO 3. 2KClO 3  2KCl + 3O 2 Given V= ? T = 25 o C = 298 K P = 1.00 atm R = atm L/mol K n = 10.5 g KClO 3 V = nRT P ____ V = (0.128 mol) ( atm L/mol K)(298 K) _______________________________ 1.00 atm V = 3.13 L x __________ mol KClO 3 mol O = mol x ___________ g KClO 3 mol KClO

CHALLENGE! What would the value of the Gas Constant, R, be with the following units? 1)kPa*L mol*K 2) atm*L kmol*K