Intermolecular Forces& Liquids

and Gasses

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Kinetic Molecular Theory of MatterThe kinetic-molecular theory describes the behaviour of matter:

i) Molecules are in constant motion in random directions.

ii) All molecules have the same average kinetic energy at a given temperature.

iii) States of matter:

a) gases, distances between particles are much larger than the particles themselves. b) solids, particles are packed in a three-dimensional lattice. This motion is averaged about the particle’s location in the lattice.

c) liquids, particles are much closer together than in gases, but they are still able to change locations. Particles in a liquid undergo significant amounts of translational, rotational and vibrational motion.

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Kinetic Molecular Theory of MatterThe kinetic energy of molecules tends to keep them separated and disordered, hence there must be some countervailing force(s) to pull them together – particularly in solids and liquids.

These attractive forces are intermolecular forces.

There are six kinds of intermolecular forces, each of which is based on electrostatic interactions.

The strength of an intermolecular force is determined by the strength of the charges/dipoles involved and by the distance between them.

i) ion – ion forcesii) ion – dipole forcesiii) ion – induced dipole forcesiv) dipole – dipole forcesv) dipole – induced dipole forcesvi) induced dipole – induced dipole forces

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Bond PolarityWhen the electrons in a bond are will be shared unequally a charge difference exists over a given distance.

This resulting dipole, makes the bond polar.

Dipoles can be shown graphically using a vector.

Another way to indicate bond polarity is via partial charges (+ and -) on the relevant atoms:

C-O H-F Cl-Br

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Polarity of MoleculesTo determine whether a molecule is polar or nonpolar, we need to look at:

i) Bond dipolesii) Molecular geometry

If a molecule has no dipoles or all of the dipoles cancel out due to symmetry, it is nonpolar.

If a molecule has dipoles that don’t cancel out, it has a permanent dipole moment () and is polar.

Dipoles have direction! They must be added as vectors.

e.g. H2CO SF2

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Ion-Ion ForcesCoulombs Law:

This force is the strongest force outside of those operating at subatomic levels.

Hence ionic compounds tend to form strong solid lattices.

As a result, they have very high boiling points, requiring large amounts of heat to overcome the attractive forces holding the lattice together.

2

))((4

1d

eZeZF

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Ion-Dipole ForcesThe attractive forces between ions and dipoles are also strong.

When an ionic solid (such as the NaCl shown below) is dissolved in polar solvent such as water, many of the solvent molecules are organized around each ion to maximize the ion-dipole attractions:

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Dipole-Dipole ForcesMolecules with permanent dipoles also experience attractive forces.

They will align themselves to maximize the attractions between the positive ends of the dipoles and the negative ends of the dipoles:

Hydrogen bonding: is a special case of dipole-dipole attraction. This is due to the very large dipole moment that occurs when a hydrogen atom is bonded to a very small, very electronegative atom (i.e. F, O or N).

The large dipole moment results in a particularly strong dipole-dipole attraction.

Remember that for a hydrogen bond to occur both the atom bound to H and the atom attracted to H must be either F, O or N.

- +- +

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Hydrogen BondingHydrogen bonding is responsible for the open cage structure of ice along with the unusual relationship between temperature and density of water/ice:

Hydrogen bonds also holds the strands of DNA together to form the double helix

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Dipole-Induced Dipole ForcesInduced dipoles occur when the dipole of a polar molecule forces the electrons to move in a nearby non-polar molecule, resulting in a net dipole on the non-polar molecule.

Atoms whose valence electrons are less strongly attracted to their nucleus are more susceptible to induced dipoles.

Hence larger atoms are more polarizable than smaller atoms in the same group.

The polarizability of molecules also increases with the size of the molecule. This is why large molecules tend to be more viscous and have higher boiling points than smaller molecules of similar polarity.

Ex) The induction of a dipole in carbon disulfide, CS2, by the polar solvent acetone, (CH3)2C=O.

- +- +

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Induced Dipole-Induced Dipole ForcesNonpolar species exist as solids and/or liquids at low enough temperatures.

Ex) Liquid N2 and liquid He. Why?

A temporary dipole on a molecule can induce temporary dipoles on nearby molecules

The interaction between these fluctuation-induced dipoles are known as London dispersion forces.

Their strength depends on the polarizability of the atoms/molecules in question.

e.g. Cl2 vs. Br2 vs. I2

- +- +

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Boiling Points of P Block Hydrides

Consider the following:i) The boiling points for the Group 14 hydrides.ii) The anomalously high boiling points of the hydrides of the second period elements of groups 15 to 17.iii) The relative order of the third-period element hydrides.iv) The sequence of boiling points for the fourth- and fifth-period elements.

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Surface TensionDrops of a liquid tend to be round. Why?

i) Molecules within a liquid are attracted to all of the molecules around them via the IMFs. ii) Molecules on the surface can only interact with the neighbors immediately below them and beside them. iii) The surface molecules feel a net pull into the liquid and thus act as a skin for the liquid.

The energy required to break through this surface skin is referred to as surface tension.

Sphere: Smallest surface area-to-volume ratio. Hence, the smallest ratio of surface molecules to bulk molecules. This maximizes the IMFs, hence circular drops.

Ex) The convex meniscus of mercury (Hg) in a glass test tube.

Some insects take advantage of surface tension to literally walk on water!

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Surface Tension What happens if we add a solute to the liquid?

A) Solute-solvent IMFs are stronger than in solvent: Solute will be pulled into solution. Miscibility (“like dissolves like”)B) Solute-solvent IMFs are weaker than in solvent: Solute will stay at the surface. Surfactant (“surface active agent”).

Surfactants reduce surface tension.

Detergents are surfactants. Long non-polar tail and a polar head.

0

HO

H HO

H HO

H

HO

H HO

H

HO

H HO

H HO

H

O

H

H HO

HHO

HO

H

HHO

H HO

H

smooth surface;lots of intermolecular attractions

surface tension broken;intermolecular attractions interfered with

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Capillary Action

A) IMFs between liquid & surface are stronger than in liquid: Wetting: liquid spreads over the surface to maximize attractions. Ex. water in a glass test tubeB) IMFs in liquid are stronger than between liquid and surface: Non-wetting: liquid beads on the surface. Ex. Hg in a glass test tube The concave meniscus of water on glass: Wetting of the glass surface leads to capillary action: capillary rise. The polar Si-O bonds of the glass strongly attract water => Water moves along the surface. => Neighboring water molecules pulled along by surface tension. Until: Weight of the water = Surface tension

Hence narrow capillaries allow the liquid to rise higher compared to wide capillaries.

HO

H

HO

H

HO

H

HO

H

HO

H

Si

O

Si

O

Si

O

OO

OO

OH

OH H

OH

simplified structure for glass(it's much more 3-dimensional!)

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ViscosityViscosity is a liquid’s resistance to fluid flow.

Liquids with high viscosities tend to be thick and difficult to pour. Viscosity increases as IMFs increase.

Viscous liquids are either large or polar (or both).

Ex) Gasoline vs. Mineral oil (nonpolar, ~8 C’s) (nonpolar, ~15-40 C’s)

Ex) Engine oil vs. molasses

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Kinetic Molecular Theory of Gases/Ideal Gases

Distances between gas particles are much larger than the size of the particles. Therefore particles therefore occupy a negligible fraction of the volume.Gas particles are in constant motion. Therefore particles do not interact except when colliding, where the collisions are elastic.Gas particles move at different speeds, where the average speed is proportional to temperature. Hence all gases have the same average kinetic energy at a given T.

Law of Large Numbers :The behaviour of many particle system is unlikely to deviate significantly from the behaviour predicted by the statistical average of the properties of the individual particles.

“The Law of Averages”

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Kinetic Molecular Theory of Gases/Ideal Gases

The kinetic energy of a particle depends on its mass and speed: where K is kinetic energy, m is mass and v is speed.

Speeds of molecules are distributed statistically according to the Maxwell-Boltzmann distribution: as temperature increases, the average speed increases and the distribution of speeds widens.

221mvK

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Kinetic Molecular Theory of Gases/Ideal Gases

There are three different ways to look at the speed of gas particles in a sample:i) vmp = most probable speedii) vav = average speediii) vrms = root mean square speed. (similar to the variance of a statistical distribution)

As kinetic energy is proportional to v2, it makes most sense to use vrms in kinetic energy and temperature calculations.

Where: K is the average kinetic energy of gas particles, m is the mass of one particle, T is temperature (in K). kb is the Boltzmann Constant, which is the ideal gas constant R for one

particle. (kb = R/A)

Therefore for one mole of gas: where M is the molar Mass.

Hence:

TkmvK brms 23

21 2

RTMvK rms 23

21 2

3rms

RTvM

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Kinetic Molecular Theory of Gases/Ideal Gases

The Maxwell-Boltzmann equation can be derived from the kinetic-molecular theory of gases, which states that:

or

where P is pressure, V is volume, N is the number of gas particles, m is the mass of one particle, and vrms is the root-mean-square speed.

Combining the Maxwell-Boltzmann equation and the Ideal Gas Law and

Therefore: or

VNmvP rms

3

2

3

2rmsNmvKEPV

32rmsNmvPV nRTPV

nRTNmvrms 32

RTn

Nmvrms 32

The mass of one particle (m) multiplied by the number of particles (N) gives the total mass of gas particles.(mN = M)

or

RTMvrms 32 MRTvrms

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Pressure is force exerted on an area. P = F/A

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Kinetic Molecular Theory of Gases/Ideal Gases

Ex) At a constant temperature room temperature of 25 oC: O2 particles with mass of 32 amu will have __________ vrms

He particles with mass of 4 amu will have __________ vrms

Speed of sound ________ => ________ the frequency of sound.

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Kinetic Molecular Theory of Gases/Ideal Gases

You have a sample of helium gas at 0.00 ˚C. To what temperature should the gas be heated in order to increase the root-mean-square speed of helium atoms by 10.0%?

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Non-ideal Gases

The ideal gas law and kinetic molecular theory are based on two simplifying assumptions: i) The actual gas particles have negligible volume. ii) There are no forces of attraction between gas particles.

Are these assumptions are not always valid?

Ideally the volume of a container of gas is 100% empty space – so the volume available for gas particles to move into is the entire volume of the container. Actually there is less available volume, which can be corrected via an excluded volume term to the ideal gas law:

where b is an experimentally determined constant specific to the gas.

This constant tends to scales with the size of the gas particles.The excluded volume is a downward correction to the actual volume thus increasing the actual pressure of the gas.

nRTnbVP

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Non-ideal Gases

Under ideal conditions, particles in a gas sample don’t experience IMFs. Under non-ideal conditions, the gas particles are close enough together that they do experience IMFs. The Ideal Gas Law is corrected accordingly:

where a is an experimentally determined constant specific to the gas.

This constant tends to increase as the polarity of the gas particles increases.The effect of the IMFs is to decrease the pressure of the gas.

2

2

nP a V nRTV

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Non-ideal Gases

When both corrections are applied, we get the van der Waals equation:

The table below gives some sample values for a and b

nRTnbVVnaP

2

2

a (Pa·m6·mol-2) b (m3·mol-1)

Hydrogen H2 0.0245 2.65 10-5

Methane CH4 0.2303 4.31 10-5

Ammonia NH3 0.4225 3.71 10-5

Water H2O 0.5537 3.05 10-5

Sulfur dioxide SO2 0.6865 5.68 10-5

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Non-ideal Gases

You have two 1.00 L containers at 298 K. One contains 1.00 mol of hydrogen gas while the second contains 1.00 mol of ammonia gas. (a) Calculate the pressure in each container according to the ideal gas law. (b) Calculate the actual pressure in each container.

a (Pa·m6·mol-2) b (m3·mol-1)

Hydrogen H2 0.0245 2.65 10-5

Ammonia NH3 0.4225 3.71 10-5

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Brownian MotionThe kinetic-molecular theory doesn’t just apply to gases. Brownian motion is the random motion of small particles (e.g. micrometer-sized) in a fluid.

Einstein showed that the mean squared displacement is given by:

where D is the diffusion coefficient of the particle in that fluid. It can be found using the equation below

where r is the radius of the particle and is the viscosity coefficient of the solvent

Dtx 22

rTkD B

6

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Brownian Motion

The HIV-1 virus has a radius of about 50 nm. The viscosity coefficient of water at 20 °C is 1.00 mPa·s. How far will a particle of HIV-1 typically travel in 1 minute?