CHEM 200/202

Professor Jing GuOffice: EIS-210

All emails are to be sent to:chem200@sdsu.edu

My office hours will be held on zoom on Tuesday from 9:00 to 11:00 am or by appointment (https://SDSU.zoom.us/s/

99415148959)

UPCOMING IMPORTANT DATES

• Owl Assignment chapter 7&8, Nov.12th-11:59 pm

• Exam 3 Nov. 13th-3 pm to Nov. 14th 3 pm

• Lab report: Al-Zn alloy, Nov. 15th-11:59 pm

• Owl pre-assignment: freezing point depressing, Nov.15th-11:59 pm

• Pre-lab: freezing point depressing, Nov.15th-11:59 pm

• SIM: Molar Volume of Ideal Gas, Nov.15th-11:59 pm

LECTURE OBJECTIVES• Chapter 9.1-9.3

• Describe the unique properties of gasses.

• Quantify measurements of pressure.

• Define the ideal gas law relationships.

• Calculate the density of ideal gasses.

• Define standard temperature, and pressure.

• Calculate partial pressures of gasses in a mixture.

THE IDEAL GAS LAWAn ideal gas’ physical behavior can be

completely described by only four variables:

Pressure (P)Temperature (T)

Volume (V)Amount (moles, n)

PV = nRT

R = Universal gas constant = 0.08206 L•atm/mol•K

CHANGING CONDITIONSThe Ideal Gas Law can also explain the manner in which a gas changes when conditions change

(e.g. increase P, decrease T...):

= RP1V1

n1T1

P2V2

n2T2=

Subscript 1: Initial conditionsSubscript 2: Final conditions

COMBINED GAS LAW

STOICHIOMETRIC RELATIONSHIPS BETWEEN GASEOUS REAGENTS

P, V, T of gas A

moles of gas A

moles of gas B

P, V, T of gas B

Ideal gas law

Ideal gas law

Molar ratio from balanced

equation

AN EXAMPLE IN THE BOOK

GAS DENSITY AND MOLAR MASSn =mass

MW

n = PVRT

MW = (mass)RTPV

MW = dRTP

d =massV

•The ideal gas law (PV=nRT) can be used to determine the density (d) and/or molecular weight (MW) of the gas.

•The MW of a gas will always remain the same, as it is based on the mass of the atoms of the gas.

•The density of a gas will change with pressure, and temperature.

PROBLEMA 0.50 L bottle contains an unknown gas under a pressure of 3.0 atm at T = 300.K. The mass of the container is 267.37 g when evacuated and 269.08 g when filled with the gas. Which of the following could

be the identity of the gas?nitrogenoxygenfluorineargon

carbon dioxide

STANDARD MOLAR VOLUME

One mole of any idea gas will occupy 22.4 L at standard temperature and

pressure.The difference will be in the mass of the gas (and the

density of the gas).

Standard Temperature and Pressure (STP) = 0°C (273.15 K) and 1.00 atm

QUESTIONList the following gases in order of increasing density.

Assume temperature and pressure are constant.

Cl2<Kr<SO2Kr<SO2<Cl2SO2<Cl2<KrSO2<Kr<Cl2Cl2<SO2<Kr

Answer:ABCDE

DALTON’S LAW OF PARTIAL PRESSURES

• When there is a mixture of gases, the total pressure of the mixture is due to the sum of the individual gas pressures.

• These are termed partial pressures - the amount of pressure produced by each individual type of gas.

Pair = Pnitrogen + Poxygen + Pcarbon dioxide + Pargon + ...

Ptotal = P1 + P2 + P3 + P4 + ...

Py = Xy × Ptotal

Xy = mole fraction of gas y = (moles of y)÷(total moles)

DALTON’S LAW PROBLEMWhat is the total pressure (in atm) when 1.00 mol of Ar, 0.400 mol of He, and 1.60 mol of N2 gases are injected into a 9.12 L flask at 0.00°C?

What is the pressure of each gas in the mixture?

LECTURE OBJECTIVES• Chapter 9.4

• Differentiate between diffusion and effusion.

• Employ Graham’s law of effusion to compare effusion rates of gasses.

• Chapter 9.5

• Define the postulates of the kinetic-molecular theory of gasses.

• Employ the kinetic-molecular theory to explain gas laws.

• Calculate the root-mean-square velocities of gasses.

DIFFUSIONThe random thermal motion of

gases causes gas particles to spread out.

Gas will diffuse from areas of high concentration to areas of

low concentration.

Given enough time the gas particles will be distributed

evenly (homogeneous mixture).

DIFFUSION• If gas molecules move so fast (~500 m/s) why is diffusion so slow?

• Each molecule collides once every ~1 ns.

• The mean free path of a gas molecule (the average distance it moves before it hits something) is ~70 nm (or 103 molecular diameters).

EFFUSION• Effusion - The process by

which a gas molecule escapes from a container through a tiny hole(s).

• Graham’s Law of Effusion - The rate of effusion of a gas is inversely proportional to the square root of its molar mass.

• Root-mean-squared speed (urms)

rateA

rateB MA

MB=

Rate: volume or number of moles of gas per unit time.

urms =3RTMW

EFFUSIONThe escape of molecules through a tiny hole into a vacuum is fastest for smaller mass gasses.

rateA

rateB MA

MB=

AN EXAMPLE OF EFFUSION

HOW TO FIND A MOLECULAR MASS USING GRAHAM’S LAW

QUESTIONThe rate of effusion for nitrogen gas has been measured in an apparatus, and found to be 79 mL/s. If measurement is repeated with sulfur dioxide, at the same temperature and pressure, what will be the effusion rate for sulfur dioxide?

QUESTIONIf it takes 20.0 minute for 0.350 moles of H2S(g) to diffuse

through a porous wall, how long would it take for 0.175 moles of krypton gas (Kr(g)) to diffuse through the same barrier?

rateA

rateB MA

MB=

Answer:A - 10.0 minB - 15.7 minC - 20.0 minD - 31.4 minE - 42.1 min

THE KINETIC-MOLECULAR THEORY OF GASES

• A gas consists of a large collection of individual particles that are very small (no volume).

• Gas particles are in constant, random, straight-line, motion (except for collisions)

• Collisions between particles are elastic - their total kinetic energy (Ek) is constant.

• Between collisions, the gas particles do not influence each other in any way (act independently).

HOW FAST DO THE PARTICLES OF A GAS MOVE?

Very fast!500 m/s = 1800 km/hSpeed increases with

temperature.= (3/2)(R/NA)TEk

Temperature is a measure of molecular motion.

NA=Avogadro's number

AVOGADRO’S LAW REVISITEDWhy do equal numbers of particles of an

ideal gas occupy equal volumes at constant temperature and pressure?

He (4 g/mol) Ar (40 g/mol)

= (3/2)(R/NA)T = ½mu2Ek m = mass, u = speed

MASS VERSUS SPEED

Gas particles with lower mass have higher speeds

Root-mean-squared speed (urms) urms =3RTMW

QUESTIONPressure is a measure of force per unit area. What

does this imply regarding the velocity of gas particles?

•The velocity of gas particles is independent of the mass of the particle.•The velocity of gas particles is directly proportional to the mass of the particles.•The velocity of gas particles is inversely proportional to the mass of the particles.•All of the above statements are true.•None of the above statements are true.

AnswerA

B

C

DE

CALCULATION QUESTIONWhat is the root-mean-square velocity for a

molecule of nitrogen gas at 30°C?

How fast does a molecule of SF6 travel at the same temperature?

QUESTIONA sample of an ideal gas is heated in a steel container from

25°C to 100°C. Which quantity will remain unchanged?

The average kinetic energy of the gas particles.The collision frequency.The density.The pressure of the gas.

Answer:ABCD

POSTULATES OF KINETIC-MOLECULAR THEORY

Postulate 1: Particle volumeBecause the volume of an ideal gas particle is so small compared to the volume of its container, the gas particles are considered to have mass, but no volume.Postulate 2: Particle motionGas particles are in constant, random, straight-line motion except when they collide with each other or with the container walls.Postulate 3: Particle collisionsCollisions are elastic, therefore the total kinetic energy of the particles is constant.

IDEAL VS. REAL GASES

Pext (atm)

PVRT

2.0

1.5

1.0

0.5

0.00 300 900 1200 1500

• We have assumed that gasses behave ideally.

• But they do not, at the extremes they deviate from the predictions we have made.

• What in our model is breaking down?

Ideal Gas

Real Gas

REAL GASEShttps://www.youtube.com/watch?v=WomsUEVVtCk

REAL VS IDEAL GASES

• Real gases do not act exactly as we predict ideal gases would behave.

• Intermolecular Attractions - are much weaker than bonding, so only seen under extreme conditions. Intermolecular attractions reduce the force of the impact with the walls of the container.

• Molecular Volume - as the free volume (empty space) decreases, the volume of gas molecules becomes significant.

INTERPARTICLE ATTRACTIONS• Interparticle attractions are very weak forces - much

weaker than the bonds in a molecule.

• At low pressures gas particles are far from each other so the Interparticle attractions have little influence.

• At high external pressures the particles are closer together and the Interparticle attractions becomes significant. This also happens at very low temperatures.

INTERPARTICLE ATTRACTION• Impact of interparticle attractions is a reduction in the velocity of the

particles.

• A lower particle velocity reduces the force of the collision with the walls.

• Overall this means the gas exerts less pressure on the container walls.

MOLECULAR VOLUME• In the ideal model of a gas we presume that the volume of

the gas molecule is negligible in comparison to the free space around each particle.

• As the pressure increases, the amount of free space for particles to move is reduced, to the point where the gas particles become a meaningful amount of that “free space”.

QUESTIONAt very high pressures (~1000 atm) the measured pressure exerted by a real gas is greater than that

predicted by an ideal gas. Why is that?

•Because it is difficult to measure high pressures accurately.•Because real gases will condense to form liquids at that pressure.•Because gas phase collisions prevent the molecules from colliding with the container walls.•Because of the attractive intermolecular forces between the gas molecules.•Because the volume occupied by the gas molecules becomes significant.

Answer:ABC

D

E

PVDW=45.9 atm

ADJUSTING THE IDEAL GAS LAW• To better describe real gasses we need to:

• Adjust P up, to account for inter particle attractions.

• Adjust V down, to account to particle volume.

• The values a and b were determined experimentally by Johannes van der Waals.

4.89 mol CO2 in 1.98 L at 299K:Preal=44.8 atmPIGL=60.6 atm