AP Chemistry

Pages
- Class
  Laboratory report rubric
  Notes
  1. Chemical foundations
  2. Atoms, molecules, and ions
  3. Stoichiometry
  4. Types of chemical reactions and solution stoichiometry
  5. Gases
  6. Thermochemistry
  7. Atomic structure and periodicity
  8. Bonding: general concepts
  9. Covalent bonding: orbitals
  10. Liquids and solids
  11. Properties of solutions
  12. Chemical kinetics
  13. Chemical equilibrium
  14. Acids and bases
  15. Acid-base equilibria
  16. Solubility and complex ion equilibria
  17. Spontaneity, entropy, free energy
  18. Electrochemistry
  Drug unit
  Basics
  Analgesics
  Antacids
  Anesthetics
  Depressants
  Stimulants
  Antibiotics
  Antiviral drugs
  Mind-altering drugs
- Textbook (incomplete)
  1. Chemical foundations
  2. Atoms, molecules, and ions
  3. Stoichiometry
  4. Types of chemical reactions and solution stoichiometry
  5. Gases
  6. Thermochemistry
  7. Atomic structure and periodicity
  8. Bonding: general concepts
- CED
  1. Atomic structure and properties
  2. Compound structure and properties
  3. Properties of substances and mixtures
  4. Chemical reactions
  5. Kinetics
  6. Thermochemistry
  7. Equilibrium
  8. Acids and bases
  9. Thermodynamics and electrochemistry

AP Chemistry

...

5. Gases

Explore

5. Gases

Pressure

gas

uniformly fills any container

easily compressed

mixes completely with any other gas

exerts pressure on surroundings

barometer: used to measure atmospheric pressure

invented in 1643 by Italian scientist Evangelista Torricelli, student of Galileo

filled glass tube with liquid mercury and inverting it in a dish of mercury

atmospheric pressure: results from mass of air being pulled towards the center of the earth by gravity (weight of the air)

varies with:

changing weather conditions

altitude

Units of pressure

manometer: instrument used for measuring pressure

instruments used for measuring pressure often contain mercury, so most commonly used units are based on the height of the mercury column (mm) that the pressure can support

mm Hg (millimeter of mercury)/torr

standard atmosphere (atm)

1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr

⁠

SI system:

unit of force: newton (N)

unit of area: meters squared (m²)

pascal (Pa): newtons per meter squared (N/m²)

1 atm = 101,325 Pa

Gas laws

Boyle’s law

first quantitative experiments on gases: Irish chemist Robert Boyle

J-shaped tube closed at one end

relationship between pressure of trapped gas and volume

product of pressure and volume for trapped air sample is constant

Boyle’s law:

⁠

V: volume

k: constant for giving sample of air at specific temperature

P: pressure

holds precisely only at very low pressures

ideal gas: gas that strictly obeys Boyle’s law

often used to predict new volume of gas when pressure changes or vice versa

Charles’s law

French physicist Jacques Charles

first person to fill a balloon with hydrogen gas

made the first solo balloon flight

found that the volume of a gas at constant pressure increases linearly with temperature of the gas

Charles’s law:

⁠

V: volume

T: temperature in kelvins

b: proportionality constant

the volume of each gas is directly proportional to temperature

absolute zero: 0 K

Avogadro’s law

volumes of gases at same temperature and pressure contain the same number of “particles”

Avogadro’s law:

⁠

V: volume of gas

a: proportionality constant

n: number of moles of gas particles

for a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas

Ideal gas law

ideal gas law:

⁠

R: universal gas constant

combined proportionality constant

⁠

ideal gas law is an equation of state

pressure

volume

temperature

number of moles

limiting law; expresses behavior that real gases approach at low pressures and high temperatures (hypothetical)

place variables that change on one side of the equal sign and constants on the other

Gas stoichiometry

standard temperature and pressure (STP): 0℃ and 1 atm

molar volume: volume of one mole of ideal gas

Molar mass of a gas

⁠

d: gas density (grams per liter)

Dalton’s law of partial pressures

Dalton’s law of partial pressures:

⁠

subscripts: individual gases (gas 1, gas 2, gas 3, etc.)

P₁, P₂, P₃: partial pressure

partial pressure: pressure that a particular gas would exert if it were alone in the container

can be calculated from ideal gas law

⁠

pressure exerted by an ideal gas is not affected by the identity (composition) of the gas particles

the volume of the individual gas particle is not important

the forces among the particles are not important

mole fraction: ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture

represented by χ (Greek lowercase letter chi)

⁠

Collecting a gas over water

mixture of gases results whenever a gas is collected by displacement of water

e.g. collection of oxygen gas produced by decomposition of solid potassium chlorate

gas in the bottle is mixture of water vapor and oxygen

water vapor present because molecules of water escape from surface of liquid and collect in space above

molecules of water also return to liquid

vapor pressure of water: when rate of escape equals rate of return

number of water molecules in vapor state remain constant

pressure of water vapor remains constant

Kinetic molecular theory of gases

any model is an approximation

kinetic molecular theory (KMT): simple model that attempts to explain the properties of an ideal gas

based on speculations bout the behavior of the individual gas particles

postulates:

volume of the individual particles can be assumed to be negligible (zero) because the particles are so small compared with the distances between them

particles are in constant motion; collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas

particles are assumed to exert no forces on each other; neither attract nor repel

average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas

real gases do not conform to these assumptions

Pressure and volume (Boyle’s law)

⁠

nRT: constant

KMT: decrease in volume → gas particles will hit the wall more often → pressure increases

Pressure and temperature

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nR/V: constant

KMT: temperature of gas increases → speeds of particles increase → particles hit the wall with greater force and frequency → pressure increases

Volume and temperature (Charles’s law)

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nR/P: constant

KMT: temperature of gas increases → speeds of molecules increase → particles hit walls with greater force and frequency → pressure must stay constant → volume increases

Volume and number of moles (Avogadro’s law)

⁠

RT/P: constant

KMT: increase in number of gas particles at same temperature → pressure must increase if volume constant

volume of gas at constant temperature and pressure depends only on number of gas particles, not volume of particles

Mixture of gases (Dalton’s law)

total pressure exerted by a mixture of gases is the sum of the pressures of the individual gases

KMT: assumes all gas particles are independent of each other and that the volumes of the individual particles are unimportant → identities of the gas particles do not matter

Deriving the ideal gas law

⁠

equation using definitions of velocity, momentum, force, pressure to collection of particles in ideal gas

P: pressure of gas

n: number of moles of gas

Nₐ: Avogadro’s number

1/2mu²: average kinetic energy of gas particles

m: mass of each particle

u²: average of square of velocities of particles

V: volume of container

average kinetic energy for mole of gas particles:

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expression for pressure can be rewritten as either of:

⁠

since average kinetic energy is directly proportional to temperature in kelvin:

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ideal gas law:

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Meaning of temperature

using:

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summarizes meaning of Kelvin temperature of a gas

index of random motions of the particles of a gas

higher temperatures means greater motion

Root mean square velocity

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root mean square velocity: square root of the average of the squares of the particle velocities

equation

use equations:

⁠

combine equations:

⁠

take square root of both sides

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R must be expressed in different units to optain meters per second for u_rms

joule: kilogram meter squared per second squared (kg × m²/s²)

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mean free path: average distance a particle travels between collisions in a particular gas sample

the many collisions produces a large range of velocities as the particles collide and exchange kinetic energy

Maxwell-Boltzmann distribution: velocity distribution

as temperature increases, the curve peak moves to higher values and the range of velocities increases

peak: most probable velocity

Effusion and diffusion

diffusion: mixing of gases

effusion: passive of gas through tiny orifice/pinhole into evacuated chamber

Effusion

Graham’s law of effusion

⁠

M: molar masses

relative rates of effusion of two gases at the same temperature and pressure are given by the inverse ratio of the square roots of the masses of the gas particles

Diffusion

often illustrated with two cotton plugs soaked in ammonia and hydrochloric acid placed at ends of long tube

white ring of ammonium chloride forms where the molecules meet

NH₃(g) + HCl(g) → NH₄Cl(s)

complicated to describe theoretically

Real gases

how to modify the assumptions of the kinetic molecular theory to fit the behavior of real gases?

Johannes van der Waals was the first to do important work in this area

ideal gas law

⁠

describes behavior of hypothetical gas consisting of volumeless entities that do not interact with each other

real gases consist of atoms or molecules with finite volumes

volume available to given particle in real gas is less than the volume of the container

volume actually available to given gas molecule: V - nb

V: volume of the container

nb: correction factor

n: number of moles

b: empirical constant (from experimental results)

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