Unit 11 The Behavior of Gases

The Properties of GasesC Recall from Unit 10 about the kinetic theory of gases

C It assumes that gases consist of hard, spherical particles that have the following propertiesC the volume of the gas particles are insignificant in comparison to the volume of the gas

C gas particles are far apart from each other; which means they can be compressed(squashed)

C there are no attractive or repulsive forces between the particlesC gases expand to take on the shape and volume of their container

C gas particles move rapidly in constant random motion.C the particles travel in straight paths and move independently of each other

Four variables are generally used to describe a gasC pressure (P) - remember that 1 atm = 760 mmHg = 101.3 kPaC volume (V) - remember that 1 L = 1000 mL = 1000 cm3 = 1 dm3

C temperature (T) - remember that K = EC + 273C number of moles (n) - remember that moles = mass of substance divided by its molar mass

Standard Temperature and Pressure• remember mole conversions concerning molar volume (1 mole of a gas @STP = 22.4 L)• those three letters mean something important

• STP means standard temperature and pressure• Standard temperature is 0EC or 273 K• Standard pressure is normal atmospheric pressure• remember 1 atm = 760 mmHg = 101.3 kPa

Factors Affecting Gas PressureC Pressure is the result of the particles of a gas colliding with the walls of the container. There

are three factors that can affect the pressure of a gas.C Factor 1 Amount of Gas - pressure is directly tied to the number of particles in the container

C the more particles hitting the walls, the higher the pressureC if you remove particles, you lower the pressure

C Factor 2 Volume of container - by changing the volume of the container, you can affect thepressureC reduce the volume = particles hit walls of container more often = higher pressureC increase the volume = particles hit walls of container less often = lower pressure

C Factor 3 Temperature - by changing the temperature of the gas, you can affect the pressureC heat gas = higher kinetic energy = particles hit walls more often = higher pressureC cool gas = lower kinetic energy = particles hit walls less often = lower pressure

The Gas Laws

The Pressure-Volume Relationship: Boyle’s LawC Boyle’s law states that for a given mass of a gas at constant temperature, the volume of the

gas varies inversely with pressure.C In other words, as the volume decreases, pressure increases. As the volume increases,pressure decreases.

• Think of a syringeC The formula needed for solving Boyle’s law problems is P1×V1 = P2×V2

P1V1

T1

'P2V2

T2

The Temperature-Volume Relationship: Charles’s LawC Jacques Charles investigated the effect of temperature on the volume of a gas at constant

pressure.C He observed an increase in the volume of a gas with an increase in temperature, and adecrease in volume with a decrease in temperature.

C He noticed that no matter the identity of the gas, the data always would produce a graphwith a straight line.

C IF that line were extrapolated to find the x-intercept, it would intercept at -273ECC Lord Kelvin recognized the significance of this number and called it absolute zero (thetemperature at which the average kinetic energy of the gas particles would theoreticallybe zero).

C Charles’s law states that the volume of a fixed mass of gas is directly proportional to its Kelvintemperature if the pressure is kept constant.C In other words, as temperature goes up, volume goes up. As temperature goes down,volume goes down

• Think of a Mylar balloon purchased on a very cold day..C The formula needed for solving Charles’s law problems is V1/T1 = V2/T2

• Please note that the temperature must be in Kelvin

The Temperature-Pressure Relationship: Gay-Lussac’s LawC Gay-Lussac’s Law states that the pressure of a gas is directly proportional to the Kelvin

temperature if the volume is kept constant.C In other words, as temperature goes up, pressure goes up. As temperature goes down,pressure goes down.

• Think of a gas can.C The formula needed for solving Gay-Lussac’s law problems is P1/T1 = P2/T2 (temperature must

be in Kelvin).

The Combined Gas LawC The combined gas law is just that; a combination of the first three laws.

C If temperature is constant, the T’s fall away, and you have Boyle’s law.C If pressure is constant, the P’s fall away, and you have Charles’s law.C If volume is constant, the V’s fall away, and you have Gay-Lussac’s law.C Sometimes no variable is constant.C Remember that the temperature must be in Kelvin.

PV ' nRT

RateA

RateB

'molar mass

B

molar massA

12.4 Ideal GasesC A truly ideal gas is one that follows the gas laws at all conditions of pressure and temperature.

C which means that the gas would have to conform to the assumptions of the kineticmolecular theory

C The ideal gas law allows you to solve for the number of moles (n) when P. V, and T are known.C These problems do not deal with initial/final conditions as do the other gas laws.

P = pressure in kPa or atm n = number of molesT = temperature in Kelvin V = volume in L or dm3

R = the ideal gas constant (depends upon pressure unit)

Gas Molecules: Mixtures and Movements

Avogadro’s HypothesisC Avogadro’s Hypothesis states that equal volumes of gases at the same temperature and

pressure contain the same number of particles.C Remember that at STP, 1 mole of particles of any gas, regardless of the size of the particles,

occupies a volume of 22.4 L.C Avogadro’s law states that the volume of a gas is directly proportional to the amount of the gas

if the temperature and pressure are kept constant.• In other words, if more gas is added to an expandable container, the volume will increase.• If some gas is removed from an expandable container, the volume will decrease.

C The formula needed for solving Avogadro’s law problems is V1/n1 = V2/n2Dalton’s LawC Dalton’s law states that at constant volume and temperature, the total pressure exerted by a

mixture of gases is equal to the sum of the partial pressures of the component gases.C The partial pressure exerted by a gas is the pressure that the gas would exert if it were theonly gas in the container.

• There are several different ways that Dalton’s Law problems will be presented to you.• Scenario 1: You will have a mixture of gases (as few as two or there could be as many asten gases). You could be given the total pressure of the gas (Ptotal ) and all of the partialpressures (Pgas) but one. The equation needed for solving Dalton’s law problems is

Ptotal = P1 + P2 + P3 + ...• The above formula will depend upon how many gases are in the mixture.

• Scenario 2: You will have a mixture of gases. You usually are given the total pressure. Then you will be given percent information (ie. 25% of the gas mixture is Argon, what is thepartial pressure of the Argon?) The formula needed would be

PAr = 25% of Ptotal• Scenario 3: Again, you will have a mixture of gases. You will be given mole information ofeach gas in the mixture and the total pressure. You have to determine the mole fraction ofthe gas in question and then multiply that fraction by the total pressure.

Pgas = Moles of gas/total moles of gas x Ptotal

Graham’s LawC Graham’s Law of effusion states that the rate of effusion of a gas is inversely proportional to

the square root of the gas’s molar mass.C In other words, if two gases are in the same container, the lighter gas will move faster than the

heavier gas.