materi ujian akhir kimia dasar

Gases
Characteristics of Gases

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Although different gasses may differ widely in their chemical properties, they share many physical properties

Characteristics of Gases

The air we breathe:

• 78% N₂ (fairly inert)
• 21% O₂ (reactive)

Some common gases:

Formula	Name	Characteristics
H2	Hydrogen	Flammable, lighter than air
He	Helium	Colorless, nonflammable, lighter than air
HCN	Hydrogen cyanide	Toxic, has been used historically to shorten people's lives
HCl	Hydrogen chloride	Toxic, corrosive
H2S	Hydrogen sulfide	Toxic, smells like rotten eggs
CO	Carbon monoxide	Toxic, Jack Kervorkian's favorite gas
CO2	Carbon dioxide	Colorless, odorless, not toxic, but unsupportive of respiration
CH4	Methane	Colorless, odorless, flammable, occasional byproduct of the digestive system
N2O	Nitrous oxide	Colorless, sweet odor, makes you feel "funny"
NO2	Nitrogen dioxide	Toxic, red-brown, irritating odor
NH3	Ammonia	Colorless, pungent odor
SO2	Sulfur dioxide

All of the above gasses

• Are composed of non-metals
• Have simple formulas, and therefore low molecular masses

Substances that are liquids or solids under standard conditions can usually also exist in the gaseous state, where they are commonly referred to as vapors

Some general characteristics of gasses which distinguish them from liquids or solids:

• gasses expand spontaneously to fill their container (the volume of a gas equals the volume of its container)
• gasses can be readily compressed (and its volume will decrease)
• gasses form homogenous mixtures with each other regardless of the identities or relative properties of the component gases (e.g. water and gasoline vapors will form a homogenous mixture, whereas the liquids will not)
• The individual molecules are relatively far apart

1. In air, the molecules take up about 0.1% of the total volume (the rest is empty space)
2. Each molecule, therefore, behaves as though it were isolated (as a result, each gas has similar characteristics)

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Pressure

The most readily measured properties of a gas are:

• Temperature
• Volume
• Pressure

Pressure (P) is the force (F) which acts on a given area (A)

The gas in an inflated balloon exerts a pressure on the inside surface of the balloon

Atmospheric Pressure and the Barometer

Due to gravity, the atmosphere exerts a downward force and therefore a pressure upon the earth's surface

• Force = (mass*acceleration) or F=ma
• The earth's gravity exerts an acceleration of 9.8 m/s²
• A column of air 1 m² in cross section, extending through the atmosphere, has a mass of roughly 10,000 kg

(one Newton equals 1 kg m/s²)

The force exerted by this column of air is approximately 1 x 10⁵ Newtons

The pressure, P, exerted by the column is the force, F, divided by its cross sectional area, A:

The SI unit of pressure is Nm^-2, called a pascal (1Pa = 1 N/m²)

• The atmospheric pressure at sea level is about 100 kPa

Atmospheric pressure can be measured by using a barometer

• A glass tube with a length somewhat longer than 760 mm is closed at one end and filled with mercury
• The filled tube is inverted over a dish of mercury such that no air enters the tube
• Some of the mercury flows out of the tube, but a column of mercury remains in the tube. The space at the top of the tube is essentially a vacuum
• The dish is open to the atmosphere, and the fluctuating pressure of the atmosphere will change the height of the mercury in the tube

The mercury is pushed up the tube until the pressure due to the mass of the mercury in the column balances the atmospheric pressure

Standard atmospheric pressure

• Corresponds to typical atmospheric pressure at sea level
• The pressure needed to support a column of mercury 760 mm in height
• Equals 1.01325 x 10⁵ Pa

Relationship to other common units of pressure:

(Note that 1 torr = 1 mm Hg)

Pressures of Enclosed Gases and Manometers

A manometer is used to measure the pressure of an enclosed gas. Their operation is similar to the barometer, and they usually contain mercury

• A closed tube manometer is used to measure pressures below atmospheric
• An open tube manometer is used to measure pressures slightly above or below atmospheric

In a closed tube manometer the pressure is just the difference between the two levels (in mm of mercury)

In an open tube manometer the difference in mercury levels indicates the pressure difference in reference to atmospheric pressure

Other liquids can be employed in a manometer besides mercury.

• The difference in height of the liquid levels is inversely proportional to the density of the liquid
• i.e. the greater the density of the liquid, the smaller the difference in height of the liquid
• The high density of mercury (13.6 g/ml) allows relatively small manometers to be built

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The Gas Laws

Four variables are usually sufficient to define the state (i.e. condition) of a gas:

• Temperature, T
• Pressure, P
• Volume, V
• Quantity of matter, usually the number of moles, n

The equations that express the relationships among P, T, V and n are known as the gas laws

The Pressure-Volume Relationship: Boyle's Law

Robert Boyle (1627-1691)

Studied the relationship between the pressure exerted on a gas and the resulting volume of the gas. He utilized a simple 'J' shaped tube and used mercury to apply pressure to a gas:

• He found that the volume of a gas decreased as the pressure was increased
• Doubling the pressure caused the gas to decrease to one-half its original volume

Boyle's Law:

The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure

• The value of the constant depends on the temperature and the amount of gas in the sample
• A plot of V vs. 1/P will give a straight line with slope = constant

The Temperature-Volume Relationship: Charles's Law

The relationship between gas volume and temperature was discovered in 1787 by Jacques Charles (1746-1823)

• The volume of a fixed quantity of gas at constant pressure increases linearly with temperature
• The line could be extrapolated to predict that gasses would have zero volume at a temperature of -273.15°C (however, all gases liquefy or solidify before this low temperature is reached

• In 1848 William Thomson (Lord Kelvin) proposed an absolute temperature scale for which 0°K equals -273.15°C
• In terms of the Kelvin scale, Charles's Law can be restated as:

The volume of a fixed amount of gas maintained at constant pressure is directly proportional to its absolute temperature

• Doubling the absolute temperature causes the gas volume to double

• The value of constant depends on the pressure and amount of gas

The Quantity-Volume Relationship: Avogadro's Law

The volume of a gas is affected not only by pressure and temperature, but by the amount of gas as well.

Joseph Louis Gay-Lussac (1778-1823)

Discovered the Law of Combining Volumes:

• At a given temperature and pressure, the volumes of gasses that react with one another are in the ratios of small whole numbers
• For example, two volumes of hydrogen react with one volume of oxygen to form two volumes of water vapor

Amadeo Avogadro interpreted Gay-Lussac's data

• Avogadro's hypothesis:

Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules

• 1 mole of any gas (i.e. 6.02 x 10²³ gas molecules) at 1 atmosphere pressure and 0°C occupies approximately 22.4 liters volume
• Avogadro's Law:

The volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of the gas

• Doubling the number of moles of gas will cause the volume to double if T and P remain constant

Gases
The Ideal-Gas Equation

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The Ideal Gas Equation

The three historically important gas laws derived relationships between two physical properties of a gas, while keeping other properties constant:

These different relationships can be combined into a single relationship to make a more general gas law:

If the proportionality constant is called "R", then we have:

Rearranging to a more familiar form:

This equation is known as the ideal-gas equation

• An "ideal gas" is one whose physical behavior is accurately described by the ideal-gas equation
• The constant R is called the gas constant
• The value and units of R depend on the units used in determining P, V, n and T
• Temperature, T, must always be expressed on an absolute-temperature scale (K)
• The quantity of gas, n, is normally expressed in moles
• The units chosen for pressure and volume are typically atmospheres (atm) and liters (l), however, other units may be chosen
• PV can have the units of energy:

• Therefore, R can include energy units such as Joules or calories

Values for the gas constant R
Units	Value
L atm/mol K	0.08206
cal/mol K	1.987
J/mol K	8.314
m3 Pa/mol K	8.314
L torr/mol K	62.36

Example:

If we had 1.0 mol of gas at 1.0 atm of pressure at 0°C (273.15 K), what would be the volume?

PV = nRT

V = nRT/P

V = (1.0 mol)(0.0821 L atm/mol K)(273 K)/(1.0 atm)

V = 22.41 L

• 0 °C and 1 atm pressure are referred to as the standard temperature and pressure (STP)

The molar volume of an ideal gas (any ideal gas) is 22.4 liters at STP

Example: Nitrate salts (NO₃^-) when heated can produce nitrites (NO₂^-) plus oxygen (O₂). A sample of potassium nitrate is heated and the O₂ gas produced is collected in a 750 ml flask. The pressure of the gas in the flask is 2.8 atmospheres and the temperature is recorded to be 53.6 °C.

How many moles of O₂ gas were produced?

PV = nRT

n = PV/RT

n = (2.8 atm * 0.75 L) / (0.0821 L atm/mol K * (53.6 + 273)K

n = (2.1 atm L) / (26.81 L atm/mol)

n = 0.078 mol O₂ were produced

Relationship Between the Ideal-Gas Equation and the Gas Laws

Boyle's law, Charles's law and Avogadro's law represent special cases of the ideal gas law

• If the quantity of gas and the temperature are held constant then:

PV = nRT

PV = constant

P = constant * (1/V)

P 1/V (Boyle's law)

• If the quantity of gas and the pressure are held constant then:

PV = nRT

V = (nR/P) * T

V = constant * T

V T (Charles's law)

• If the temperature and pressure are held constant then:

PV = nRT

V = n * (RT/P)

V = constant * n

V n (Avogadro's law)

• A very common situation is that P, V and T are changing for a fixed quantity of gas

PV = nRT

(PV)/T = nR = constant

• Under this situation, (PV/T) is a constant, thus we can compare the system before and after the changes in P, V and/or T:

Example:

A 1 liter sample of air at room temperature (25 °C) and pressure (1 atm) is compressed to a volume of 3.3 mls at a pressure of 1000 atm. What is the temperature of the air sample?

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1996 Michael Blaber

Gases
Molar Mass and Gas Densities

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Molar Mass and Gas Densities

Density

• Has the units of mass per unit volume

• (n/V) has the units of moles/liter. If we know the molecular mass of the gas, we can convert this into grams/liter (mass/volume). The molar mass (M) is the number of grams in one mole of a substance. If we multiply both sides of the above equation by the molar mass:

• The left hand side is now the number of grams per unit volume, or the mass per unit volume (which is the density)
• Thus, the density (d) of a gas can be determined according to the following:

• Alternatively, if the density of the gas is known, the molar mass of a gas can be determined:

Example:

What is the density of carbon tetrachloride vapor at 714 torr and 125°C?

The molar mass of CCl₄ is 12.0 + (4*35.5) = 154 g/mol. 125°C in degrees Kelvin would be (273+125) = 398K. Since we are dealing with torr, the value of the gas constant, R, would be 62.36 L torr/mol K.

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Caesar's Las Breath

Of the molecules in Caesar's last gasp, how many of them are in the breath you just took?

Given:

• One breath= 2 liters of air at a pressure of 730 mmHg and 37 degrees Celsius.
• Earth is a sphere with a radius of 6370 Km and an average barometric pressure of 760mm Hg. (D of Hg=13.6g/cm³)
• The avg. molecular mass of air is 29 g/mol.

1. Number of moles in Caesar’s last breathe:

n = PV/RT = (0.96 atm)(2L)/(0.0821 L atm/mol K)(310 K)

n = 0.075 mol

2. Number of moles in the atmosphere:

a. Surface area of earth:

Area = (4)(p)(r²)

Area = 5.10 x 10¹⁴ square meters

b. Pressure of the atmosphere on the earth’s surface:

Pressure = 760 mm Hg = 1.01 x 10⁵ Pascals = 1.01 x 10⁵ Newtons/square meter

Pressure = 1.01 x 10⁵ kg/m s²

c. Force of the atmosphere on the earth

Pressure = Force/Area

Therefore

Force = (Pressure)(Area)

Force = (1.01 x 10⁵ kg/m s²)(5.10 x 10¹⁴ m²)

Force = 5.15 x 10¹⁹ kg m /s²

d. Mass of the atmosphere

Force = (mass)(acceleration)

therefore

mass = Force/acceleration

mass = (5.15 x 10¹⁹ kg m/s²)/(9.8 m/s²) note: this is the acceleration due to gravity

mass = 5.26 x 10¹⁸ kg or 5.26 x 10²¹ g

e. Moles in the atmosphere

mol = (5.26 x 10²¹ g)(1 mol/29 g)

mol = 1.81 x 10²⁰ mol

3. Fraction of atmosphere which represents molecules from Caesar’s last breath:

(0.075 mol)/(1.81 x 10²⁰ mol) = 4.14 x 10^-22

4. Moles of Caesar’s last breath in your last breath:

Assume your breath holds 0.075 mol:

(0.075 mol)(4.14 x 10^-22) = 3.11 x 10^-23mol

5. Number of molecules:

(6.022 x 10²³ molecules/mol)(3.11 x 10^-23mol) = 18.7 molecules

(An even more disconcerting fact is that he probably had flatulence as well.)

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1996 Michael Blaber

Gases
Gas Mixtures and Partial Pressures

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Gas Mixtures and Partial Pressures

How do we deal with gases composed of a mixture of two or more different substances?
John Dalton (1766-1844) - (gave us Dalton's atomic theory)

The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone

The partial pressure of a gas:

• The pressure exerted by a particular component of a mixture of gases

Dalton's Law of Partial Pressures:

• P_t is the total pressure of a sample which contains a mixture of gases
• P₁, P₂, P₃, etc. are the partial pressures of the gases in the mixture

P_t = P₁ + P₂ + P₃ + ...

If each of the gases behaves independently of the others then we can apply the ideal gas law to each gas component in the sample:

• For the first component, n₁ = the number of moles of component #1 in the sample
• The pressure due to component #1 would be:

• For the second component, n₂ = the number of moles of component #2 in the sample
• The pressure due to component #2 would be:

And so on for all components. Therefore, the total pressure P_t will be equal to:

• All components will share the same temperature, T, and volume V, therefore, the total pressure P_t will be:

• Since the sum of the number of moles of each component gas equals the total number of moles of gas molecules in the sample:

At constant temperature and volume, the total pressure of a gas sample is determined by the total number of moles of gas present, whether this represents a single substance, or a mixture

Example

A gaseous mixture made from 10 g of oxygen and 5 g of methane is placed in a 10 L vessel at 25°C. What is the partial pressure of each gas, and what is the total pressure in the vessel?

(10 g O₂)(1 mol/32 g) = 0.313 mol O₂

(10 g CH₄)(1 mol/16 g) = 0.616 mol CH₄

V=10 L

T=(273+25K)=298K

P_t = P_O2 + P_CH4 = 0.702 atm + 1.403 atm = 2.105 atm

Partial Pressures and Mole Fractions

The ratio of the partial pressure of one component of a gas to the total pressure is:

thus...

• The value (n₁/n_t) is termed the mole fraction of the component gas
• The mole fraction (X) of a component gas is a dimensionless number, which expresses the ratio of the number of moles of one component to the total number of moles of gas in the sample

The ratio of the partial pressure to the total pressure is equal to the mole fraction of the component gas

• The above equation can be rearranged to give:

The partial pressure of a gas is equal to its mole fraction times the total pressure

Example

a) A synthetic atmosphere is created by blending 2 mol percent CO₂, 20 mol percent O₂ and 78 mol percent N₂. If the total pressure is 750 torr, calculate the partial pressure of the oxygen component.

Mole fraction of oxygen is (20/100) = 0.2

Therefore, partial pressure of oxygen = (0.2)(750 torr) = 150 torr

b) If 25 liters of this atmosphere, at 37°C, have to be produced, how many moles of O₂ are needed?

P_O2 = 150 torr (1 atm/760 torr) = 0.197 atm

V = 25 L

T = (273+37K)=310K

R=0.0821 L atm/mol K

PV = nRT

n = (PV)/(RT) = (0.197 atm * 25 L)/(0.0821 L atm/mol K * 310K)

n = 0.194 mol

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1996 Michael Blaber

Gases
Volumes of Gases in Chemical Reactions

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Volumes of Gases in Chemical Reactions

• Gasses are often reactants or products in chemical reactions
• Balanced chemical equations deal with the number of moles of reactants consumed or products formed
• For a gas, the number of moles is related to pressure (P), volume (V) and temperature (T)

Example

The synthesis of nitric acid involves the reaction of nitrogen dioxide gas with water:

3NO₂(g) + H₂O(l) -> 2HNO₃(aq) + NO(g)

How many moles of nitric acid can be prepared using 450 L of NO₂ at a pressure of 5.0 atm and a temperature of 295 K?

(5.0 atm)(450 L) = n(0.0821 L atm/mol K)(295 K)

= 92.9 mol NO₂

92.9 mol NO₂ (2HNO₃/3NO₂) = 61.9 mol 2HNO₃

Collecting Gases Over Water

• Certain experiments involve the determination of the number of moles of a gas produced in a chemical reaction
• Sometimes the gas can be collected over water

Potassium chlorate when heated gives off oxygen:

2KClO₃(s) -> 2KCl(s) + 3O₂(g)

• The oxygen can be collected in a bottle that is initially filled with water

• The volume of gas collected is measured by first adjusting the beaker so that the water level in the beaker is the same as in the pan.
• When the levels are the same, the pressure inside the beaker is the same as on the water in the pan (i.e. 1 atm of pressure)
• The total pressure inside the beaker is equal to the sum of the pressure of gas collected and the pressure of water vapor in equilibrium with liquid water

P_t = P_O2 + P_H2O

• The pressure exerted by water vapor at various temperatures is usually available in tables:

Temperature (°C)	Pressure (torr)
0	4.58
25	23.76
35	42.2
65	187.5
100	760.0

Example

A sample of KClO₃ is partially decomposed, producing O₂ gas that is collected over water. The volume of gas collected is 0.25 L at 25 °C and 765 torr total pressure.

a) How many moles of O₂ are collected?

P_t = 765 torr = P_O2 + P_H2O = P_O2 + 23.76 torr

P_O2 = 765 - 23.76 = 741.2 torr

P_O2 = 741.2 torr (1 atm/760 torr) = 0.975 atm

PV = nRT

(0.975 atm)(0.25 L) = n(0.0821 L atm/mol K)(273 + 25K)

n = 9.96 x 10^-3 mol O₂

b) How many grams of KClO₃ were decomposed?

9.96 x 10^-3 mol O₂ (2KC lO₃/3 O₂) = 6.64 x 10^-3 mol KClO₃

6.64 x 10^-3 mol KClO₃ (122.6 g/mol) = 0.814 g KClO₃

c) If the O₂ were dry, what volume would it occupy at the same T and P?

P_O2 = (P_t)(X_O2) = 765 torr (1.0) = 765 torr (1 atm/760 torr) = 1.007 atm

(1.007 atm)(V) = (9.96 x 10^-3 mol)(0.0821 L atm/mol K)(273 + 25 K)

V = 0.242 L

Alternatively...

If the number of moles, n, and the temperature, T, are held constant then we can use Boyle's Law:

P₁V₁ = P₂V₂

V₂ = (P₁V₁)/ P₂

V₂ = (741.2 torr * 0.25 L)/(765 torr)

V₂ = 0.242 L

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1996 Michael Blaber

Gases
Kinetic-Molecular Theory

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Kinetic-Molecular Theory

The ideal gas equation

PV = nRT

describes how gases behave.

• A gas expands when heated at constant pressure
• The pressure increases when a gas is compressed at constant temperature

But, why do gases behave this way?

What happens to gas particles when conditions such as pressure and temperature change?

The Kinetic-Molecular Theory ("the theory of moving molecules"; Rudolf Clausius, 1857)

1. Gases consist of large numbers of molecules (or atoms, in the case of the noble gases) that are in continuous, random motion
2. The volume of all the molecules of the gas is negligible compared to the total volume in which the gas is contained
3. Attractive and repulsive forces between gas molecules is negligible
4. The average kinetic energy of the molecules does not change with time (as long as the temperature of the gas remains constant). Energy can be transferred between molecules during collisions (but the collisions are perfectly elastic)
5. The average kinetic energy of the molecules is proportional to absolute temperature. At any given temperature, the molecules of all gases have the same average kinetic energy. In other words, if I have two gas samples, both at the same temperature, then the average kinetic energy for the collection of gas molecules in one sample is equal to the average kinetic energy for the collection of gas molecules in the other sample.

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Pressure

• The pressure of a gas is causes by collisions of the molecules with the walls of the container.
• The magnitude of the pressure is related to how hard and how often the molecules strike the wall
• The "hardness" of the impact of the molecules with the wall will be related to the velocity of the molecules times the mass of the molecules

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Absolute Temperature

• The absolute temperature is a measure of the average kinetic energy of its molecules
• If two different gases are at the same temperature, their molecules have the same average kinetic energy
• If the temperature of a gas is doubled, the average kinetic energy of its molecules is doubled

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Molecular Speed

• Although the molecules in a sample of gas have an average kinetic energy (and therefore an average speed) the individual molecules move at various speeds
• Some are moving fast, others relatively slowly

• At higher temperatures at greater fraction of the molecules are moving at higher speeds

What is the speed (velocity) of a molecule possessing average kinetic energy?

• The average kinetic energy, e, is related to the root mean square (rms) speed u

Example:

Suppose we have four molecules in our gas sample. Their speeds are 3.0, 4.5, 5.2 and 8.3 m/s.

• The average speed is:

• The root mean square speed is:

·         Because the mass of the molecules does not increase, the rms speed of the molecules must increase with increasing temperature

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Application of the "Kinetic Molecular Theory" to the Gas Laws

Effect of a volume increase at a constant temperature

• Constant temperature means that the average kinetic energy of the gas molecules remains constant
• This means that the rms speed of the molecules, u, remains unchanged
• If the rms speed remains unchanged, but the volume increases, this means that there will be fewer collisions with the container walls over a a given time

• Therefore, the pressure will decrease (Boyle's law)

Effect of a temperature increase at constant volume

• An increase in temperature means an increase in the average kinetic energy of the gas molecules, thus an increase in u
• There will be more collisions per unit time, furthermore, the momentum of each collision increases (molecules strike the wall harder)
• Therefore, there will be an increase in pressure
• If we allow the volume to change to maintain constant pressure, the volume will increase with increasing temperature (Charles's law)

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Gases
Molecular Effusion and Diffusion

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Molecular Effusion and Diffusion

Kinetic-molecular theory stated that
The average kinetic energy of molecules is proportional to absolute temperature

• Thus, at a given temperature, to different gases (e.g. He vs. Xe) will have the same average kinetic energy
• The lighter gas has a much lower mass, but the same kinetic energy, therefore its rms velocity (u) must be higher than that of the heavier gas

where M is the molar mass

Example

Calculate the rms speed, u, of an N₂ molecule at room temperature (25°C)

T = (25+273)°K = 298°K

M = 28 g/mol = 0.028 kg/mol

R = 8.314 J/mol °K = 8.314 kg m²/s² mol °K

Note: this is equal to 1,150 miles/hour!

Effusion

The rate of escape of a gas through a tiny pore or pinhole in its container.

• Latex is a porous material (tiny pores), from which balloons are made
• Helium balloons seem to deflate faster than those we fill with air (blow up by mouth)

The effusion rate, r, has been found to be inversely proportional to the square root of its molar mass:

and a lighter gas will effuse more rapidly than a heavy gas:

Basis of effusion

• The only way for a gas to effuse, is for a molecule to collide with the pore or pinhole (and escape)
• The number of such collisions will increase as the speed of the molecules increases

Diffusion: the spread of one substance through space, or though a second substance (such as the atmosphere)

Diffusion and Mean Free Path

• Similarly to effusion, diffusion is faster for light molecules than for heavy ones
• The relative rates of diffusion of two molecules is given by the equation

·         The speed of molecules is quite high, however...

the rates of diffusion are slower than molecular speeds due to molecular collisions

·         Due to the density of molecules comprising the atmosphere, collisions occur about 10¹⁰ (i.e. 10 billion) times per second

• Due to these collisions, the direction of a molecule of gas in the atmosphere is constantly changing

The average distance traveled by a molecule between collisions is the mean free path

• The higher the density of gas, the smaller the mean free path (more likelyhood of a collision)
• At sea level the mean free path is about 60 nm
• At 100 km altitude the atmosphere is less dense, and the mean free path is about 0.1 m (about 1 million times longer than at sea level)

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1996 Michael Blaber

Gases
Deviation from Ideal Behavior

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Deviations from Ideal Behavior

All real gasses fail to obey the ideal gas law to varying degrees
The ideal gas law can be written as:

For a sample of 1.0 mol of gas, n = 1.0 and therefore:

Plotting PV/RT for various gasses as a function of pressure, P:

• The deviation from ideal behavior is large at high pressure
• The deviation varies from gas to gas
• At lower pressures (<10 atm) the deviation from ideal behavior is typically small, and the ideal gas law can be used to predict behavior with little error

Deviation from ideal behavior is also a function of temperature:

• As temperature increases the deviation from ideal behavior decreases
• As temperature decreases the deviation increases, with a maximum deviation near the temperature at which the gas becomes a liquid

Two of the characteristics of ideal gases included:

• The gas molecules themselves occupy no appreciable volume
• The gas molecules have no attraction or repulsion for each other

Real molecules, however, do have a finite volume and do attract one another

• At high pressures, and low volumes, the intermolecular distances can become quite short, and attractive forces between molecules becomes significant
• Neighboring molecules exert an attractive force, which will minimize the interaction of molecules with the container walls. And the apparent pressure will be less than ideal (PV/RT will thus be less than ideal).
• As pressures increase, and volume decreases, the volume of the gas molecules becomes significant in relationship to the container volume
• In an extreme example, the volume can decrease below the molecular volume, thus PV/RT will be higher than ideal (V is higher)
• At high temperatures, the kinetic energy of the molecules can overcome the attractive influence and the gasses behave more ideal
• At higher pressures, and lower volumes, the volume of the molecules influences PV/RT and its value, again, is higher than ideal

The van der Waals Equation

• The ideal gas equation is not much use at high pressures
• One of the most useful equations to predict the behavior of real gases was developed by Johannes van der Waals (1837-1923)
• He modified the ideal gas law to account for:
• The finite volume of gas molecules
• The attractive forces between gas molecules

van der Waals equation:

• The van der Waals constants a and b are different for different gasses
• They generally increase with an increase in mass of the molecule and with an increase in the complexity of the gas molecule (i.e. volume and number of atoms)

Substance	a (L2 atm/mol2)	b(L/mol)
He	0.0341	0.0237
H2	0.244	0.0266
O2	1.36	0.0318
H2O	5.46	0.0305
CCl4	20.4	0.1383

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Example

Use the van der Waals equation to calculate the pressure exerted by 100.0 mol of oxygen gas in 22.41 L at 0.0°C

V = 22.41 L

T = (0.0 + 273) = 273°K

a (O₂) = 1.36 L² atm/mol²

b (O₂) = 0.0318 L /mol

P = 117atm - 27.1atm

P = 90atm

• The pressure will be 90 atm, whereas if it was an ideal gas, the pressure would be 100 atm
• The 90 atm represents the pressure correction due to the molecular volume. In other words the volume is somewhat less than 22.41 L due to the molecular volume. Therefore the molecules must collide a bit more frequently with the walls of the container, thus the pressure must be slightly higher. The -27.1 atm represents the effects of the molecular attraction. The pressure is reduced due to this attraction.

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Intermolecular Forces
The Kinetic-Molecular Description of Liquids and Solids

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The physical properties of a substance depends upon its physical state.
Water vapor, liquid water and ice all have the same chemical properties, but their physical properties are considerably different.
Covalent bonds determine

• molecular shape
• bond energies
• chemical properties

Intermolecular forces (non-covalent bonds) influence

• physical properties of liquids and solids

The Kinetic-Molecular Description of Liquids and Solids

Gases

• A collection of widely separated molecules
• The kinetic energy of the molecules is greater than any attractive forces between the molecules
• The lack of any significant attractive force between molecules allows a gas to expand to fill its container
• If attractive forces become large enough, then the gases exhibit non-ideal behavior

Liquids

• The intermolecular attractive forces are strong enough to hold molecules close together
• Liquids are more dense and less compressible than gasses
• Liquids have a definite volume, independent of the size and shape of their container
• The attractive forces are not strong enough, however, to keep neighboring molecules in a fixed position and molecules are free to move past or slide over one another

Thus, liquids can be poured and assume the shape of their containers

Solids

• The intermolecular forces between neighboring molecules are strong enough to keep them locked in position
• Solids (like liquids) are not very compressible due to the lack of space between molecules
• If the molecules in a solid adopt a highly ordered packing arrangement, the structures are said to be crystalline

Due to the strong intermolecular forces between neighboring molecules, solids are rigid

The state of a substance depends on the balance between the kinetic energy of the individual particles (molecules or atoms) and the intermolecular forces

• Kinetic energy keeps the molecules apart and moving around, and is a function of the temperature of the substance
• Intermolecular forces try to draw the particles together

Gases have weaker intermolecular forces than liquids

Liquids have weaker intermolecular forces than solids

• Solids and liquids have particles that are fairly close to one another, and are thus called "condensed phases" to distinguish them from gases

Changing the state of a substance

Temperature

• Heating and cooling can change the kinetic energy of the particles in a substance, and so, we can change the physical state of a substance by heating or cooling it.
• Cooling a gas may change the state to a liquid
• Cooling a liquid may change the state to a solid

Pressure

• Increasing the pressure on a substance forces the molecules closer together, which increases the strength of intermolecular forces
• Increasing the pressure on a gas may change the state to a liquid
• Increasing the pressure on a liquid may change the state to a solid

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1996 Michael Blaber

Intermolecular Forces
Intermolecular Forces

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Intermolecular Forces

Intermolecular forces are generally much weaker than covalent bonds

• Only 16 kJ/mol of energy is required to overcome the intermolecular attraction between HCl molecules in the liquid state (i.e. the energy required to vaporize the sample)
• However, 431 kJ/mol of energy is required to break the covalent bond between the H and Cl atoms in the HCl molecule

Thus, when a molecular substance changes states the atoms within the molecule are unchanged

The temperature at which a liquid boils reflects the kinetic energy needed to overcome the attractive intermolecular forces (likewise, the temperature at which a solid melts).

Thus, the strength of the intermolecular forces determines the physical properties of the substance

Attractive forces between neutral molecules

• Dipole-dipole forces
• London dispersion forces
• Hydrogen bonding forces

Typically, dipole-dipole and dispersion forces are grouped together and termed van der Waals forces (sometimes the hydrogen bonding forces are also included with this group)

Attractive forces between neutral and charged (ionic) molecules

• ion-dipole forces

Note that all of these forces will be electrostatic in nature

Ion-dipole

• Involves an interaction between a charged ion and a polar molecule (i.e. a molecule with a dipole)
• Cations are attracted to the negative end of a dipole
• Anions are attracted to the positive end of a dipole
• The magnitude of the interaction energy depends upon the charge of the ion (Q), the dipole moment of the molecule (u) and the distance (d) from the center of the ion to the midpoint of the dipole

• Ion-dipole forces are important in solutions of ionic substances in polar solvents (e.g. a salt in aqueous solvent)

Dipole-Dipole Forces

A dipole-dipole force exists between neutral polar molecules

• Polar molecules attract one another when the partial positive charge on one molecule is near the partial negative charge on the other molecule
• The polar molecules must be in close proximity for the dipole-dipole forces to be significant
• Dipole-dipole forces are characteristically weaker than ion-dipole forces
• Dipole-dipole forces increase with an increase in the polarity of the molecule

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Boiling points increase for polar molecules of similar mass, but increasing dipole:

Substance	Molecular Mass (amu)	Dipole moment, u (D)	Boiling Point (°K)
Propane	44	0.1	231
Dimethyl ether	46	1.3	248
Methyl chloride	50	2.0	249
Acetaldehyde	44	2.7	294
Acetonitrile	41	3.9	355

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London Dispersion Forces

Nonpolar molecules would not seem to have any basis for attractive interactions.

• However, gases of nonpolar molecules can be liquefied indicating that if the kinetic energy is reduced, some type of attractive force can predominate.
• Fritz London (1930) suggested that the motion of electrons within an atom or non-polar molecule can result in a transient dipole moment

A Model To Explain London Dispersion Forces:

Helium atoms (2 electrons)

• Consider the particle nature of electrons
• The average distribution of electrons around each nucleus is spherically symmetrical
• The atoms are non-polar and posses no dipole moment
• The distribution of electrons around an individual atom, at a given instant in time, may not be perfectly symmetrical
• Both electrons may be on one side of the nucleus
• The atom would have an apparent dipole moment at that instant in time (i.e. a transient dipole)
• A close neighboring atom would be influenced by this apparent dipole - the electrons of the neighboring atom would move away from the negative region of the dipole

Due to electron repulsion, a temporary dipole on one atom can induce a similar dipole on a neighboring atom

• This will cause the neighboring atoms to be attracted to one another
• This is called the London dispersion force (or just dispersion force)
• It is significant only when the atoms are close together

The ease with which an external electric field can induce a dipole (alter the electron distribution) with a molecule is referred to as the "polarizability" of that molecule

• The greater the polarizability of a molecule the easier it is to induce a momentary dipole and the stronger the dispersion forces
• Larger molecules tend to have greater polarizability
• Their electrons are further away from the nucleus (any asymmetric distribution produces a larger dipole due to larger charge separation)
• The number of electrons is greater (higher probability of asymmetric distribution)

thus, dispersion forces tend to increase with increasing molecular mass

• Dispersion forces are also present between polar/non-polar and polar/polar molecules (i.e. between all molecules)

Hydrogen Bonding

A hydrogen atom in a polar bond (e.g. H-F, H-O or H-N) can experience an attractive force with a neighboring electronegative molecule or ion which has an unshared pair of electrons (usually an F, O or N atom on another molecule)

Hydrogen bonds are considered to be dipole-dipole type interactions

• A bond between hydrogen and an electronegative atom such as F, O or N is quite polar:

• The hydrogen atom has no inner core of electrons, so the side of the atom facing away from the bond represents a virtually naked nucleus
• This positive charge is attracted to the negative charge of an electronegative atom in a nearby molecule
• Because the hydrogen atom in a polar bond is electron-deficient on one side (i.e. the side opposite from the covalent polar bond) this side of the hydrogen atom can get quite close to a neighboring electronegative atom (with a partial negative charge) and interact strongly with it (remember, the closer it can get, the stronger the electrostatic attraction)
• Hydrogen bonds vary from about 4 kJ/mol to 25 kJ/mol (so they are still weaker than typical covalent bonds.
• But they are stronger than dipole-dipole and or dispersion forces.
• They are very important in the organization of biological molecules, especially in influencing the structure of proteins

Water is unusual in its ability to form an extensive hydrogen bonding network

• As a liquid the kinetic energy of the molecules prevents an extensive ordered network of hydrogen bonds
• When cooled to a solid the water molecules organize into an arrangement which maximizes the attractive interactions of the hydrogen bonds
• This arrangement of molecules has greater volume (is less dense) than liquid water, thus water expands when frozen
• The arrangement has a hexagonal geometry (involving six molecules in a ring structure) which is the structural basis of the six-sidedness seen in snow flakes
• Each water molecule can participate in four hydrogen bonds
• One with each non-bonding pair of electrons
• One with each H atom

Intermolecular Forces
Properties of Liquids: Viscosity and Surface Tension

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Properties of Liquids: Viscosity and Surface Tension

Viscosity

The resistance of a liquid to flow is called its viscosity

• The greater the viscosity, the more slowly it flows

Measuring viscosity

• How long a liquid takes to flow out of a pipette under the force of gravity
• How fast an object (steel ball) sinks through the liquid under gravitational force

The Physical Basis of Viscosity

• Viscosity is a measure of the ease with which molecules move past one another
• It depends on the attractive force between the moleculees
• It depends on whether there are structural features which may cause neighboring molecules to become "entangled"
• Viscosity decreases with increasing temperature - the increasing kinetic energy overcomes the attractive forces and molecules can more easily move past each other

Surface Tension

By definition the molecules of a liquid exhibit intermolecular attraction for one another.

What happens to molecules at the surface in comparison to those in the interior of a liquid?

• Molecules in the interior experience an attractive force from neighboring molecules which surround on all sides
• Molecules on the surface have neighboring molecules only on one side (the side facing the interior) and thus experience an attractive force which tends to pull them into the interior

The overall result of this asymmetric force on surface molecules is that:

• The surface of the liquid will rearrange until the least number of molecules are present on the surface
• In other words the surface area will be minimized
• A sphere has the smallest surface area to volume ratio
• The surface molecules will pack somewhat closer together than the rest of the molecules in the liquid
• The surface molecules will be somewhat more ordered and resistant to molecular disruptions
• Thus, the surface will seem to have a "skin"

The "inward" molecular attraction forces, which must be overcome to increase the surface area, are termed the "surface tension"

Surface tension is the energy required to increase the surface area of a liquid by a unit amount

Water

• Intermolecular hydrogen bonds
• Surface tension at 20°C is 7.29 x 10^-2 J/m²

Mercury

• Intermolecular metallic (electrostatic) bonds
• Surface tension at 20°C is 4.6 x 10^-1 J/m²

Cohesive forces bind molecules of the same type together

Adhesive forces bind a substance to a surface

For example, attractive forces (hydrogen bonding) exists between glass materials (Silicon dioxide) and water.

• This is the basis of "capillary" action, where water can move up a thin capillary, against the force of gravity. Surface tension "pulls" neighboring water molecules along.
• The liquid climbs until the adhesive and cohesive forces are balance by the force of gravity

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Intermolecular Forces
Changes of State

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Changes of State

The three states of matter include

• solid
• liquid
• gas

In general, matter in one state can be changed into either of the other two states.

Such transformations are called "phase changes"

Energy Changes Accompanying Changes of State

Each change of state is accompanied by a change in the energy of the system

• Whenever the change involves the disruption of intermolecular forces, energy must be supplied
• The disruption of intermolecular forces accompanies the state going towards a less ordered state
• As the strengths of the intermolecular forces increase, greater amounts of energy are required to overcome them during a change in state

The melting process for a solid is also referred to as fusion

• The enthalpy change associated with melting a solid is often called the heat of fusion (DH_fus)
• Ice DH_fus = 6.01 kJ/mol

The heat needed for the vaporization of a liquid is called the heat of vaporization (DH_vap)

• Water DH_vap = 40.67 kJ/mol

Less energy is needed to allow molecules to move past each other than to separate them totally

Vaporization requires the input of heat energy.

• Our bodies use this as a mechanism to remove excess heat from ourselves. We sweat, and its evaporation requires heat input (the excess heat from ourselves).
• Refrigerators use the evaporation of Freon (CCl₂F₂) to remove heat inside the fridge. The Freon is condensed outside the cabinet (usually in coils at the back) in a process which releases heat energy (the coils will be warm)

Heating Curves

The heating of ice at -25 °C to +125 °C at constant pressure (1 atm) will exhibit the following characteristics

• Initially, the heat input is used to increase the temperature of the ice, but the ice does not change phase (remains a solid)
• As the temperature approaches some critical point (i.e. the melting temperature of ice), the kinetic energy of the molecules of water is sufficient to allow the molecules to begin sliding past one another.
• As the ice begins to melt, additional input of heat energy does not raise the temperature of the water, rather it is used to overcome the intermolecular attraction during the phase change from solid to liquid
• Once the water is in a liquid phase, increasing the amount of heat input raises the temperature of the liquid water
• As the temperature approaches another critical point (the vaporization, or boiling, temperature of water) the kinetic energy of the molecules is sufficient to allow the separation of molecules into the gas phase
• As the liquid begins to boil. Additional input of heat energy does not raise the temperature of the water, rather it is used to overcome the intermolecular attractions during the phase change from liquid to gas
• Once the water is in the gas phase, additional heat input raises the temperature of the water vapor

Note: greater energy is needed to vaporize water than to melt it

Heating ice, water and water vapor

In the region of the curve where we are not undergoing a phase transition, we are simply changing the temperature of one particular phase of water (either solid, liquid or gas) as a function of heat input

• The slope of the lines relates temperature to heat input
• The greater the slope, the greater the temperature change for a given unit of heat input
• The amount of heat needed to change the temperature of a substance is given by the specific heat or molar heat capacity
• Specific heat of ice = 2.09 J/g K
• Specific heat of water = 4.18 J/g K
• Specific heat of water vapor = 1.84 J/g K

In the regions of the curve where we are undergoing a phase transition, the heat energy input is not raising the temperature of the sample, rather it is being used to disrupt the intermolecular forces

• DH_fus = 6.01 kJ/mol
• DH_vap = 44.0 kJ/mol

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Calculate the enthalpy change for converting 2 moles of ice at -25°C to +125°C.

• Converting to grams: (2 mol)*(18 g/mol) = 36 g
• Heating ice from -25 to 0°C: (25K)*(2.09 J/g K)*(36 g) = 1.88 kJ
• Fusion of ice to liquid water: (6.01 kJ/mol)*(2 mol) = 12.0 kJ
• Heating of water from 0 to 100°C: (100K)*(4.18 J/g K)*(36 g) = 15.1 kJ
• Vaporization of water to water vapor: (44.0 kJ/mol)*(2 mol) = 88.0 kJ
• Heating of water vapor from 100 to 125°C: (1.84 J/g K)*(25K)*(36 g) = 1.66 kJ
• Grand total: 1.88 + 12.0 + 15.1 + 88.0 + 1.66 = 119 kJ

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Critical Temperature and Pressure

Gases can be liquified by either decreasing the temperature or increasing the pressure

• As long as the temperature is not too high, we can use pressure to liquefy a gas
• As temperatures increase it becomes more difficult to use pressure to liquefy a gas (due to the increasing kinetic energy)
• For every substance there is a temperature above which it is impossible to liquefy the gas regardless of the increase in pressure

The highest temperature at which a substance can exist as a liquid is called its critical temperature

The critical pressure is the pressure required to bring about condensation at the critical temperature

For example, oxygen has a critical temperature of 154.4 K. It cannot be liquefied until the temperature is reduced to this point. At this temperature, the pressure needed to liquefy oxygen is 49.7 atm.

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1996 Michael Blaber

Intermolecular Forces
Vapor Pressure

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Vapor Pressure

Suppose we have a closed container into which we pour some water. As soon as we add the water we check a pressure gauge connected to the container. We let the container sit for a while and then we check the pressure again. What might the pressure guage indicate?
As the water evaporates the pressure exerted by the vapor above the liquid increases, until at some point, the pressure reaches a constant value, the vapor pressure of the substance:

The molecular basis of vapor pressure
The kinetic energy of the molecules at the surface of a liquid varies over a range of values:

• Some of the molecules have enough kinetic energy to overcome the attractive forces between the molecules
• The weaker the attractive forces, the greater the fraction of molecules with enough kinetic energy to escape
• The greater the fraction of molecules which can escape the liquid, the greater the vapor pressure

Not only can water molecules leave the surface, but molecules in the vapor phase can also hit and go into the water

• Initially, there are no molecules in the vapor phase and the number of molecules in the vapor which are rejoining the water is zero
• As time goes on there are more molecules in the vapor phase and the number of a vapor molecule striking the water increases
• At some point in time the number of vapor molecules rejoining the water equals the number leaving to go into the vapor phase
• an equilibrium has been reached, and the pressure has stabilized at the characteristic vapor pressure of the substance

Vapor pressure increases with temperature

• At higher temperature more molecules have the necessary kinetic energy to escape the attractive forces of the liquid phase
• The more molecules in the vapor phase, the higher the vapor pressure

What if molecules in the interior of the liquid decides to leave the liquid phase and go into the vapor phase?

• This interior bubble will rapidly collapse if the external pressure is greater than the vapor pressure
• If the external pressure is equal to, or lower than the vapor pressure, then the bubble will remain or expand and the liquid boils

Vapor pressure increases with increasing temperature

• At 100°C the vapor pressure of water is 760 torr (1 atm) or equal to the atmospheric pressure on the liquid (in an open container)
• At this temperature, interior bubbles will not collapse and the water boils
• At high altitudes (i.e. up in the Mountains) the air pressure is less than at sea level. Thus, water will boil at a lower temperature (the vapor pressure needed to support a bubble is lower at high altitude). Therefore, cooking times are longer for things that need to be boiled (e.g. boiled eggs take longer to cook at high altitudes).

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1996 Michael Blaber

Intermolecular Forces
Phase Diagrams

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Phase Diagrams

Equilibrium can exist not only between the liquid and vapor phase of a substance but also between the solid and liquid phases, and the solid and gas phases of a substance.
A phase diagram is a graphical way to depict the effects of pressure and temperature on the phase of a substance:

The curves indicate the conditions of temperature and pressure under which equilibrium between different phases of a substance can exist

• The vapor pressure curve is the border between the liquid and gaseous states of the substance
• For a given temperature, it tells us the vapor pressure of the substance
• The vapor pressure curve ends at the critical point.

The temperature above which the gas cannot be liquefied no matter how much pressure is applied (the kinetic energy simply is too great for attractive forces to overcome, regardless of the applied pressure)

• The line between the gas and solid phase indicates the vapor pressure of the solid as it sublimes at different temperatures
• The line between the solid and liquid phases indicates the melting temperature of the solid as a function of pressure
• For most substances the solid is denser than the liquid
• An increase in pressure usually favors the more dense solid phase
• Usually higher temperatures are required to melt the solid phase at higher pressures
• The "triple point" is the particular condition of temperature and pressure where all three physical states are in equilibrium
• Regions not on a line represent conditions of temperature and pressure where only one particular phase is present
• Gases are most likely under conditions of high temperature
• Solids are most likely under conditions of high pressure

Phase Diagram for Water

• The frozen state of water (ice) is actually less dense than the liquid state, thus, the liquid state is more compact than the solid state
• Increasing pressure, which will favor compactness of the molecules, will thus favor the liquid state

Increasing pressure will thus lower the temperature at which the solid will melt

• The melting curve slopes to the left, unlike most compounds
• At 100 °C the vapor pressure of water is 760 torr or 1 atm, thus at this temperature water will boil if it is at 1 atm of pressure
• At pressures below 4.58 torr, water will be present as either a gas or solid, there can be no liquid phase

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1996 Michael Blaber

Intermolecular Forces
Structures of Solids

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Structures of Solids

Crystalline solids

• The atoms, molecules or ions pack together in an ordered arrangement
• Such solids typically have flat surfaces, with unique angles between faces and unique 3-dimensional shape
• Examples of crystalline solids include diamonds, and quartz crystals

Amorphous solids

• No ordered structure to the particles of the solid
• No well defined faces, angles or shapes
• Often are mixtures of molecules which do not stack together well, or large flexible molecules
• Examples would include glass and rubber

Unit Cells

The ordered arrangement of atoms, molecules or ions in a crystalline solid means that we can describe a crystal as being constructed by the repetition of a simple stuctural unit.

• Since the crystal is made up of an arrangement of identical unit cells, then an identical point on each unit cell represents an identical environment within the crystal
• The array of these identical points is termed the crystal lattice

• The unit cells shown are cubic
• All sides are equal length
• All angles are 90°
• The unit cell need not be cubic
• The unit cell lengths along the x,y, and z coordinate axes are termed the a, b and c unit cell dimensions
• The unit cell angles are defined as:
• a, the angle formed by the b and c cell edges
• b, the angle formed by the a and c cell edges
• g, the angle formed by the a and b cell edges

The crystal structure of sodium chloride

The unit cell of sodium chloride is cubic, and this is reflected in the shape of NaCl crystals

The unit cell can be drawn with either the Na⁺ ions at the corners, or with the Cl^- ions at the corners.

• If the unit cell is drawn with the Na⁺ ions at the corners, then Na⁺ ions are are also present in the center of each face of the unit cell
• If the unit cell is drawn with the Cl^- ions at the corners, then Cl^- ions are are also present in the center of each face of the unit cell

Within the unit cell there must be an equal number of Na⁺ and Cl^- ions.

For example, for the unit cell with the Cl^- ions at the center of the faces

• The top layer has (1/8+1/8+1/8+1/8+1/2)=1 Cl^- ion, and (1/4+1/4+1/4+1/4)=1 Na⁺ ion
• The middle layer has (1/2+1/2+1/2+1/2)=2 Cl^- ions and (1/4+1/4+1/4+1/4+1)=2 Na⁺ ions
• The bottom layer will contain the same as the top or 1 each Cl^- and Na⁺ ions
• The unit cell has a total of 4 Cl^- and 4 Na⁺ ions in it. This equals the empirical formula NaCl.

Close packing of spheres

Many ions are spherical and many small molecules pack in a crystal lattice as essentially spherical entities.

Spheres can pack in three-dimensions in two general arrangements:

• Hexagonal close packing
• Cubic close packing

The coordination number is the number of particles surrounding a particle in the crystal structure.

• In each packing arrangement above (hexagonal close pack, cubic close pack), a particle in the crystal has a coordination number of 12
• The NaCl (face centered cubic) has a coordination number of 6

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Intermolecular Forces
Bonding in Solids

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Bonding in Solids

Molecular Solids

• Consist of atoms or molecules held together by intermolecular forces (dipole-dipole, dispersion and hydrogen bonds)
• These forces are weaker than chemical (covalent) bonds. Therefore molecular solids are soft, and have a generally low melting temperature
• Most substances that are gasses or liquids at room temperature form molecular solids at low temperature (e.g. H₂O, CO₂)

Comparison of bond energies for different types of bonds

Type of bond	Energy (kJ/mol)
Dispersion (Carbon - carbon van der Waals)	~1.0
Hydrogen bond (strongest dipole-dipole)	~12-16
Ionic	~50-100
Covalent	~100-1000

• The properties of molecular solids also depends upon the shape of the molecule

• Benzene (six carbon ring with a symmetrical structure) packs efficiently in three dimensions
• Toluene is related to benzene but has a methyl group attached to one carbon of the ring. It is not symmetrical and does not pack efficiently. Its melting point is lower than benzene

Covalent Network Solids

• Consist of networks or chains of molecules held together by covalent bonds
• Covalent bonds are stronger than intermolecular forces and covalent substances are subsequently harder and have higher melting temperatures
• Diamond is a covalent structure of carbon. It is extremely hard and has a melting temperature of 3550°C

Ionic Solids

• Held together by ionic bonds
• The strength of the ionic interactions depends on the magnitude of the charge of the ions. Thus, NaCl (single charge on both ions) has a melting point of 801°C, whereas MgO (2⁺, 2^- charge on the ions) has a melting point of 2852°C

Metallic Solids

• Consist entirely of metal atoms.
• Typically hexagonal close packed, cubic close packed or body-centered cubic structures. These have coordination numbers of either 12 or 8.
• Bonding is due to valence electrons which are delocalized throughout the entire solid
• Bonding is stronger than simple dispersion forces, but there are insufficient electrons to form ordinary covalent bonds. The strength of the bonding increases with the number of electrons available for bonding
• Delocalization of electrons is the physical basis for the ability of metals to carry electrical current (electrons are free to move about the metal structure)
• The nucleus and inner core of electrons are in a "sea" of delocalized, mobile valence electrons

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1996 Michael Blaber