GAS AND CONDENSED MATTER

Bonding model for covalent molecular substances

Bonding for covalent molecular substances falls into two categories

1. The strong forces of attraction which holds atoms together within molecules

2. The weak forces of attraction between molecules

Forces between molecules (intermolecular forces) we will learn about the forces between

molecules or compounds are called intermolecular forces

Inter means between or among Internet, interstate, international What would Interstellar travel be?

Intermolecular Forces Forces that occur between

molecules.

Intramolecular forces What would intramolecular forces be? Forces within molecules e.g covalent, metallic or

ionic intra means within Intrastate, intranet, intracellular Most of the intermolecular forces we look at occur

between covalently bonded molecules or covalent molecular substances

Intramolecular bonds are stronger than intermolecular forces.

Overview All matter is held together by force. The force between atoms within a

molecule is a chemical or intramolecular force.

The force between molecules are a physical or intermolecular force.

These physical forces are what we overcome when a chemical changes its state (e.g. gas liquid).

What causes intermolecular forces? Molecules are made up of charged particles: positive

nuclei and negative electrons. When one molecule approaches another there is a

multitude of forces between the particles in the two molecules.

Each electron in one molecule is attracted to the nuclei in the other molecule but also repelled by the electrons

in the other molecule. The same applies for nuclei

Types of Intermolecular forces The three main types of intermolecular

forces are:1. Dipole-dipole attraction occur only btw

polar molecules2. H bonding – only with Hydrogen and

Oxygen, Fluorine and Nitrogen)3. Dispersion forces (London Dispersion

Forces)

Intermolecular Forces Forces that occur between

molecules. Dipole–dipole forces

Hydrogen bonding London dispersion forces

Dipole–Dipole Attraction

Dipole-Dipole ForcesDipole moment – molecules with polar

bonds often behave in an electric field as if they had a center of positive charge and a center of negative charge.

Molecules with dipole moments can attract each other electrostatically. They line up so that the positive and negative ends are close to each other.

Only about 1% as strong as covalent or ionic bonds.

Hydrogen BondingStrong dipole-dipole forces.Hydrogen is bound to a highly electronegative atom – nitrogen, oxygen, or fluorine.

Hydrogen Bonding in Water Blue dotted

lines are the intermolecular forces between the water molecules.

Hydrogen BondingAffects physical properties

Boiling point

London Dispersion Forces Instantaneous dipole that occurs

accidentally in a given atom induces a similar dipole in a neighboring atom.

Significant in large atoms/molecules. Occurs in all molecules, including

nonpolar ones.

London Dispersion ForcesNonpolar Molecules

London Dispersion Forces

Become stronger as the sizes of atoms or molecules increase.

Melting and Boiling Points In general, the stronger the

intermolecular forces, the higher the melting and boiling points.

Strength of Intermolecular Interactions

Hydrogen Bonding

↑ Dipole – Dipole

↑ London Dispersion Forces

The kinetic theory of matter is based on the following postulates:

1. Matter is composed of small particles called molecules

2. The particles are in constant random motionThey possess kinetic energy due to their motion

3. There are repulsive and attractive forces between particles.

They posses potential energy due to these forces

4. Average particle speed increases with temperature5. No energy is lost when the particles collide, called

elastic collision

Kinetic Molecular Theory

The kinetic energy of a particle is given by the equation:

Where:

m = particle mass in kg

v = particle velocity in m/s

KE = kg-m2/s2 = j (joule)According to postulate 4 of our kinetic theory particle velocity increases with temperature. This means as temperature increases then kinetic energy increases.

22

1KE mv

Kinetic Molecular Theory

Potential energy is the sum of the attractive and repulsive forces between particles.

Examples of these types of forces are the gravitational attractive forces between objects and the repulsive forces between the same poles of magnets.

Alternatively we can say forces between particles may be either cohesive or disruptive.

Potential Energy

Cohesive forces include dipole-dipole interactions, dispersion forces, attraction between oppositely charged ions.Cohesive forces are largely temperature independent.

e.g. magnets and gravity function the same way at different temperature.

Interparticle Forces

Disruptive forces are those forces that make particles move away from each other.

These forces result predominately from the particle

motion. Disruptive forces increase with temperature in agreement with postulate 4. We can conclude that as we increase the temperature particles will become further apart from each other.

Interparticle Forces

Tutorial 1 State and describe briefly three (3) main types of

intermolecular forces. State five (5) assumption in the kinetic molecular

theory

A Gas

Has neither a definite volume nor shape.

Uniformly fills any container.

Mixes completely with any other gas

Exerts pressure on its surroundings.

Composition of Earth’s AtmosphereCompound %(Volume) Mole Fractiona

Nitrogen 78.08 0.7808

Oxygen 20.95 0.2095

Argon 0.934 0.00934

Carbon dioxide 0.033 0.00033

Methane 2 x 10-4 2 x 10-6

Hydrogen 5 x 10-5 5 x 10-7

a. mole fraction = mol component/total mol in mixture.

Earth-like Atmosphere

A mercury barometer

The column height is proportional to the atmospheric pressure.

Atmospheric pressure results from the mass of the atmosphere and gravitational forces.

The pressure is the force per unit area.

P = F/A

1 atm = 760 mmHg

1 atm = 1.01325 E5 Pa

1 mmHg = 1 torr

Units for Expressing Pressure

Unit Value

Atmosphere 1 atm

Pascal (Pa) 1 atm = 1.01325 x 105 Pa

Kilopascal (kPa) 1 atm = 101.325 kPa

mmHg 1 atm = 760 mmHg

Torr 1 atm = 760 torr

Bar 1 atm = 1.01325 bar

mbar 1 atm = 1013.25 mbar

psi 1 atm = 14.7 psi

Pressure is equal to force/unit area SI units = Newton/meter2 = 1 Pascal (Pa) 1 standard atmosphere = 101,325 Pa

(100,000 Pa = 1 bar) 1 standard atmosphere = 1 atm =

760 mm Hg = 760 torr = 1013.25 hPa= 14.695 psi

Meteorologists often report pressure inmillibar; 1 mbar =0.001bar =0.1 kPa = 1hPa

Variables Affecting Gases Pressure (P)

Volume (V)

Temperature (T)

Number of Moles (n)

Elevation and Atmospheric Pressure

ManometerManometers are used to measure gas pressure in closed systems. For instance in a reaction vessel.

The Gas Laws and Absolute TemperatureThe relationship between the volume, pressure, temperature, and mass of a gas is called an equation of state.

We will deal here with gases that are not too dense.

Boyle’s Law: the volume of a given amount of gas is inversely proportional to the pressure as long as the temperature is constant.

Boyle Law…pressure is inversely proportional to volume (at constant T and moles, n).

The Gas Laws and Absolute Temperature

The volume is linearly proportional to the temperature, as long as the temperature is somewhat above the condensation point and the pressure is constant:

Extrapolating, the volume becomes zero at −273.15°C; this temperature is called absolute zero.

Avogadro’s Law

For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures).

V n

V1 = V2

n1 n2

The Gas Laws and Absolute TemperatureThe concept of absolute zero allows us to define a third temperature scale – the absolute, or Kelvin, scale.

This scale starts with 0 K at absolute zero, but otherwise is the same as the Celsius scale.

Therefore, the freezing point of water is 273.15 K, and the boiling point is 373.15 K.

Finally, when the volume is constant, the pressure is directly proportional to the temperature:

Combined Gas Law

Combining the gas laws the relationship P T(n/V) can be obtained.

If n (number of moles) is held constant, then PV/T = constant.

P1V1

T1

= P2V2

T2

Ideal Gas LawPV = nRT

R = universal gas constant = 0.08206 L atm K-1 mol-1

P = pressure in atm V = volume in liters n = moles T = temperature in Kelvin

Standard Temperature and Pressure (for gases)

“STP” P = 1 atmosphere T = 0C The molar volume of an ideal gas is 22.42 liters at

STP (put 1 mole, 1 atm, R, and 273 K in the ideal gas law and calculate V)

Note STP is different for other phases, e.g. solutions or enthalpies of formation.

The Ideal Gas Law

A mole (mol) is defined as the number of grams of a substance that is numerically equal to the molecular mass of the substance:

1 mol H2 has a mass of 2 g

1 mol Ne has a mass of 20 g

1 mol CO2 has a mass of 44 g

The number of moles in a certain mass of material:

• We can combine these into a general gas law:

The Ideal Gas The Ideal Gas EquationEquation

), (constant 1

TnP

V

), (constant PnTV

),(constant TPnV

• Boyle’s Law:

• Charles’s Law:

• Avogadro’s Law:

PnT

V

• R = gas constant, then

• The ideal gas equation is:

• R = 0.08206 L·atm/mol·K = 8.3145 J/mol·K• J = kPa·L = kPa·dm3 = Pa·m3

• Real Gases behave ideally at low P and high T.

The Ideal Gas The Ideal Gas EquationEquation

P

nTRV

nRTPV

Ideal Gas Law in Terms of Molecules: Avogadro’s Number

Since the gas constant is universal, the number of molecules in one mole is the same for all gases. That number is called Avogadro’s number:

The number of molecules in a gas is the number of moles times Avogadro’s number:

Ideal Gas Law in Terms of Molecules: Avogadro’s Number

Therefore we can write:

where k is called Boltzmann’s constant.

(13-4)

The Ideal Gas The Ideal Gas EquationEquation

Calculate the pressure exerted by 84.0 g of ammonia, NH3, in a 5.00 L container at 200. oC using the ideal gas law.

PV = nRTP = nRT/V n = 84.0g * 1mol/17 g T = 200 + 273P = (4.94mol)(0.08206 L atm mol-1 K-1)(473K)

(5 L)P = 38.3 atm

Tutorial 2. The pressure on a sample of an ideal gas was

increased from 715 torr to 3.55 atm at constant temperature. If the initial volume of the gas was 485. mL, what would be the final volume?

A 7.9 L sample of gas was cooled from 79°C to a temperature at which the volume of the gas was 4.3 L. Assuming the pressure remains constant, calculate the final temperature.

Calculate the pressure in atmospheres and Calculate the pressure in atmospheres and pascals of a 1.2 mol sample of methane gas in a pascals of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C.3.3 L container at 25°C.

Real Gases: Deviations from Ideality

Real gases behave ideally at ordinary temperatures and pressures.

At low temperatures and high pressures real gases do not behave ideally.

The reasons for the deviations from ideality are:

1. The molecules are very close to one another, thus their volume is important.

2. The molecular interactions also become important. J. van der Waals, 1837-1923, J. van der Waals, 1837-1923,

Professor of Physics, Professor of Physics, Amsterdam. Nobel Prize 1910.Amsterdam. Nobel Prize 1910.

Real Gases:Deviations from Ideality

van der Waals’ equation accounts for the behavior of real gases at low temperatures and high pressures.

P + n a

VV nb nRT

2

2

• The van der Waals constants a and b take into account two things:

1. a accounts for intermolecular attractiona. For nonpolar gases the attractive forces are London Forcesb. For polar gases the attractive forces are dipole-dipole attractions

or hydrogen bonds.

2. b accounts for volume of gas molecules

At large volumes a and b are relatively small and van der Waal’s equation reduces to ideal gas law at high temperatures and low pressures.

The van der Waals Equation

• General form of the van der Waals equation:

Real Gases: Deviations from Ideal Real Gases: Deviations from Ideal BehaviorBehavior

2

2

V

annbV

nRTP

nRTnbVV

anP

2

2

Corrects for molecular volume

Corrects for molecular attraction

Example

Condensed matter : the three states of matter.

Some Characteristics of Gases, Liquids and Solids and the Microscopic Explanation for the Behavior

gas liquid solid

assumes the shape and volume of its container particles can move past

one another

assumes the shape of the part of the container

which it occupies particles can move/slide

past one another

retains a fixed volume and shape

rigid - particles locked into place

compressible lots of free space between particles

not easily compressible little free space between

particles

not easily compressible little free space between

particles

flows easily particles can move past

one another

flows easily particles can move/slide

past one another

does not flow easily rigid - particles cannot move/slide past one

another

Clearly, a theory used to describe the condensed states of matter must include an attraction between the particles in the substanceCondensed States

of Matter:

Liquids

Solids

.

Kinetic Theory Description of the Liquid State. Like gases, the

condensed states of matter can consist of atoms, ions, or molecules.

What separates the three states of matter is the proximity of the particles in the substance.

For the condensed states of matter the particles are close enough to interact.

Phase Changes

Triple Point Diagram of Water Regions: Each region

corresponds to one phase which is stable for any combination of P and T within its region

Lines Between Region: Lines separating the regions representing phase-transition curves

Triple Point: The triple point represents the P and T at which all 3 phases coexist in equilibrium

Critical Point: At the critical point the vapor pressure cannot be condensed to liquid no matter what pressure is applied.

Tutorial 3 Van der Waals, realized that two of the

assumptions mentioned above were questionable. He then developed the Van der Waals equation of state which predicted the formation of liquid phase. Write the equation and state two corrections that he made.

(a) Calculate the pressure exerted by 1.00 mol of CO2 in a 1.00 L vessel at 300 K, assuming that the gas behaves ideally. (b) Repeat the calculation by using the van der Waals equation.

Sketch and label the liquid region, gas region solid region and triple point in water phase diagram