Gaseous State of Matter and Gas Laws
Concepts
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What is a gas ?
Gaseous State of Matter
The Ideal Gas Law
What is a gas ?
Gases appear to us as materials of very low density that must be enclosed to keep
them together. Unlike solids, gases have no definite shape. Unlike liquids, gases have no
definite volume but they completely fill the container. The volume of the container is the
volume of the gas in it. A gas exerts a pressure on all sides of the container that holds it.
Gas can be compressed by pressures greater than the pressure of the gas on its container.
The words vapour, fume, air also describe a gas. Air describes the common mixture of
gases in the atmosphere. The words vapour and fume suggest that the gas comes from a
particular liquid.
Gaseous State of Matter
Gaseous state is one of the physical state of matter. Near absolute zero of
temperature, a substance exists as a solid. As heat is added to this substance, it melts into
a liquid at its melting point, boils into a gas at its boiling point. A pure gas may be made
up of individual atoms ( e.g. a noble gas like neon ), elemental molecules made from one
type of atoms ( e.g. oxygen ) or compound molecules made from a variety of atoms
(e.g. carbon dioxide ). A gas mixture would contain a variety of pure gases much like the
air.
Physical characteristics of Gases
In a gas, the particles are the farthest apart, have the least force of attraction
between them and have the highest freedom of motion to the particles as compared to that
in solids and liquids. In a gas, the particles have enough kinetic energy so that the effect
of the intermolecular force is small ( or zero for an ideal gas ) and the typical distance
between neighboring particles is much greater than the size of the particles themselves. A
gas has no definite shape or volume but occupies the entire container in which it is
confined. A gas can be liquefied by compression without cooling or a liquid can be
converted to a gas by reducing the pressure at constant temperature.
Activity 1 – Let us take a few pieces of crushed ice in a closed container. Observe the
shape of the pieces of ice and the space occupied by them. Now heat the closed container.
Ice melts and is converted to water which does not have any shape but it occupies some
space or has definite volume. Heat the water for sometime. It is converted to water
vapour which has no shape nor definite volume . It occupies the entire space given to it
i.e. the volume of the container becomes the volume of water vapour. When we heat ice,
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we add kinetic energy to it. This increases the distance between the particles, gives them
more freedom of motion and thus changes the physical state from solid to liquid to gas.
Most gases are difficult to observe directly with our senses. They are described
through the use of four physical properties which are also called macroscopic
characteristics. They are - pressure, volume, number of particles ( also expressed as
moles ) and temperature. These four characteristics of gases were repeatedly observed by
scientists for many gases which ultimately led to the suggestion of a mathematical
relationship called ideal gas law.
The Ideal Gas Law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good
approximation to the behaviour of many gases under many conditions, although it has
many limitations.
The ideal gas law neglects both molecular size and intermolecular attractions
hence the law is most accurate for monoatomic gases at high temperatures and low
pressures. The neglect of molecular size becomes less important for larger volumes i.e.
for lower pressures. The relative importance of intermolecular attractions diminishes with
increasing thermal kinetic energy i.e. with increasing temperature. More sophisticated
equations of states such as van- der - Waals equation, allow deviations from adeality
caused by molecular size and intermolecular forces to be taken into account.
The ideal gas law is based on following physical approximations :
a) Gas molecules are moving in random directions
b) Molecules of a gas have negligible size as compared to the average distance between
them.
c) Interaction between gas molecules can be neglected because the average distance
between the molecules is very large.
d) When molecules collide with one another or the container, the collisions are elastic i.e.
no kinetic energy is lost.
e) The average energy of gas molecules is proportional to the temperature of the gas.
A gas may be completely described by its makeup – pressure, volume and
temperature. The ideal gas law gives an equation PV = n RT where P is the pressure, V
is the volume, T is the absolute temperature, n is the number of moles of the gas and R is
the Universal Gas Constant.
Check your understanding :
1) Gases are compressible but solids and liquids are not . Why ?
2) Why is it that the ideal gas law is accurate for monoatomic gases ?
3) What is the relation between temperature and kinetic energy of gases ?
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Different Gas Laws
Concepts
* Boyle’s law
* Charles’ law
* Absolute scale of temperature
* Combined Gas Law Equation * Gay – Lussac’s Law of Combining volumes
* Avogadro’s Law
* Dalton’s Law of Partial Pressures
* Graham’s Law of Diffusion
The early gas laws were mostly developed at the end of the eighteenth century,
when scientists began to realize that the relationships between the pressure, volume and
temperature of a gas could be obtained which would hold for all gases. The earlier gas
laws are now considered as special cases of the ideal gas law with one or more of the
variables kept constant.
Boyle’s Law
Boyle’s law is one of the several gas laws and a special case of the ideal gas law.
It describes the inversely proportional relationship between the absolute pressure and
volume of a gas at constant temperature. Boyle’s law was published in 1662. It is stated
as follows.
Temperature remaining constant, the volume of a given mass of an ideal gas
is inversely proportional to the pressure exerted by the gas.
Mathematically, Boyle’s law is stated as follows.
P α 1 / V or PV = K ( constant )
Graphically, the relationship
between volume and pressure
at constant temperature i.e.
Boyle’s law is shown here.
↑
V
------------------------------P →
Activity 2 – Let us do some simple activity to illustrate Boyle’s law. Take a hand bicycle
pump. Push down its piston. The pressure on the air inside the pump increases. Hence
volume of the air decreases. The reduced volume increases the pressure of the air inside
so that it is forced into the tyre. Wait for a while. Take the piston up. Air from outside
rushes in the pump and occupies greater volume. The increased volume reduces the
pressure of air inside the pump. By repeating this operation of pushing and pulling the
piston, we can fill air in the tyre of the bicycle. The operation shows that when pressure
increases, volume decreases and vice versa. This illustrates the Boyle’s law.
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Charles’ Law
Charles’ law is another gas law which presents a special case of the ideal gas law.
It describes the direct relationship between absolute temperature and volume of a gas at
constant pressure. The law was first published in 1787 and then confirmed in 1802.
Charles’ law is stated as follows.
Pressure remaining constant, the volume of a given mass of gas increases or
decreases by 1 / 273 times its volume at 00C for every one degree rise or fall
in temperature respectively.
The modern version of Charles’ law is given as follows.
At constant pressure, the volume of a given mass of an ideal gas is directly
proportional to the absolute temperature.
Mathematically, Charles’ law is stated as follows.
V α T
or V / T = K ( constant )
Graphically, the relationship
between temperature and
volume at constant pressure
i.e. Charles’ law is shown here.
↑
V
---------------------------T →
Charles’ law suggests that the coefficient of expansion of all gases is the same.
Activity 3 – Let us do some simple activity to illustrate Charles’ law. Take an empty
closed bottle of about 200 ml capacity made of thin plastic material. Put it in a deep
freezer for about half an hour. The bottle gets deshaped and reduces in volume. Take out
that bottle from the deep freezer and keep it at room temperature for half an hour. The
bottle regains its shape and becomes normal. This experiment shows that at atmospheric
pressure, volume of air inside the bottle decreases with decreasing temperature and
increases with increasing temperature.
.
Activity 4 – Take a sealed soda can or beer can. Heat it for some time. It explodes. As the
temperature of the can increases, volume of air inside the can also tries to increase. But
the can is sealed. So in order to increase the volume explosion takes place.
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Absolute Scale of Temperature
Charles’ law appears to imply that as we reduce the temperature, volume of a gas
goes on decreasing. Eventually, at some stage ( at – 273 0C ) , the volume of gas would
become zero. But this is impossible. Gas molecules themselves have some volume so
they will occupy some volume. This means the volume of a gas will never be zero.
The temperature at which the volume of a gas would theoretically be reduced
to zero is called absolute zero of temperature.
A temperature scale with absolute zero as the starting point is called the absolute scale of
temperature.
This scale was suggested by Thomson and Kelvin in 1848. It is called Kelvin
scale or absolute scale.. All temperatures on Kelvin scale are positive. Kelvin temperature
can be obtained by adding 273 to the Celcius temperature. Kelvin temperature is
expressed in ‘K’ or ‘A’ but no degree symbol is attached to it.
Check your understanding :
1) What is the nature of graph, if we plot 1 / V against P at constant temperature ?
2) What will happen if a fully inflated balloon is kept in a deep freezer for half an hour ?
3) Why the starting point of Kelvin scale is called absolute zero ?
4) Why is it necessary to mention the temperature and pressure while stating the volume
of the gas ?
5) One liter of a gas at one atmosphere pressure and 300 K, is compressed to 473 ml.
what is the new pressure of the gas ?
6) The temperature inside my refrigerator is 40C. If I place a balloon in my refrigerator
that has a temperature of 220C and a volume of 500 ml, what will be the volume of the
balloon when it is fully cooled by my refrigerator ?
Combined Gas Law Equation
The combined gas law shows the interdependence of variables like pressure,
volume and temperature. Its statement can be given as follows.
The ratio of pressure – volume product and the temperature of a system
remains constant for a given amount of gas.
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Mathematically, it is written as PV / T = K ( constant )
For comparing the same substance under different sets of conditions, the law can be
written as follows.
P1V1 / T1 = P2V2 / T2
The expression for combined gas law can be derived by simultaneous application of
Boyle’s law and Charles’ law as follows.
For a given mass of gas, let the initial pressure be P1, volume be V1 and the
absolute temperature be T1.
At constant temperature T1, let the pressure change from P1 to P2 so that the volume
changes from V1 to Vx. Then according to Boyle’s law - Vx / V1 = P1 / P2
Or Vx = P1V1 / P2 ------------- (1)
Now, at constant pressure P2, let the volume of the gas change from Vx to V2 so that the
absolute temperature changes from T1 to T2. Then according to Charles’ law,
Vx / V2 = T1 / T2
or
Vx = T1V2 / T2 --------------- ( 2 )
Comparing equations 1 and 2, we get,
On rearrangement we get,
Thus,
Vx = P1V1 / P2 = T1V2 / T2
P1V1 / T1 = P2V2 / T2
P1V1 / T1 = P2V2 / T2
Gay Lussac’s Law of Combining Volumes
In 1808, Gay Lussac, while studying the reactions of gases made an observation
that gases react in simple proportion of their volumes. Gay Lussac’s law of combining
volumes is stated as follows.
At constant temperature and pressure, the volumes of the gaseous reactants
and products can be expressed as ratios of whole numbers.
For example, hydrogen and oxygen react in volume ratio 2/1 to produce a volume
of water vapour equal to the initial volume of hydrogen or twice the initial volume of
oxygen. In another example, nitrogen and oxygen can react in volume ratio 2/1 or 1/1
depending upon whether the product is dinitrogen oxide N2O or NO.
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These reactions can be written as follows.
2 H2 (g) + O2 (g) → 2 H2O (g)
2 N2 (g) + O2 (g) → 2 N2O (g)
N2 (g) + O2 (g) → 2 NO (g)
Gay Lussac’s law of combining volumes can be diagrammatically shown as follows.
Avogadro’s Law
In 1811, Avogadro established a relationship between volume and number of moles of
different gases under similar conditions of temperature and pressure. Avogadro’s law is
also called Avogadro’s hypothesis or Avogadro’s principle. Avogadro’s law is stated as
follows.
Equal volumes of different ideal or perfect gases, at the same
temperature and pressure, contain same number of molecules.
Thus, the number of molecules in a specific volume of a gas is independent of the size or
mass of gas molecules at a given temperature and pressure.
Mathematically, it is written as V / n = K ( constant )
Where V is the volume and n is the number of moles of the gas.
For example, equal volumes of molecular hydrogen and nitrogen would contain the same
number of molecules as long as they are at the same temperature and pressure and they
follow ideal or perfect gas behaviour.
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Avogadro’s law can be diagrammatically illustrated as follows.
Note that the volume stays the same but the mass varies.
Activity 5 - Let us do some simple activity to illustrate Avogadro’s law. Take a balloon.
Blow air in it by a pump or mouth. What do you observe ? Normally, in the first attempt
the balloon does not get inflated even when you try hard. Then you say ‘ there is no
enough air in the balloon, so it does not get inflated’ This is the direct observation from
Avogadro’s law. The more air you put in the balloon, the greater is its volume because
the volume of the balloon is the volume of the gas ( air ) trapped in it.
Avogadro’s number
It is one of the fundamental constants used in chemistry. It permits calculations
of the amount of pure substance ( mole ) which is the basis of stoichiometric
relationships. It also makes possible determination of how much heavier a molecule of
gas is than that of another. As a result, the relative molecular weights of gases can be
determined by comparing the weights of equal volumes. Avogadro’s number is defined
as follows.
The number of elementary particles in one mole of a substance is called
Avogadro’s number N. Numerically, it is equal to 6.02214 x 1023.
Avogadro number has a unit per mole.
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Check your understanding:
1) How many volumes of SO3 will be produced if SO2 and O2 react in a stoichiometric
proportion at a given temperature and pressure?
2) How many molecules will be present in 44 g of CO2?
3) A balloon filled with helium weighs much less than an identical balloon filled with air.
Why?
Dalton’s Law of Partial Pressure
One of the important predictions made by Avogadro is that the identity of a
gas is unimportant in determining P – V – T properties of the gas. This behaviour means
that a gas mixture behaves in exactly the same manner as a pure gas. In 1801, Dalton
proposed the law of partial pressures. Dalton’s law of partial pressures is stated as
follows.
The total pressure of a mixture of non-reacting gases is equal to the sum
of the pressures that each gas would exert, if it was present alone.
In this case, the pressure exerted by each gas in the mixture is called the partial pressure
of that gas.
Mathematically, it is written as
P total = P1 + P2 + ------- Pn
where P1, P2, Pn etc are the partial pressures of gas 1, 2 --- n.
Dalton’s law of partial pressure tells us that each gas behaves independently of the other
gases in the mixture i.e. each gas exerts its own pressure (partial pressure).
The ideal gas equation of state applies to mixtures just as to pure gases. It was in
fact with a gas mixture i.e. ordinary air, that Boyle, Gay Lussac and Charles did their
early experiments.
Application – A simple application of Dalton’s law of partial pressure can be given as
follows. When a gas like oxygen is collected by downward displacement of water, the
volume of the moist gas is actually the volume of dry oxygen and volume of water
vapour at that temperature. Hence the pressure exerted by the gas is the sum of pressure
of dry oxygen and the pressure of water vapour at that temperature. The pressure of water
vapour at a given temperature (aqueous tension) is known from the literature. If we
subtract the aqueous tension from the observed pressure of the gas, we get the pressure of
dry oxygen gas. Here we treat the pressure of moist gas as the sum of the partial pressures
of dry oxygen gas and water vapour. This is an application of Dalton’s law of partial
pressure.
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Graham’s Law of Diffusion
Gases have a tendency to spontaneously intermix and form a homogeneous
mixture without the help of external agency. This is called diffusion of gases. Diffusion is
a physical phenomenon. Gases diffuse very quickly due to the presence of large empty
spaces between the gas molecules that makes their movement rapid into each other.
Gases move from a region of higher concentration to a region of lower concentration
until the mixture attains uniform concentration.
Graham studied the rate of diffusion of various gases and gave a quantitative relation
between the density and rate of diffusion of gases in 1837. Graham’s law of diffusion can
be stated as follows.
The rate of diffusion of a gas is inversely proportional to the square root of its density.
Mathematically, it is written as
r α 1 / (d) 1/2
or r = K / ( d )1/2 ( K = constant )
It follows then that comparative rates of diffusion of two gases are inversely proportional
to the square root of their densities. Under similar conditions of temperature and pressure,
the relation between comparative rates of diffusion and densities is given as follows.
r1 / r2 = ( d2 / d1) 1/2
Since density is proportional to molecular mass i.e. d α M , we can replace density by
molecular mass and write the equation as follows.
r1 / r2 = ( M2 / M1) 1/2
The rate of diffusion is given by the formula
Volume of the gas diffused
Rate of diffusion = ---------------------------------Time taken for diffusion
When the gas contained in the vessel is allowed to escape through a small aperture or pin
hole, the phenomenon is called effusion. Graham’s law is also applicable to effusion of
gases.
Graphically, Graham’s law can be shown as follows.
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Time taken for 25 ml samples of
different gases to diffuse through
a pin-hole into vacuum is shown
in the diagram here.
Activity 6 - Take a clean and transparent glass tube of 8 to 10 inches in length and 0.5 to
1 inch in diameter. Close its two ends by rubber stoppers. This is called a diffusion tube.
In the beginning, remove the rubber stoppers. Fit cotton plugs loosely in to the ends of
the diffusion tube. Take concentrated solutions of hydrochloric acid and ammonia in two
small beakers. Place a few drops of concentrated HCl on the cotton plug on one side of
the diffusion tube. Place a few drops of ammonia solution on the cotton plug on the other
side of the diffusion tube. Immediately replace the rubber stoppers and start recording the
time. Ammonia and HCl both vapourise and mix. A white deposit of NH4Cl is seen
inside the tube. As soon as it appears, note the time. Measure to the nearest of 0. 1 cm the
distance from the inside end of each cotton plug to the center of the white deposit.
Distance divided by the time will give you the rate of diffusion of the gas. Find out the
ratio of rates of diffusion of ammonia to HCl. Apply Graham’s law of diffusion. From the
molecular weights of ammonia and HCl find out the theoretical ratio of the expected
rates of diffusion. It comes out to be nearly 1.5. Compare your experimental result of this
ratio with the theoretical one. You will find that ammonia diffuses 50 % faster than HCl.
The experimental set up of diffusion of gases is shown in the following figure.
Figure:
dHCl
HCl
dNH3
NH3
smoky white ring
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Check your understanding
1) A container with two gases, helium and argon, is 30 % by volume of helium. Calculate
the partial pressure of helium and argon, if the total pressure inside the container is
four atmospheres.
2) A mixture of 14 g hydrogen, 84 g nitrogen and 2 moles of oxygen is placed in a flask.
When the partial pressure of oxygen is 78 mm of mercury, what is the total pressure in
the flask ?
3) If equal amounts of helium and argon are placed in a porous container and allowed to
escape which gas will escape faster and how much faster ?
4) What is the molecular weight of a gas which diffuses 1/50 times as fast as hydrogen ?
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References – Figures / Graphs etc.
1) Boyle’s law - Graph
Wikipedia, the free encyclopedia – en.wikipedia.org / wiki / Boyle’s_ law
2) Charles’ law – Graph
Wikipedia, the free encyclopedia – en.wikipedia.org / wiki / Charles’s_ law
3) Gay – Lussac’s law - llustration
Hillchem3/medialib/media_portfolio/05html
4) Avogadro’s law – Illustration
http://library.thinkquest.org/12596/avagadro.html
5) Graham’s law – Graph
www.chem.edu/class/majors/tutorialnotefiles/graham.htm
6) Graham’s law – Illustration
(DOC) Graham’s law lab – Graham’s law
https://www.glastonburyus.org/.../firstlabs/.../Graham’s law