Kinetic Theory of Gases
A gas consists of small particles that
• are very far apart.
• move rapidly in straight lines.
• collide with each other and with walls of container
elastically and exert pressure
• are of same size and mass but differ from
molecule of another gas
• have kinetic energies that increase with an
increase in temperature.
• have low average distance at high pressure and
• have essentially no attractive (or repulsive) forces.
• have very small volumes compared to the volume
of the container they occupy.
Properties That Describe a Gas
Gases are described in terms of four properties:
Pressure (P),Volume(V),Temperature(T), and Amount(n).
• Deduced by R J Clausius –To calculate Pressure of an Ideal
• P = pressure,V = volume, m = mass of one molecule
of gas, N = number of particles of the gas and 𝑐2 =
Avg. root mean square velocity of gas molecules
• If n1 molecules have c1 velocity , n2 molecules have
c2 velocity then
𝑛1+𝑛2+ 𝑛3+ ….
Motion of Particles of a Gas
• Due to their motion, gas molecules have certain
• The increase and decrease in temperature will
increase or decrease their motion.
• In gases, molecular motion is of three types:
• Translational motion
• Rotational motion
• Vibrational motion
• The motion imparted to gas molecules
due to their motion in all possible
direction is called translational
• In this case, the entire molecules
move from place to place.
• Monoatomic gases like He will show
only translational motion.
• The motion imparted to gas molecules as a result
of net angular momentum about the their center
of gravity is called rotational motion and the
energy as Kinetic rotational energy.
• In this case molecule spins like a propeller.
• The motion imparted to gas molecules due to
oscillations is called vibrational motions and the
energy as Kinetic vibrational energy.
• In this case the molecules vibrates back and forth
about the same fixed location.
Symmetric stretching Asymmetric stretching
Absolute Temperature Scale
• The Charles's law states that: “the volume of a
given mass of a gas increases or decreases by 1/273
by 1/273 times of its original volume and reduces to 0
reduces to 0 at -273.15oC”.
• At this temperature a gas doesn’t remain in its
gaseous state but changes into liquid.
• Lord Kelvin presented a new scale – Absolute
temperature Scale or Kelvin temperatures
0°C = 273.16 K
K = oC + 273
Relationship between Temperature
and Average Kinetic Energy of a
Particle in Gas
• The temperature of a gas depends upon K.E .
• The avg. K.E of a gaseous molecules is
redistributed with rise and fall of temperature.
• A/c to the Kinetic equation of gases:
• 𝑃𝑉 =
• And 𝐾. 𝐸 =
• Multiply and divide Kinetic equation by 2:
• 𝑃𝑉 =
• Now consider one mole of a gas. It will possess
Avogadro’s number (NA) of molecule.
• Then N = NA
• Therefore PV =
• According to General Gas Equation:
• PV = nRT
• For one mole of a gas n=1 then PV = RT…….(5)
• Comparing equation 4 and 5 we get,
𝑁𝐴(K.E) = RT …..(6)
• 2NA (K.E) = 3RT
• 𝐾. 𝐸 =
• 𝐾. 𝐸 =
• K.E = KT where
= K, a constant quantity.
• Or K.E αT
• the kelvin temperature of a gas is actually the
measure of average translational K.E of its