The first scheduled quiz will be given next Tuesday during Lecture. It will last 15 minutes. Bring pencil, calculator, and your book. The coverage will be pp , i.e. Sections 10.0 through 11.4.

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 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 (forces between gas molecules) 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 Kinetic Molecular Theory

Kinetic Molecular Theory Magnitude 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 calculate v xy from v x and v y ? And how about v from all three components? Remember these equations!! They’ll pop up again in Chap. 11.

u mp u rms

1.Be careful of speed versus velocity. The former is the magnitude of the latter. 2.The momentum of a molecule is p = mv. During a collision, the change of momentum is Δp wall = p final – p initial = (-mv x ) – (mv x ) = 2mv x. 3.Δt = 2ℓ / v x Δp x / Δt =... = mv x 2 / ℓ, where ℓ is length of the box 4.force = f = ma = m(Δv / Δt) = Δp / Δt = mv x 2 / ℓ = force along x 5.And for N molecules, F = N(m(v x 2 ) avg / ℓ ) 6.But 7.And

But N = nN 0, so we can divide both sides by n to obtain

Application to Gas Laws As volume increases at constant temperature, the average kinetic of the gas remains constant. Therefore, u is constant. However, volume increases so 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 Diffusion As 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 rms than the heavier gas. Mathematically: Kinetic Molecular Theory

Molecular Effusion and Diffusion The lower the molar mass, M, the higher the rms. Kinetic Molecular Theory

Graham’s Law of Effusion As kinetic energy increases, the velocity of the gas molecules increases. Effusion is the escape of a gas through a tiny hole (a balloon will deflate over time due to effusion). The rate of effusion can be quantified.

Graham’s Law of Effusion Consider two gases with molar masses M 1 and M 2, 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

Graham’s Law of Effusion Consider two gases with molar masses M 1 and M 2, 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 25  C 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  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 first scheduled quiz will be given next Tuesday during Lecture. It will last 15 minutes. Bring pencil, calculator, and your book. The coverage will be pp , i.e. Sections 10.0 through 11.4.

The van der Waals Equation We 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 Behavior Corrects for molecular volume Corrects for molecular attraction

Chapter Intermolecular Forces, Liquids, and Solids In many ways, this chapter is simply a continuation of our earlier discussion of ‘real’ gases.

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

This plot for SO 2 is a more representative one of real systems!!!

And this is a plot for an ideal gas of the dependence of Volume on Temperature.

Now this one includes a realistic one for Volume as a function of Temperature!

Why do the boiling points vary? Is there anything systematic? London Dispersion Forces

Hydrogen Bonding

Dipole-Dipole Forces

Intermolecular Forces -- forces between molecules -- are now going to be considered. 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 polarizability Hydrogen Bonding

How do you know the relative strengths of each? Virtually impossible experimentally!!! Most important though: Establish which are present. London Dispersion Forces: Always All others depend on defining property such as existing dipole for d-d. It has been possible to calculate the relative strengths in a few cases.

Relative Energies of Various Interactions d-dd-iddisp Ar0050 N C 6 H C 3 H HCl CH 2 Cl SO H 2 O HCN

Ion-dipole interaction Let’s take a closer look at these interactions:

Let’s take a closer look at dipole-dipole interactions. This is the simple one.

But we also have to consider other shapes. Review hybridization and molecular shapes.

Recall the discussion of sp, sp 2, and sp 3 hybridization?

London dispersion forces (interactions) A Polarized He atom with an induced dipole

moleculeF 2 Cl 2 Br 2 I 2 CH 4 polarizability molecular wt Molecular Weight predicts the trends in the boiling points of atoms or molecules without dipole moments because polarizability tends to increase with increasing mass.

But polarizability also depends on shape, as well as MW.

Water provides our best example of Hydrogen Bonding.

But hydrogen bonding is not limited to water:

These boiling points demonstrate the enormous contribution of hydrogen bonding.

Water is also unusual in the relative densities of the liquid and solid phases.

The crystal structure suggests a reason for the unusual high density of ice.

But water isn’t the only substance to show hydrogen bonding!

Viscosity—the resistance to flow of a liquid, such as oil, water, gasoline, molasses, (glass !!!) Surface Tension – tendency to minimize the surface area compare water, mercury Cohesive forces—bind similar molecules together Adhesive forces – bind a substance to a surface Capillary action results when these two are not equal Soap reduces the surface tension, permitting one material to ‘wet’ another more easily 11.3 Some Properties of Liquids

Examples of Viscosity The unit of viscosity is poise, which is 1 g/cm-s, but typical values are much smaller and are usually listed as cP = 0.01 P.

Rationale for Surface Tension

Surface Tension Surface molecules are only attracted inwards towards the bulk molecules. –Therefore, surface molecules are packed more closely than bulk molecules. Surface tension is the amount of energy required to increase the surface area of a liquid, in J/m 2. Cohesive forces bind molecules to each other. Adhesive forces bind molecules to a surface.

Surface Tension Meniscus is the shape of the liquid surface. –If adhesive forces are greater than cohesive forces, the liquid surface is attracted to its container more than the bulk molecules. Therefore, the meniscus is U-shaped (e.g. water in glass). –If cohesive forces are greater than adhesive forces, the meniscus is curved downwards. Capillary Action: When a narrow glass tube is placed in water, the meniscus pulls the water up the tube. Remember that surface molecules are only attracted inwards towards the bulk molecules.

also called FUSION

Sublimation: solid  gas. Vaporization: liquid  gas. Melting or fusion: solid  liquid. Deposition: gas  solid. Condensation: gas  liquid. Freezing: liquid  solid. Phase Changes

C p (s): J/mol-K ΔH fus : 6,010 J/mol C p (l): J/mol-K ΔH vap : 40,670 J/mol C p (g): J/mol-K