Gas Laws Chapter 5

Pressure Force per unit area Measured in Atmospheres (atm) Mm of Hg = Torr Pascals or kiloPascals (Pa or kPa)

Conversions 1 mm = 1 torr 1 atm = 760 mm 1 atm = Pa 1 atm = kPa

Example Problem Convert 4.39 atm to torr, Pa, and kPa.

Example Problem Convert 369 mm to atm and kPa.

Example Problem Convert Pa to kPa, atm, and torr.

Boyle’s Law Pressure and volume vary inversely PV = k or P 1 V 1 = P 2 V 2

Sample Problem As part of the training for high altitude flight, pilots and flight crews are placed in a hypobaric chamber where the pressure is dropped to approximately.250 atm to simulate the thinner atmosphere at altitude. If a person’s stomach has a 30.0 ml gas bubble when they enter the chamber, what will be the new volume of the bubble at “altitude”?

In your Scientist’s Notebook: The pressure of water increases as depth increases. If you immerse a balloon containing 1.25 L of air in 10.0 meters of water, the new pressure is 1.10 atm. What will be the volume of the balloon?

Charles Law Temperature and volume are directly proportional V/T = K or V 1 /T 1 = V 2 /T 2

Example Problem A 10.0 ml canister of compressed carbon dioxide at room temperature (25* C) is allowed to expand into a balloon with a volume of 3.00 liters. Assuming the pressure remained constant, what is the new temperature?

In your Scientist’s Notebook: A balloon contains 534 ml of gas at 22.0 o C. If the temperature increases to 44 o C, what is the new volume of the balloon?

Gay-Lussac’s Law Temperature and pressure vary directly P/T = K or P 1 /T 1 = P 2 /T 2

Example Problem The pressure inside your basketball is only 2.20 atm., and it has lost its bounce. You put it in the sun to warm its temperature from 19.2 o C to 27 o C. Assuming very insignificant volume change, what is the new pressure?

In your Scientist’s Notebook When you leave for school on a chilly morning (5.00 o C), the pressure in your car tires is 29.6 psi. What is the pressure after you have driven to school and friction with the road increased the temperature to 28.0 o C?

Combined Gas Law All three of the preceding laws can be combined into one equation: P 1 V 1 P 2 V 2 T 1 T 2 =

Example Problem A weather balloon at the surface (25 o C and 760 torr) has a volume of 425 L. What is the volume at feet where the pressure is 245 torr and the temperature is -35 o C?

In your Scientist’s Notebook: A whale releases 34.5 ml of air under water where pressure is 4.32 atm. The volume of the air bubble at the surface is 170. ml. The temperature and pressure at the surface are 28.0*C and 1.00 atm. What was the temperature under the water?

Avogadro’s Law Volume is directly proportional to the # of moles of gas V/n = K or V 1 /n 1 = V 2 /n 2

Combined or Ideal Gas Law PV = nRT R = L atm/K mol

Example Problem: What mass of oxygen gas occupies 34.5 L at 1.5 atm and 27* C ?

In your Scientist’s Notebook: What mass of carbon dioxide is needed to fill a 3.0 L fire extinguisher at 25.0* C with a pressure of 5.64 atm?

Example Problem The density of a gas at 1.50 atm and 27* C is found to be 1.95 g/L. What is the molar mass of the gas?

In your Scientist’s Notebook: What is the atomic mass of an elemental gas that has a density of.178 g/L at 0.00* C and 1.00 atm? What is the gas?

Example What is the volume of 1.00 mole of a gas at 0* C and 1.00 atm pressure?

Example Problem What is the volume of 2.00 moles of a gas at 0* C and 1.00 atm?

STP Standard Temperature and Pressure 0* C or 273 K atm

Molar Volume 1 mole of any gas at STP has a volume of L

Example Problem What is the density of oxygen at STP?

In your Scientist’s Notebook: The density of an elemental gas at STP is 3.16 g/L. What is the gas?

Dalton’s Law The total pressure of a mixture of gases is equal to the sum of the partial pressures of all gases present. P total = P 1 + P 2 + P 3...

Example Problem Air is a mixture of gases in the following percentages: N % ; O 2 —20.9%; Ar--0.93%; CO 2 —0.035%. At 760. torr, what is the partial pressure of each gas?

Example Problem Oxygen was collected over water at a temperature of 22* C and a pressure of 754 torr. If water’s vapor pressure at this temperature is 21 torr, what is the partial pressure of the oxygen?

Kinetic Molecular Theory A model that explains the behavior of individual gas particles Oversimplifies the true nature of gases for ease of understanding

Ideal Gases 1. Particles have no volume 2. Rapid, random motion & collisions with the walls of the container cause pressure 3. No attraction between particles so collisions are perfectly elastic 4. Kinetic energy is directly proportional to Kelvin temperature

Ideal Gases Hypothetical—none really exist Conditions approach ideal as temperature increases and pressure decreases.

Deviations from Ideal “Concentrated” gases hit the sides of a container slightly less often— lower P Gases with attraction for each other have lower pressure and lower energy Volume of particles becomes significant at small overall volumes

How Does KMT Account for: Boyle’s Law (V & P)—less volume should produce more collisions so pressure increases (and vice versa) Gay-Lussac’s Law (P & T)—at increased temperature, particles collide with greater energy producing higher pressure

How Does KMT Account for: Charles’s Law (V & T)—at higher temperature, particles collide with greater energy & can expand a flexible container Avogadro’s Law—individual particles have no volume or attractions—should all occupy the same molar volume

Meaning of Temperature Temperature = average kinetic energy of particles The relationship between temperature and energy: (KE) avg = 3/2 RT R = J/K mol

What is the average kinetic energy of He particles at 67 o C? (KE) avg = 3/2 RT

What is the average kinetic energy of Ne particles at 67 o C?

What is the average kinetic energy of Cl 2 particles at 67 o C?

Velocity of Gas Particles Since kinetic energy depends only on temperature, how does mass affect the motion of the particles? KE = ½ mv 2 and KE = 3/2 RT Since kinetic energy must remain the same, velocity must decrease as mass increases.

Root Mean Square Velocity R = J/K mol T = Kelvin Temperature M = mass of 1 mole of particles in kg Since a joule = kg m 2 /s 2, units cancel leaving m/s (velocity)

Calculate the root mean square velocity of atoms in helium gas at 25 o C.

Graham’s Law Diffusion—the mixing of gases Effusion—passage of gas molecules through a small opening

Graham’s Law At equal temperatures, the rate of effusion is inversely proportional to the square root of the molar mass

Graham’s Law Equation Rate of effusion 1 M 2 Rate of effusion 2 M 1 =

Example Problem How much faster will H 2 effuse than O 2 ?

Example Problem Samples of hydrogen gas and chlorine gas are placed at opposite ends of a tube that is 1.00 m long. At what distance from the hydrogen end will the reaction which forms HCl occur?

In your Scientist’s Notebook: A vial of ammonia (NH 3 ) and chlorine gas are opened simultaneously. You detect the odor of ammonia in 15 seconds. How long will it be before you detect the chlorine?