CHEM 1411 CH.11 notes PDF

Preview

Summary

Thorough notes over properties of gases & gas laws...

Description

Chapter 11: Gases Overview • •

The reason we study gases in Chemistry: The observable properties of gases give us a window into what’s happening at the molecular level. For example: o Why does the pressure of a gas increase when compressed o Why does a gas expand when heated o Why does a gas diffuse through a room

Pressure • • • • • •

•

4 variables completely describe the state of any gas: P (pressure), V (volume), T (Temperature), n (moles) Definition of pressure: P = F/A SI unit of force: N SI unit of area: m^2 Therefore, 1 Pa = 1N/(m^2), Pa = Pascal, Si unit for pressure This is a very small unit o 1 atm = 101,325 Pa o 1 atm = 101.325 kPa o 1 atm = 760 mm Hg = 760 torr o 1 mm Hg = 1 torr o 1 atm = 14.7 psi Methods of measuring pressure: o Manometer

o Barometer

Boyle’s Law •

Under constant T (also mols) condition,

Charles’ Law •

Under constant pressure (and mols) conditions

o Must be in Kelvin (K) for calculation

Avogadro’s Hypothesis and Avogadro’s Law •

Avogadro’s hypothesis: Equal volumes of gases at the same temperature and pressure contain equal numbers of particles (atom or molecules)

•

Avogadro’s Law: At constant P & T, V is directly proportional to mols

•

Two important consequences of Avogadro’s hypothesis and Avogadro’s Law: o We can focus on volumes in gas stoichiometry problems:

o Be careful: 1) This only applies to gases. 2) This only applies to gases measured at the same T & P.

•

The molar volume of a gas at STP is 22.4 L. o STP = Standard Temperature and Pressure o This gives us 2 conversion factors:

o Be careful: 1) This only applies to gases. 2) This only applies to gases measured at STP.

Ideal Gas Law • PV=nRT o o o o o

R = 0.08206 (L*atm)/(mol*K) = 8.314 J/mol*K P = pressure (atm) V = volume (L) n = mole ΔG = -RT*ln(K)

▪ •

K = equilibrium

Examples:

The Combined Gas Law

•

4 Special cases

o 1)

o 2)

o 3)

o 4)

Molar Mass from Density •

Derivation of an important relationship:

o Molar mass:

o Rearrange:

o Ideal gas law:

o Substitute:

o Rearrange: o Extra equations:

o

o

•

Examples: o H

Dalton’s Law of Partial Pressures

•

Definition of Partial Pressure: The pressure that an individual gas in a mixture of gas would exert if it were by itself at the same T & V.

•

Easy way to express Dalton’s Law:

• •

More useful form of Dalton’s Law: Where X_A = mol fraction of A (n_A/n_total) o It is a part of a whole, which means it has to be less than 1 Example:

•

The Kinetic Molecular Theory of Gases •

•

Two main questions: o 1) What causes pressure? o 2) How can we explain the gas laws? ▪ Boyle’s Law ▪ Charles’ Law ▪ Avogadro’s Law ▪ Dalton’s Law 5 postulates of the kinetic molecular theory: o 1) Gases consist of individual particles in constant, random, motion. o 2) The volume of gas particles is extremely small compared to the volume of the container (i.e., a gas is mostly empty space) o 3) Collisions between gas particles are elastic (The total kinetic E after a collision is equal to the total kinetic E before the collision) o 4) Attractions between gas particles are extremely weak and are negligible o 5) The average kinetic E of gas particles depends only on temperature and is directly proportional to T

The Kinetic-Molecular Theory can be used to explain the properties of gases.

• •

The pressure of a gas is caused by the collisions of gas particles with the wall of the container Boyle’s Law at constant T, P is inversely proportional to 1/V. (In a smaller volume, gas particles collide more frequently with the walls of the container)

Temperature and Molecular Velocities

•

Two Boltzmann Distributions, based on temperature and mass:

o What is the relationship between temperature and the average kinetic energy of a gas? ▪ E_k is dependent only on temperature, and independent of volume, pressure, and the identity of the gas.

o Examples:

Root Mean Square Velocity

•

•

•

BE CAREFUL o Use the correct units o R is not in L*atm, they’re in J/(mol*k) o Molar Mass is in SI units (kg/mol) Examples:

Notice: At 298 K, O_2(g) and He(g) have the same average kinetic energy, but He has a higher root-mean square velocity than O_2

Effusion/Diffusion • • •

Diffusion: The spontaneous spreading of one substance through another Effusion: When gas particles escape from a container through a tiny hole. Graham’s Law of Effusion:

o

•

o r_1 and r_2 are the rate of effusion of gases 1 and 2 o M_1 and M_2 are the molar masses of the gases RATE AND TIME ARE NOT THE SAME THING

•

Three important points:

•

o Lighter gases effuse faster than heavier gases o Diffusion works the same as effusion o Rate is inversely proportional to time. Example:

Deviation from Ideal Behavior •

• •

•

•

What is an “ideal gas”? o A gas that obeys the ideal gas law. o PV = nRT What does it mean for a gas to deviate from ideal behavior? o It doesn’t obey the ideal gas law Most gases deviate from ideal behavior at low temperatures and high pressures o This is easy to remember because: ▪ At low temp and at high pressures, a gas will condense into a liquid ▪ Plot of PV/RT vs P (for 1 mol of a gas):

To understand why real gases deviate from ideal behavior, recall two of the postulates of the Kinetic Molecular Theory: o The volume of gas particles is extremely small compared to the volume of the container. But gas particles do have a volume, it occupies space o Attractions between gas particles are extremely weak and negligible. But attractive forces between gas particles do exist

•

•

•

• • •

Gases deviate from ideal behavior at high pressure because: o The volume of the gas particles is a greater fraction of the container o The gas particles are closer, and the intermolecular attractions are more important Gases deviate from ideal behavior at low temperature because: o Gas particles are moving more slowly. They do not have the E to overcome the attractive forces The van de Waals equation is an attempt to correct the ideal gas equation for real gases.

o b & a are our correction factors Pressure correction, because the pressure exerted by the gas is less than it would be if there were no attractive forces between gas molecules. Volume correction, because the volume available to the gas molecules is less than the total volume of the container. a and b are constants that are experimentally determined for each gas. o The constant a is a measure of: The intermolecular attraction between gas particles o The constant b is a measure of: The particle size o Example:...