Download van der Waals equation

Properties of Gases
1
Prepared byPatel chirag(120340102021)
Phases of Matter
There are three basic phases of matter:

Gas


Liquid


Particles are separated by distances that are large
compared with the size of the molecules. Gases
completely fill the container they occupy, taking on the
shape of the container. Intermolecular interactions are
minimal.
Particles are close together but are not held rigidly in
position and can move past one another. Liquids do not
completely fill the container they occupy but do take on
the shape of the container.
Solid

Particles are held close together in an orderly fashion
with little freedom of motion. Solids do not completely
fill a container and do not take on the shape of the
container they occupy.
Ideal Gases
Many useful thermodynamic principles are illustrated by considering
ideal, or perfect, gases.
Ideal
Gas

A hypothetical gas, or collection of molecules or atoms, which
undergo continuous random motion (or Brownian motion).
Characteristics:




The speeds of the particles increase with increasing
temperature.
The molecules are widely separated from each
other, with the only interactions being infrequent
elastic collisions with the walls of the container and
other particles.
The particles do not experience any intermolecular
forces, such as dipole-dipole forces or dispersion
forces.
Particles are considered to be “point-masses,”
having mass, but no volume.
Avogadro’s Principle



Avogadro’s Principle – equal volumes of gases at the
same pressure and temperature contain the same
number of molecules.
This is based on the observation that at a given
pressure and temperature, the molar volume , the
volume per mole of molecules, is approximately the
same regardless of the identity of the gas.
At constant pressure and temperature:
Ideal Gas Law

Combining Boyle’s Law, Gay-Lussac’s Law, and the
Avogadro’s Principle gives the proportionality:

This may also be written as the ideal gas equation:

R is the constant of proportionality, and is called the
gas constant. Experimentally, it is found to be the
same for all gases.
R has different values depending on the units used:

Ideal Gas Law




The ideal gas equation represents the approximate
equation of state for any gas, and becomes
increasingly exact as the pressure approaches zero.
A real gas, or actual gas, behaves like an ideal gas at
the limit of zero pressure.
The ideal gas equation is very useful in calculating
the properties of gases under different conditions.
For example, the molar volume, Vm, of a gas is
calculated to be:

24.789 L mol-1 at Standard Ambient
Temperature and Pressure (SATP), which is
298.15 K and 1 bar.

22.414 L mol-1 at Standard Temperature and
Pressure (STP), which is 0 C and 1 atm.
Combined Gas Law

The ideal gas equation can be used to calculate the change in
conditions when a fixed amount of gas is subjected to different
temperatures and pressures and allowed to occupy a different
volume.
Since under one set of conditions:

And under another set of conditions:

It follows that:

which is known as the combined gas law.
Gaseous Mixtures
To understand the physical behavior of a gaseous mixture,
we need to know the contribution that each component
makes to the total pressure of the sample.
 Dalton’s Law of Partial Pressures – the pressure exerted by
a mixture of gases is the sum of the partial pressures of the
gaseous components.
 Mathematically:

where pA and pB are the partial pressures of the perfect
gases A and B, and p is the total pressure of the mixture.
 The partial pressure of a perfect gas is the pressure it
would exert if it occupied the container alone at the same
temperature, determined from the ideal gas equation:
Mole Fraction

Dalton’s Law may be expressed in
terms of the mole fraction of the
components and is valid for any gas:
van der Waals Equation
• The ideal gas equation is based upon the model that:
–
–
Gases are composed of particles so small compared to the
volume of the gas that they can be considered to be zerovolume points in space.
There are no interactions, attractive or repulsive, between
the individual gas particles.
• In 1873, Johannes H. van der Waals (1837-1923), a
Dutch physicist, developed an approximate equation of
state for real gases that takes these factors into account:
–
–
A semiempirical equation, based upon experimental
evidence, as well as thermodynamic arguments.
Awarded 1910 Nobel Prize in Physics for his work.
van der Waals Equation
• Repulsive interactions between particles are taken into account by
assuming that the particles behave as small, impenetrable hard
spheres.
• Assume that there are N molecules of gas in a volume V, each
having a volume β. The actual volume for the gas molecules to
occupy is:
• If b is the volume per mole of gas molecules:
• The actual volume for the gas molecules to occupy is:
van der Waals Equation
• Correcting for the volume of the particles into the ideal
gas equation:
• Since
• Taking into account the actual volume of the gas particle
results in an increase in pressure relative to that
predicted by the ideal gas law.
van der Waals Equation
• The pressure of the gas also depends on:
–
–
The frequency of collisions of the gas particles with the
walls of the container.
The force with which the particles strike the container.
• Both are reduced by attractive forces between
particles.
• The attractive forces act with a strength proportional
to the number density of the gas molecules in the
container:
van der Waals Equation
• The pressure is thus reduced by the attractive forces in
proportion to the square of the number density. Taking
this into account, the corrected pressure is:
which is known as the van der Waals equation.
• In terms of the molar volume, Vm, the van der Waals
equation is:
van der Waals Equation
• The van der Waals constants:
–
a
•
•
•
–
Pressure correction
Represents the magnitude of attractive forces between
gas particles
Does not specify any physical origin to these forces
b
•
•
Volume correction
Related to the size of the particles
• These constants:
–
–
Are unique to each type of gas.
Are not related to any specific molecular properties.
van der Waals Isotherms
• The van der Waals equation
Generates ideal gas isotherms at high temperatures and at large
molar volumes.
• At high temperature, the first term may be much greater than the
second term.
• At large molar volumes,
and the ideal gas law is achieved:
Principle of Corresponding
•States
Because the van der Waals equation is only an approximation, it
is useful to have a common scale on which properties of different
gases can be compared.
• Because the critical constants are characteristic properties of
gases, they serve as a useful scale to compare different gases.
• The reduced variables of a gas are determined by dividing the
actual variable by the corresponding critical constant:
• The reduced compression factor, Zr , may be defined as:
Gibbs –daltton law

The total pressure of a mixtures of gases is equal to the
sum of individual gas components of the mixtures this
is known as Dalton law of partical pressure

The gas a & b originally occupying volume v and temp t
are mixed in third vessel which has same volume thus
Dalton law can be written as

P=pa+pb

By consideration of mass
M =ma+mb

Dalton law was re formulated by gibbs to include a
second statement on the properties of mixtures
the cobined statement is known as the gibbsDalton law

“ the internal energy enthalpy and entropy of a
gas are respectively equal to the sums of internal
energies,enthalpies,and entropies of the
consitituents”

M.u=maua+mbub+mchc+…..

M.h=maha+mbhb+mchc+….

M.s=masa+mbsb+mcsc+……
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