AP Chemistry

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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

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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:

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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:

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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:

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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:

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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

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d: gas density (grams per liter)

Dalton’s law of partial pressures

Dalton’s law of partial pressures:

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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)

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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

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