# week 2 lectures--tentative

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Week 2 lectures--tentative. 10.7 Kinetic Molecular Theory. Theory developed to explain gas behavior. Theory based on properties at the molecular level . Kinetic molecular theory gives us a model for understanding pressure and temperature at the molecular level. - PowerPoint PPT PresentationTRANSCRIPT

Week 2 lectures--tentative

Theory developed to explain gas behavior.Theory based on properties at the molecular level.Kinetic molecular theory gives us a model for understanding pressure and temperature at the molecular level.Pressure of a gas results from the number of collisions per unit time on the walls of container.

10.7 Kinetic Molecular Theory

There is a spread of individual energies of gas molecules in any sample of gas.As the temperature increases, the average kinetic energy of the gas molecules increases.Kinetic Molecular Theory

Assumptions:Gases consist of a large number of molecules in constant random motion.Volume of individual molecules negligible compared to volume of container.Intermolecular forces (attractive or repulsive forces between gas molecules) are negligible.Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature.Average kinetic energy of molecules is proportional to temperature.

10.7 Kinetic Molecular Theory

Kinetic Molecular TheoryMagnitude of pressure given by how often and how hard the molecules strike. Gas molecules have an average kinetic energy.Each molecule may have a different energy.

As kinetic energy increases, the velocity of the gas molecules increases.Root mean square speed, u, is the speed of a gas molecule having average kinetic energy.Average kinetic energy, , is related to root mean square speed:Kinetic Molecular Theory

Do you remember how to calculatevxy from vx and vy ?And how about v from all threecomponents?Remember these equations!! Theyll popup again in Chap. 11.

Note that the mean value of velocity is zero!The Maxwell-Boltzmann Distribution of Velocities

The Maxwell Distribution of Speeds

ump

urms

The Maxwell-Boltzmann Distribution of VelocitiesThis is also theform of a Gaussian (normal) distribution,where ump = = urms.

Application to Gas LawsAs volume increases at constant temperature, the average kinetic of the gas remains constant. Therefore, u is constant. However, as the volume increases the gas molecules have to travel further to hit the walls of the container. Therefore, pressure decreases.If temperature increases at constant volume, the average kinetic energy of the gas molecules increases. Therefore, there are more collisions with the container walls and the pressure increases.Kinetic Molecular Theory

Molecular Effusion and DiffusionAs kinetic energy increases, the velocity of the gas molecules increases.Average kinetic energy of a gas is related to its mass:

Consider two gases at the same temperature: the lighter gas has a higher velocity than the heavier gas.Mathematically:Kinetic Molecular Theory

Molecular Effusion and DiffusionThe lower the molar mass, M, the higher the urms.Kinetic Molecular Theory

Comment: This corresponds to a speed of 1150 mi/hr. Because the average molecular weight of air molecules is slightly greater than that of N2, the rms speed of air molecules is a little slower than that for N2. The speed at which sound propagates through air is about 350 m/s, a value about two-thirds the average rms speed for air molecules.

Kinetic Molecular TheoryGrahams Law of EffusionAs kinetic energy increases, the velocity of the gas molecules increases.Effusion is the escape of a gas through a tiny hole. The rate of effusion can be quantified.

Grahams Law of Effusion Consider two gases with molar masses M1 and M2, the relative rate of effusion is given by:

Only those molecules that hit the small hole will escape through it.Therefore, the higher the urms the greater the likelihood of a gas molecule hitting the hole.Kinetic Molecular Theory

Because we are told that the unknown gas is composed of homonuclear diatomic molecules, it must be an element. The molar mass must represent twice the atomic weight of the atoms in the unknown gas. We conclude that the unknown gas is I2.SAMPLE EXERCISE 10.15 continued

Grahams Law of Effusion Consider two gases with molar masses M1 and M2, the relative rate of effusion is given by:

Only those molecules that hit the small hole will escape through it.Therefore, the higher the rms the more likelihood of a gas molecule hitting the hole.Kinetic Molecular Theory

Diffusion and Mean Free Path Diffusion of a gas is the spread of the gas through space.Diffusion is faster for light gas molecules.Diffusion is significantly slower than rms speed (consider someone opening a perfume bottle: it takes while to detect the odor but rms speed at 25C is about 1150 mi/hr).Diffusion is slowed by gas molecules colliding with each other.Kinetic Molecular Theory

Diffusion and Mean Free Path Average distance of a gas molecule between collisions is called mean free path.At sea level, mean free path is about 6 10-6 cm.

Kinetic Molecular Theory

From the ideal gas equation, we have

For 1 mol of gas, PV/nRT = 1 for all pressures.In a real gas, PV/nRT varies from 1 significantly and is called Z.

The higher the pressure the more the deviation from ideal behavior.Real Gases: Deviations from Ideal Behavior

From the ideal gas equation, we have

For 1 mol of gas, PV/RT = 1 for all temperatures.As temperature increases, the gases behave more ideally.The assumptions in kinetic molecular theory show where ideal gas behavior breaks down:the molecules of a gas have finite volume;molecules of a gas do attract each other.Real Gases: Deviations from Ideal Behavior

As the pressure on a gas increases, the molecules are forced closer together.As the molecules get closer together, the volume of the container gets smaller.The smaller the container, the more space the gas molecules begin to occupy.Therefore, the higher the pressure, the less the gas resembles an ideal gas.Real Gases: Deviations from Ideal Behavior

As the gas molecules get closer together, the smaller the intermolecular distance.Real Gases: Deviations from Ideal Behavior

The smaller the distance between gas molecules, the more likely attractive forces will develop between the molecules.Therefore, the less the gas resembles and ideal gas.As temperature increases, the gas molecules move faster and further apart.Also, higher temperatures mean more energy available to break intermolecular forces.Real Gases: Deviations from Ideal Behavior

Therefore, the higher the temperature, the more ideal the gas.Real Gases: Deviations from Ideal Behavior

The van der Waals EquationWe add two terms to the ideal gas equation one to correct for volume of molecules and the other to correct for intermolecular attractions The correction terms generate the van der Waals equation:

where a and b are empirical constants characteristic of each gas. Real Gases: Deviations from Ideal Behavior

The van der Waals Equation

General form of the van der Waals equation:Real Gases: Deviations from Ideal BehaviorCorrects for molecular volumeCorrects for molecular attraction

Check: We expect a pressure not far from 1.000 atm, which would be the value for an ideal gas, so our answer seems very reasonable.

SAMPLE INTEGRATIVE EXERCISE Putting Concepts TogetherCyanogen, a highly toxic gas, is composed of 46.2% C and 53.8% N by mass. At 25C and 751 torr, 1.05 g of cyanogen occupies 0.500 L. (a) What is the molecular formula of cyanogen? (b) Predict its molecular structure. (c) Predict the polarity of the compound.

SAMPLE INTEGRATIVE EXERCISE continuedThe molar mass associated with the empirical formula, CN, is 12.0 + 14.0 = 26.0 g/mol. Dividing the molar mass of the compound by that of its empirical formula gives (52.0 g/mol)/(26.0 g/mol) = 2.00. Thus, the molecule has twice as many atoms of each element as the empirical formula, giving the molecular formula C2N2The Lewis structure shows that each atom has two electron domains. (Each nitrogen has a nonbonding pair of electrons and a triple bond, whereas each carbon has a triple bond and a single bond.) Thus the electron-domain geometry around each atom is linear, causing the overall molecule to be linear.(c) Plan: To determine the polarity of the molecule, we must examine the polarity of the individual bonds and the overall geometry of the molecule.Solve: Because the molecule is linear, we expect the two dipoles created by the polarity in the carbonnitrogen bond to cancel each other, leaving the molecule with no dipole moment.

Chapter 11 -- Intermolecular Forces, Liquids, and SolidsIn many ways, this chapter is simply acontinuation of our earlier discussion ofreal gases.

Remember this nice, regular behavior described by the ideal gas equation.

This plot for SO2 is a morerepresentativeone of real systems!!!

This plot includes a realistic one for Volume as a function of Temperature!

Why do the boiling points vary? Is there anything systematic?

What determines whether a substance existsas a gas, liquid, or solid?

Two primary factors are involved:

Kinetic Energy of the particles.

Strength of attractions betweenthe particles.

What are the important Intermolecular Forces i.e, forces between molecules ?Note that earlier chapters concentrated on Intramolecular Forces, those within the molecule.

Important ones:

ion-ionsimilar to atomic systems

ion-dipole (review definition of dipoles)

dipole-dipole

dipole-induced dipole

London Dispersion Forces:(induced dipole-induced dipole) related to polarizability

Hydrogen Bonding

van der Waalsfor

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