Gas Laws
VIDEO CLIPS MENTIONED
Rock Me Avogadro (3:08)
Railroad Tank Car (.20)
Mythbusters Tank Car (3:08)
Egg in a Bottle (3:05)
Egg out of a Bottle (.16)
Peep Bunnies (1:46)
Ammonia and HCl Diffusion (.56)
Ideal Gas Law (.51)
Animal Balloons (1:18)
Liquid Nitrogen & Balloons (2:40)
Boiling Water with Ice (1:55)
CONCEPTS AND PROBLEMS RELATED TO GAS PROPERTIES
Mixture of Gases and Kinetic Energy
Given mixture of three gases: Oxygen (O2), Nitrogen (N2), and Helium (He) at 40°C
Questions:
Which gas has the most kinetic energy?
Which gas has the highest velocity?
If 3 moles of O2, 2 moles of N2, and 5 moles of He are present, total pressure = 30 atm; need to calculate partial pressure for each gas.
If temperature is doubled to 80°C, describe changes in kinetic energy.
Calculate density of nitrogen gas at STP.
Comparison of Gases Kinetic Properties
Argon gas (Ar) deviates more from ideal behavior compared to Neon gas (Ne) at extremely high pressures.
Factor impacting behavior:
(A) Particle volume: The volume of Ar particles is greater than Ne.
(B) Interparticle forces: Ar has more valence electrons resulting in greater interparticle forces.
(C) Intermolecular forces: Ne has stronger intermolecular forces than Ar.
(D) Attraction to walls: Ar is more attracted to container walls than Ne.
Ideal Gas Behavior at 400 K
At 400 K, comparison between CH₄ (g) and CCl₄ (g) in terms of ideal gas behavior.
Justification for behavior: Consider molecular characteristics of both compounds leading to their behaviors under specified conditions.
Comparing Deviation from Ideal Behavior
Two Xe gas samples at 280 K:
Sample 1: Generally less deviation due to larger average distance between Xe atoms insuring fewer intermolecular interactions.
Sample 2: Deviates more due to closer proximity of Xe atoms, increasing intermolecular attractions.
Stické under Ideal Gas Law Conditions
The pressure of CH₄ (g) is closer to that predicted by ideal gas law compared to NH₃ (g).
Reasons:
(A) NH₃ moleculess are polar, resulting in greater attractive forces, leading to less forceful collisions with container walls.
(B) NH₃’s greater molar mass leads to more forceful collisions.
(C) Greater hydrogen bonding in CH₄ than in NH₃ contributes to differences in intermolecular forces.
(D) Size of CH₄ being larger, occupying more volume than NH₃.
KINETIC MOLECULAR THEORY (KMT) POSTULATES
Gases are in constant, random motion and travel in straight lines.
Gas particles are significantly smaller than distances separating them.
Gas particles undergo perfectly elastic collisions with each other and with the walls of their container.
No attractive forces between gas particles or with container walls.
Average kinetic energy is directly proportional to the absolute temperature (in Kelvin) of the gas.
DEVIATIONS FROM IDEAL GAS BEHAVIOR
Conditions Leading to Deviations
High Pressure: At significant pressures, the volume of gas particles can't be ignored.
Low Temperature: Weak intermolecular forces exhibit more influence at lower temperatures causing deviations.
Stronger intermolecular forces lead to higher deviations from ideal gas behavior.
GAS BEHAVIOR WITH ABSOLUTE TEMPERATURES
Observations at various temperatures for real gases indicate progressive deviations from the ideal gas law, particularly at lower temperatures comparing nitrogen gas and other real gas behaviors.
EQUATIONS AND LAWS
Van der Waals Equation
The equation considers intermolecular forces and the volumes of gas particles with corrections for real gas behaviors:
Form: (P + a( rac{n^2}{V^2}))(V - nb) = nRT
Where
aandbare modified constants for the gas.
Graham's Law of Effusion
Rate of effusion between two gases is inversely proportional to the square root of their molecular masses:
( rac{Rate1}{Rate2} = rac{ ext{MM}2}{ ext{MM}1})
GAS LAWS AND EXAMPLES
Ideal Gas Law
Formula: PV = nRT where:
P = Pressure
V = Volume
n = Moles of gas
R = Ideal gas constant
T = Temperature in Kelvin
EXAMPLES
Example Problem #1
Determining molar mass of a gas at 1.50 atm, 27 °C, when density is found to be 1.95 g/L. Identify the gas from the diatomic series.
Example Problem #2
For gas at 15°C and 1.00 atm occupying 2.58 L, calculate the new volume at 38°C with constant pressure.
Example Problem #3
A 12.2 L sample of O₂ at 1.00 atm and 25°C predicts the equivalents for ozone at the same temperature and pressure.
Example Problem #4
Calculate the pressure when compressing ammonia gas from 3.5 L to 1.35 L at constant temperature starting from 1.68 atm.
Example Problem #5
Given a methane sample at 3.8 L and 5°C heating to 86°C at constant pressure: calculate new volume.
Example Problem #6
Calculate new volume for diborane gas transitioning from -15°C at 345 Torr and changing to 36°C and 468 Torr.
Example Problem #7
For argon gas transitioning from 13°C and 568 Torr to 56°C and 897 Torr, calculate change in volume.
Example Problem #8
Calculate volume of carbon dioxide formed when mixing methane and oxygen and igniting following the specific pressures and temperatures.
DALTON'S LAW OF PARTIAL PRESSURE
The partial pressure is defined as:
PA = P{total} * X_A
Where X_A = moles of gas A / total moles.
Summation of partial pressures for a mixture: P{total} = PA + PB + PC + …
EXAMPLE PROBLEMS
Example Problem #9
Find partial pressure of nitrogen in air, mole fraction = 0.7808 with total atmospheric pressure at 760 Torr.
Example Problem #10
Calculate mole fraction of oxygen gas when partial pressure observed is 156 Torr with total atmospheric pressure of 743 Torr.
GAS COLLECTION AND CONDITIONS
Collecting gas over water formula:
P{total} = P{gas} + P_{water}
Gas Collection Scenario
Oxygen collected by displacement of water at 22°C given the total pressure and vapor pressure to calculate various gas properties.
Final Notes on Practical Applications
Gas properties and laws heavily impact real-world applications such as in scuba diving, combustion reactions, and lab experiments involving gas measurements and behaviors under varying conditions.