Gases and AtmosphericGases and AtmosphericChemistryChemistry

SCH 3USCH 3U

Kinetic Molecular Theory Kinetic Molecular Theory (KMT)(KMT) Attempts to explain why gases behave

the way they do.• 1) Gases are mostly empty space; the

volume of particles is negligible.

• 2) Gas particles are in constant random motion.

• 3) Gas particles neither attract nor repel each

other.• 4) Pressure is due to collisions of gas

particles with container walls.• 5) The average kinetic energy of a gas

sample is proportional to the Kelvin

Temperature

Pressure and VolumePressure and Volume

• Boyle’s Law -Boyle’s Law - At a constant temperature, the volume of a given At a constant temperature, the volume of a given mass of gas is inversely proportional to the pressure.mass of gas is inversely proportional to the pressure.

V V 1/P 1/P

PP11 V V11 = P = P22 V V22

• where, Pwhere, P11 and V and V11 are the original pressure and volume and are the original pressure and volume and • PP22 and V and V22 are the new pressure and volume are the new pressure and volume

PressurePressure

• The force exerted on an object per unit of surface area.

• The pressure of a gas is determined by the kinetic motion of it’s molecules. The molecules collide with the walls of the container.

• The collective number of collisions as well as the strength of the force determine the overall gas pressure.

Units of PressureUnits of Pressure

• 760 mm Hg 760 mm Hg

• 760 torr 760 torr

• 1 atm 1 atm

• 101.3 kPa101.3 kPa

• 14.7 lb/in2 (p.s.i.)14.7 lb/in2 (p.s.i.)

• Use equivalent fractions to convert Use equivalent fractions to convert between units of pressurebetween units of pressure

Volume and TemperatureVolume and Temperature• Charles’ Law -Charles’ Law - At a constant pressure, the volume of a given At a constant pressure, the volume of a given

mass of gas is directly proportional to its absolute temperature.mass of gas is directly proportional to its absolute temperature.

V V T T

VV11 = V = V22

TT11 T T22

• TT11 and V and V11 are the initial temperature and volume and are the initial temperature and volume and

TT22 and V and V22 are the final temperature and volume are the final temperature and volume

Kelvin TemperatureKelvin Temperature

• Temperature is a measure of the average Temperature is a measure of the average kinetic energy of the particles within a kinetic energy of the particles within a substance.substance.

• Absolute zeroAbsolute zero (-273 (-273C) – the temperature at C) – the temperature at which the average kinetic energy of all which the average kinetic energy of all molecules is equal to zero. All molecular molecules is equal to zero. All molecular motion ceases. motion ceases.

• Kelvin scaleKelvin scale – a temperature scale beginning – a temperature scale beginning at absolute zero ( 0 K = -273at absolute zero ( 0 K = -273C ) where each C ) where each Kelvin unit is equal to 1Kelvin unit is equal to 1C.C.

Converting TemperatureConverting Temperature

• There are no degree signs used in the There are no degree signs used in the Kelvin scale and no negative values.Kelvin scale and no negative values.

• TK = TK = C + 273.15 C + 273.15

• Try These:Try These: Temperature C Temperature K

Freezing point of water O

Life threatening fever 314

Oil temperature for French fries 162

Hottest day on record 331

Coldest day on record -88

Pressure and TemperaturePressure and Temperature• Gay-Lussac’s Law -Gay-Lussac’s Law - The pressure of a fixed amount of gas, at a The pressure of a fixed amount of gas, at a

constant volume, is directly proportional to its Kelvin constant volume, is directly proportional to its Kelvin temperature.temperature.

• P P T T PP11 = P = P22

TT11 T T22

• • TT11 and P and P11 are the initial temperature and pressure and are the initial temperature and pressure and • TT2 2 and Pand P22 are the final temperature and pressure are the final temperature and pressure

So far we have seen three gas laws: So far we have seen three gas laws:

Jacques Charles

Robert Boyle

PP11VV11 == PP22VV22VV11

TT11

==VV22

TT22These are all subsets of a more encompassing law:

the combined gas law

PP11

TT11

==PP22

TT22

P1V1 P2V2

T1 T2

=

Joseph Louis Gay-Lussac

Time to PracticeTime to Practice

• A 350 mL sample of helium gas is A 350 mL sample of helium gas is collected at 22.0 collected at 22.0 ooC and 99.3 kPa.  C and 99.3 kPa.  What volume would this gas What volume would this gas occupy at STP?occupy at STP?

The Ideal Gas LawThe Ideal Gas Law

PV = nRTPV = nRTP = Pressure (in kPa)P = Pressure (in kPa) V = Volume (in L)V = Volume (in L)T = Temperature (in K) T = Temperature (in K) n = molesn = moles

R = 8.31 kPa • LR = 8.31 kPa • LK • molK • mol

R is constant. If we are given three of P, V, n, R is constant. If we are given three of P, V, n, or T, we can solve for the unknown value.or T, we can solve for the unknown value.

This law allows us to involve the quantity of a This law allows us to involve the quantity of a gas into our analysis.gas into our analysis.

Sample problemsSample problemsHow many moles of HHow many moles of H22 is in a 3.1 L sample of H is in a 3.1 L sample of H22

measured at 300 kPa and 20measured at 300 kPa and 20°°C?C?

PV = nRTPV = nRT(300 kPa)(3.1 L) = n (8.31 kPa•L/K•mol)(293 K)(300 kPa)(3.1 L) = n (8.31 kPa•L/K•mol)(293 K)

(8.31 kPa•L/K•mol)(293 K)(8.31 kPa•L/K•mol)(293 K)(300 kPa)(3.1 L)(300 kPa)(3.1 L)

= n = 0.38 mol= n = 0.38 mol

How many grams of OHow many grams of O22 are in a 315 mL container are in a 315 mL container that has a pressure of 12 atm at 25that has a pressure of 12 atm at 25°°C?C?

P = 300 kPa, V = 3.1 L, T = 293 KP = 300 kPa, V = 3.1 L, T = 293 K

PV = nRTPV = nRT

(8.31 kPa•L/K•mol)(298 K)(8.31 kPa•L/K•mol)(298 K)(1215.9 kPa)(0.315 L)(1215.9 kPa)(0.315 L) = n = 0.15= n = 0.15447 mol7 mol

P= 1215.9 kPa, V= 0.315 L, T= 298 KP= 1215.9 kPa, V= 0.315 L, T= 298 K

0.150.15447 mol x 32 g/mol = 4.95 g7 mol x 32 g/mol = 4.95 g

SimulationSimulation

• http://www.chem.ufl.edu/~itl/2045/Mhttp://www.chem.ufl.edu/~itl/2045/MH_sims/gas_sim.htmlH_sims/gas_sim.html