TRT 401 PHYSICAL CHEMISTRY. PART 1: INTRODUCTION TO PHYSICAL CHEMISTRY. What is physical chemistry? Physical chemistry is a study of the physical basis of phenomena related to the chemical composition and structure of substances . Or
PART 1: INTRODUCTION TO PHYSICAL CHEMISTRY
Physical chemistry is a study of the physical basis of phenomena related to the chemical composition and structure of substances.
Physical chemistry is quantitative and theoretical study of the
properties and structure of matter, and their relation to the interaction
of matter with energy.
Atoms are the submicroscopic particles that constitute the fundamental building
block of ordinary matter. They are most found in molecules, two or more atoms
joined in specific geometrical arrangement.
Carbon dioxide molecule
Carbon monoxide molecule
In the study of chemistry, atoms are often portrayed as colored spheres, with each
color representing a different kind of atom.
For example, a black sphere represents a carbon atom, a red sphere represents
an oxygen atom.
For more interactive periodic table please refer http://www.ptable.com/
Oppositely charged ions are held together by ionic bonding,
forming a crystalline lattice.
A compound that composed of cations and anions
bound together by electrostatic attraction
Compound that not contain a metallic element typically covalent compound consisting of discrete molecules.
Example: sodium metal as an array of
positively charged Na+ ion immersed in
a sea of negatively charges electron (e-).
The table below summarize the three different types of bonding
The ability of an atom to attract electrons to itself in a chemical bond
(which results in polar bonds) is called electronegativity, χ (chi).
Fluorine is the most
Francium is the
Electronegativity generally increase as we move across a row in periodic table and
decrease as we move down a column.
Bond polarity expressed numerically as dipole moment, μwhich occurs when
there is a separation between a positive and negative charge.
μ = qr
μ: dipole moment; q: separating a proton and an electron; r: distance
q = 1.6 x 10-19 C
r = 130 pm (the approximate length of a short chemical bond)
μ= q x r
= (1.6 x 10-19 C)(130 x 10-12m)
= 2.1 x 10-29 . M
= 6.2 D
The debye (D) is a common unit used for reporting dipole moment (1D = 3.34 x 10-30 C.m)
Table 1 Dipole moments of several molecules in the gas phase
Matter: anything that occupies space and has mass.
Example: book, desk, pen, pencil even your body is are all compose of matter.
Air also matter but it too occupies space and matter. These specific instance of matter- such as air, sand, water- a substance.
Matter can be classify to its state- solid, liquid, or gas according to its composition.
Glass, plastic &
Table salt, ice & diamond
Solid matter may be crystalline, in which case its atoms or molecules are
arranged in patterns with long range, repeating order.
Its may be amorphous in which case its atoms or molecules do not have any
long range order.
Gases can be compressed-squeezed into a small volume because there is so much
Empty space between atoms or molecules in the gaseous state.
Matter can be classified as either pure substances, which have fixed composition,
or mixtures, which have variable composition.
Pure substance (element and compounds) are unique materials with their own
chemical and physical properties, and are composed of only one type of atom or
A pure substance that is composed
of atoms or two more different
A substance that cannot
be chemically broken down
Into simpler substance.
Mixture are simply random combinations of two or more different types of atoms of
molecules, and retain the properties of the individual substances. They can therefore
be separated (although sometime with difficulty) by physical means (such as boiling,
distillation, melting, crystallizing, magnetism, etc.)
One in which the composition varies
from one region to another.
One with the same composition
Tea with sugar
Amount of substance(n): a measure of a number of specified entities (atoms, molecules, or formula unit) present (unit; mole; mol).
1 mol of a substance contains as many entities as exactly 12 g of carbon-12 (ca. 6.02 x 1023 objects)
Avogadro’s Number: NA = 6.02 x 1023 mol-1
Extensive Property: Dependent upon the amount of matter in
the substance (e.g., mass & volume)
Intensive Property: Independent of the amount of matter in a
substance (e.g., mass density, pressure and temperature)
Molar Property: Xm, an extensive property divided by the
amount of substance, n: Xm = X/n
Molar Concentration:“Molarity” moles of solute dissolved in
litres of solvent: 1.0 M = 1.0 mol L-1
Table 2 Example list of units
for more info: http://physics.nist.gov/cuu/Units/
Table 3 SI Prefix Multipliers
Table 4 SI Prefix – large unit
Energy is define as the ability to do work.
Work is done when a force is exerted through a distance.
Force through distance; work is done.
Energy is measured in Joules (J) or Calories (cal).
1 J = 1 kg m2 s-2
Energy may be converted from one to another, but it is neither created nor destroyed (conversion of energy).
In generally, system tend to move from situations of high potential energy (less stable) to situations having lower energy (more stable).
Energy is the capacity to supply heat or to do work. Energy can be exchanged
between objects by some combination of either heat or work:
Energy = heat + work
∆E= q + w
Example of a billiard ball rolling across the table
and colliding straight on with a second,
stationary billiard ball.
Potential energy increases when things that attract each other are separated or when things that repel each other are moved closer.
• Potential energy decreases when things that attract each other are moved closer, or when things that repel each other are separated.
• According to the law of conservation of energy, energy cannot be created or destroyed, but kinetic and potential energy can be interconverted.
Energy transformation I
Energy transformation II
Water falling in a waterfall exchanges gravitational potential energy for kinetic energy as it falls faster and faster, but the energy is never destroyed.
EK converted to
high EPdecreasing EP low EP
low EK increasing EK high EP
The chemical potential energy of a substance results from the relative positions and
the attractions and repulsions among all its particles. Under some circumstances, this
energy can be released, and can be used to do work:
Using chemical energy to do work – The compound produced when gasoline burns have
Less chemical potential energy than the gasoline molecules.
The cycle held the
The energy transformed
into kinetic energy of
Kinetic Energy, EK: Energy an object possesses as a result of its motion.
KE = ½mv2
Potential Energy, V: Energy an object possesses as a result of its position. Zero of potential energy is relative:
1. Gravitational Potential Energy:
zero when object at surface (V = 0 when h = 0)
VG = mgh, m = mass, g = 9.81 m s-2, h = height
2. Electrical Potential Energy:
zero when 2 charged particles infinitely separated
qi = charge on particle i, r = distance
ε0 = 8.85 x 10-12 C2 J-1 m-1
Molecules have a certain number of degrees of freedom: they can vibrate, rotate and translate - many properties depend on these degrees of freedom:
All degrees of freedom have the same average energy at temperature T: total energy is partitioned over all possible degrees of freedom
Quadratic energy terms:
½mvx2 + ½mvy2 + ½mvz 2
Average energy associated with each quadratic term is ½kT, where k = 1.38 x 10-23 J K-1 (Boltzmann constant), where k is related to the gas constant, R = 8.314 J K-1 mol-1 by R = NAk
However: this theorem is derived by classical physics, and can only be applied to translational motion.
The energy of a molecule, atom, or subatomic particle that is confined to a region of space
Is quantized, or districted to certain discrete values. These permitted energies are called
At temperatures > 0, molecules are distributed over available energy levels according to the Boltzmann Distribution, which gives the ratio of particles in each energy state:
Boltzmann constant k=1.381 x 10-23 JK-1
At the lowest temperature T = 0, only the lowest energy state is occupied. At infinite temperature, all states are equally occupied.
In real life, the population of states is described by an exponential function, with the highest energy states being the least populated.
Degenerate states: States which have the same energy
These will be equally populated!
Populations for (a) low
& (b) high temperatures
Boltzmann predicts an
exponential decrease in
At room T, only the
ground electronic state
is populated. However,
many rotational states
are populated, since the
energy levels are so
More states are
significantly populated if
energy level spacing
are near kT!
Light is a form of electromagnetic radiation. In classical physics, electromagnetic
radiation is understood in term of the electromagnetic field.
Electric field – charged particles (whether stationary or moving)
Magnetic field – acts only on moving charged particles.
Wavelength ,λ is the distance between the neighboring peaks of two wave, and is
frequency, v (nu) the number of times in a given interval at which its displacement
at a fixed point returns to its original value divided by the length of the time intervals.
Frequency is measure in Hertz, 1 Hz= 1 s-1.
Wavelength, λ = c/ v
Wavenumber, ṽ (nu tilde) the number of complete wavelengths in a given length.
Wavenumber, ṽ = v/c =1/λ
e.g.: A wave number of 5 cm-1 indicates there are 5 complete wavelength in 1 cm.
Matter: Substance, intensive and extensive properties, molarity and molality
Extensive and intensive properties
An extensive property is a property that depends on the amount of substance in the sample.
Examples: mass, volume…
Examples: temperature, pressure, mass density…
A molar property Xm is the value of an extensive property X divided by the amount of substance, n: Xm=X/n. A molar property is intensive. It is usually denoted by the index m, or by the use of small letters. The one exemption of this notation is the molar mass, which is denoted simply M.
A specific property Xs is the value of an extensive property X divided by the mass m of the substance: Xs=X/m. A specific property is intensive, and usually denoted by the index s.
Measures of concentration: molarity and molality
The molar concentration(‘molarity’) of a solute in a solution refers to the amount of substance of the solute divided by the volume of the solution. Molar concentration is usually expressed in moles per litre (mol L-1 or mol dm-3). A molar concentration of x mol L-1 is widely called ‘x molar’ and denoted x M.
System and surroundings:
For the purposes of Physical Chemistry, the universe is divided into two parts, the system and its surroundings.
The system is the part of the world, in which we have special interest.
The surroundings is where we make our measurements.
The type of system depends on the characteristics of the boundary which divides it from the surroundings:
(a) An open system can exchange matter and energy with its
(b) A closed system can exchange energy with its surroundings, but it cannot exchange matter.
(c) An isolated system can exchange neither energy nor matter with its surroundings.
Except for the open system, which has no walls at all, the walls in the two other have certain characteristics, and are given special names:
An adiabatic (isolated) system is one that does not permit the passage of energy as heat through its boundary even if there is a temperature difference between the system and its surroundings. It has adiabatic walls.
A diathermic (closed) system is one that allows energy to escape as heat through its boundary if there is a difference in temperature between the system and its surroundings. It has diathermic walls.
H2 + ½ O2
The macroscopic properties are identical in all parts of the system.
The macroscopic properties jump at the phase boundaries.
Homogeneous part of a (possibly) heterogeneous system.
The macroscopic properties do not change without external influence.
The system returns to equilibrium after a transient perturbation.
In general exists only a single true equilibrium state.
Equilibrium in Mechanics:
Equilibrium in Thermodynamics:
Temperature is a thermodynamic quantity, and not known in mechanics.
The concept of temperature springs from the observation that a change in physical state (for example, a change of volume) may occur when two objects are in contact with one another (as when a red-hot metal is plunged into water):
If, upon contact of A and B, a change in any physical property of these systems is found, we know that they have not been in thermal equilibrium.
The Zeroth Law of thermodynamics:
If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, than C is also in thermal equilibrium with A. All these systems have a common property: the same temperature.
Energy flows as heat from a region at a higher temperature to one at a lower temperature if the two are in contact through a diathermic wall, as in (a) and (c). However, if the two regions have identical temperatures, there is no net transfer of energy as heat even though the two regions are separated by a diathermic wall (b). The latter condition corresponds to the two regions being at thermal equilibrium.
Linear relation between the Celsius temperature and an observable quantity x, like the length of a Hg column, the pressure p of a gas at constant volume V, or the volume V of the gas for constant pressure p:
Left: The variation of the volume of a fixed amount of gas with the temperature constant. Note that in each case they extrapolate to zero volume at -273.15 C.
Right: The pressure also varies linearly with the temperature, and extrapolates to zero at
T= 0 (-273.15 C).
For the pressure p, this transforms to:
For all (ideal) gases one finds
Introduction of the thermodynamic temperature scale (in ‘Kelvin’):
The thermodynamic temperature scale:
In the early days of thermometry (and still in laboratory practice today), temperatures were related to the length of a column of liquid (e.g. Mercury, Hg), and the difference in lengths shown when the thermometer was first in contact with melting ice and then with boiling water was divided into 100 steps called ‘degrees’, the lower point being labelled 0. This procedure led to the Celsius scale of temperature with the two reference points at 0 °C and 100 °C, respectively.
The fundamental physical propertyin thermodynamics is work: work is done when an object is moved against an opposing force.
(Examples: change of the height of a weight, expansion of a gas that pushes a piston and raises the weight, or a chemical reaction which e.g. drives an electrical current)
The energy of a system is its capacity to do work. When work is done on an otherwise isolated system (e.g. by compressing a gas or winding a spring), its energy is increased. When a system does work (e.g. by moving a piston or unwinding the spring), its energy is reduced.
When the energy of a system is changed as a consequence of a temperature difference between it and the surroundings, the energy has been transferred as heat. When, for example, a heater is immersed in a beaker with water (the system), the capacity of the water to do work increases because hot water can be used to do more work than cold water.
Heat transfer requires diathermic walls.
A process that releases energy as heat is called exothermic, a process that absorbs energy as heat endothermic.
(a) When an endothermic process occurs in an adiabatic system, the temperature falls; (b) if the process is exothermic, then the temperature rises. (c) When an endothermic process occurs in a diathermic container, energy enters as heat from the surroundings, and the system remains at the same temperature; (d) if the process is exothermic, then energy leaves as heat, and the process is isothermal.
When energy is transferred to the surroundings as heat, the transfer stimulates disordered motion of the atoms in the surroundings. Transfer of energy from the surroundings to the system makes use of disordered motion (thermal motion) in the surroundings.
When a system does work, it stimulates orderly motion in the surroundings. For instance, the atoms shown here may be part of a weight that is being raised. The ordered motion of the atoms in a falling weight does work on the system.
Work, heat, and energy (continued):
example: - p and T as independent variables means: Vm (=v) = f(p,T),
i.e. the resulting molar volume is pinned down, or
- p, T, n as independent variables means: V = f(p,T,n)
- state variables, and are related to each other via the
- state functions.
The thermal equation of state and the perfect gas equation
Thermal equation of state:
V = f(p,T,n)orVm = v = f(p,T)
The “perfect gas” (or “ideal gas”):
Some empirical gas laws:
V = f(T) for p=const.:
p = f(T) for V=const.:
p = f(V) for T=const.:
V = const. ( + 273.15°C)
= const.’ T
p = const. ( + 273.15°C)
= const.’ T
p V = const.
Step 2: Isothermal change
= const. !
A region of the p,V,T surface of a fixed amount of perfect gas. The points forming the surface represent the only states of the gas that can exist.
Sections through the surface shown in the figure at constant temperature give the isotherms shown for the Boyle-Mariotte law and the isobars shown for the Gay-Lussac law.
p v = R T
p V = n R T
‘perfect gas equation’
R : ‘gas constant’
(= 8.31434 J K-1 mol-1)
Step 2: Isobaric change
= const. !
The change of a state variable is independent of the path, on which the change of the state has been made, as long as initial and final state are identical.
same result !!!
A more general approach to thermal expansion and compression:
V = f(T) for p=const.:V = V0 (1 + )
: (thermal) expansion coefficient
p = f(T) for V=const.:p = p0 (1 + )
p = f(V) for T=const.:pV = const. and d(pV) = pdV + Vdp = 0
: (isothermal) compressibility
Due to generally valid!
Exact differential of V=f(p,T):
The mole fraction, xJ, is the amount of J expressed as a fraction of the total amount of molecules, n, in the sample:
When no J molecules are present, xJ=0; when only J molecules are present, xJ=1. Thus the partial pressure can be defined as:
The partial pressure of a gas is the pressure that it would exert if it occupied the container alone. If the partial pressure of a gas A is pA, that of a perfect gas B is pB, and so on, then the partial pressure when all the gases occupy the same container at the same temperature is
where, for each substance J,
The partial pressures pA and pB of a binary mixture of (real or perfect) gases of total pressure p as the composition changes from pure A to pure B. The sum of the partial pressures is equal to the total pressure. If the gases are perfect, then the partial pressure is also the pressure that each gas would exert if it were present alone in the container.
Mixtures of gases: Partial pressure and mole fractions
The pressure exerted by a mixture of perfect gases is the sum of the partial pressures of the gases.
For a perfect gas, Z=1 under all conditions. Deviation of Z from 1 is a measure of departure from perfect behaviour.
Real gases show deviations from the perfect gas law because molecules (and atoms) interact with each other: Repulsive forces (short-range interactions) assist expansion, attractive forces (operative at intermediate distances) assist compression.
At very low pressures, all the gases have Z1 and behave nearly perfect. At high pressure, all gases have Z>1, signifying that they are more difficult to compress than a perfect gas, and repulsion is dominant. At intermediate pressure, most gases have Z<1, indicating that the attractive forces are dominant and favor compression.
The variation of the potential energy of two molecules on their separation. High positive potential energy (at very small separations) indicates that the interactions between them are strongly repulsive at these distances. At intermediate separations, where the potential energy is negative, the attractive interactions dominate. At large separations (on the right) the potential energy is zero and there is no interaction between the molecules.
The variation of the compression factor Z = pv/RT with pressure for several gases at 0C. A perfect gas has Z = 1 at all pressures. Notice that, although the curves approach 1 as p 0, they do so with different slopes.
Real gases: An introduction
Below, some experimental isotherms of carbon dioxide are shown. At large molar volumes v and high temperatures the real isotherms do not differ greatly from ideal isotherms. The small differences suggest an expansion in a series of powers either of p or v, the so-called virial equations of state:
Experimental isotherms of carbon dioxide at several temperatures. The `critical isotherm', the isotherm at the critical temperature, is at 31.04 C. The critical point is marked with a star.
The virial equation can be used to demonstrate the point that, although the equation of state of a real gas may coincide with the perfect gas law as p 0, not all of its properties necessarily coincide. For example, for a perfect gas dZ/dp = 0 (because Z=1 for all pressures), but for a real gas
as p 0, and
as v , corresponding to p 0.
Real gases: The virial equation of state
The third virial coefficient, C, is usually less important than the second one, B, in the sense that at typical molar volumes C/v2<<B/v. In simple models, and for p 0, higher terms than B are therefore often neglected.
Because the virial coefficients depend on the temperature (see table above), there may be a temperature at which Z1 with zero slope at low pressure p or high molar volume v. At this temperature, which is called the Boyle temperature, TB, the properties of a real gas coinicide with those of a perfect gas as p 0, and B=0. It then follows that pvRTB over a more extended range of pressures than at other temperatures.
Real gases: The Boyle temperature
The compression factor approaches 1 at low pressures, but does so with different slopes. For a perfect gas, the slope is zero, but real gases may have either positive or negative slopes, and the slope may vary with temperature. At the Boyle temperature, the slope is zero and the gas behaves perfectly over a wider range of conditions than at other temperatures.
Reconsider the experimental isotherms of carbon dioxide. What happens, when gas initially in the state A is compressed at constant temperature (by pushing a piston)?
Real gases: Condensation and critical point
Real gases: Critical constants, compression factors, Boyle temperatures, and the supercritical phase
A gas can not be liquefied if the temperature is above its critical temperature. To liquefy it - to obtain a fluid phase which does not occupy the entire volume - the temperature must first be lowered to below Tc, and then the gas compressed isothermally.
The single phase that fills the entire volume at T>Tc may be much denser then is normally considered typical of gases. It is often called the supercritical phase, or a supercritical fluid.
The surface of possible states allowed by the van der Waals equation.
The van der Waals equation of gases: A model
P= nRT – a n2
V- nb V2
Starting point: The perfect gas lawpv = nRT
Correction 1: Attractive forces lower the pressure
replace p by (p+∏), where is the ‘internal pressure’. More detailed analysis shows that =a/v2.
P= RT – a
Vm- b Vm2
Van der Waals equation
Correction 2: Repulsive forces are taken into account by supposing that the molecules (atoms) behave as small but impenetrable spheres
replace v by (v-b), where b is the ‘exclusion volume’. More detailed analysis shows that b is approximately the volume of one mole of the particles.
a, b: van der Waals coefficients
At the critical point the isotherm has a flat inflexion. An inflexion of this type occurs if both the first and second derivative are zero:
at the critical point. The solution is
and the critical compression factor, Zc, is predicted to be equal to
for all gases.
Van der Waals isotherms at several values of T/Tc. The van der Waals loops are normally replaced by horizontal straight lines. The critical isotherm is the isotherm for T/Tc = 1.
(2) Liquids and gases coexist when cohesive and dispersing effects are in balance. The ‘van der Waals loops’ are unrealistic because they suggest that under some conditions an increase in presure results in an increase of volume. Therefore they are replaced by horizontal lines
drawn so the loops define
equal areas above and below the
lines (‘Maxwell construction’)
Analysis of the van der Waals equation of gases
(1) Perfect gas isotherms are obtained athigh enough temperatures and large molar volumes.
If the critical constants are characteristic properties of gases, than characteristic points, like melting or boiling point, should be unitary defined states. We therefore introduce reduced variables
and obtain the reduced van der Waals equation:
b) Reduced melting temperature
c) Reduced boiling temperature
a) Compression factors
The compression factors of four gases, plotted for three reduced temperatures as a function of reduced pressure. The use of reduced variables organizes the data on to single curves.
The principle of corresponding states
d) Trouton’s rule (or: Pictet-Troutons’s rule)
A wide range of liquids gives approximately the same standard entropy of vaporization of
S 85 J K-1 mol-1
works best for gases composed of spherical particles
fails, sometimes badly, when the particles are non-spherical or polar