Discuss about the properties of gases

1. DISCUSS ABOUT THE PROPERTIES OF GASES
Presented by
U U Shwe Thein
Demonstrator
Department of Chemistry
Mandalay University of Distance Education

2. CHAPTER (2)
THE PROPERTIES OF GASES
Gas-The individual molecules have
little attraction for one another and
are free to move about.
Liquid—The individual molecules are
attracted to one another but can slide
over each other.
Solid—The individual molecules are
strongly attracted to one another and
cannot move around.

3. General Characteristics of Gas
1. Expansibility - Gases have limitless expansibility. They expand to
fill the entire vessel they placed in.
2. Compressibility - Gases are easily compressed by application of
pressure to a movable piston fitted in the container.
3. Diffusibility - Gases can diffuse rapidly through each other to form
a homogeneous mixture.
4. Pressure - Gases exert pressure on the walls of the container in
all directions.
5. Effect of heat - When a gas, confined in a vessel is heated, its
pressure increases. Upon heating in a vessel fitted
with a piston, volume of the gas increases.

4. Expansibility
Compressibility
Diffusibility
Effect of Heat
Pressure

5. 5
Only four parameters define the state of a gas
1. The volume of the gas, V (in Liters)
2. The pressure of the gas, P (in Atmospheres)
3. The temperature of the gas, T (in Kelvins)
4. The number of moles of the gas, n (in Moles)
Parameters of a Gas

6. The Gas Laws
The ideal gas equation
Boyle's Law; V 
1
P
(T, n constant)
Charles' Law; V  T (P, n constant)
Avogadro's Law; V  n (P, T constant)
 V 
nT
P
V =
RnT
P
PV = nRT
Ideal Gas Law
(The Universal Gas Law)
The volume of a given amount of gas is directly proportional to the
number of moles of gas, directly proportional to the temperature and inversely
proportional to the pressure.
V 
nT
P
Where, P = Pressure of the gas
T = Temperature of the gas
V = Volume of the gas
n = number of mole of the
gas

7. Calculation for the numerical value of Gas constant R
PV = nRT
R =
PV
nT
For one mole of gas at STP P = 1 atm, V = 22.4 dm3, T = 273 K
R =
1 atm x 22.4 dm3
1 mol x 273K
R = 0.0821 atm dm3 mol-1
K-1
If the pressure is written as force per unit area and volume as area times length,
R =
Force x area
−1
x length x area
n x T
R =
Force x length
n x T
R =
Work
nT

8. Value of 'R' in Different Units
0.0821 dm3 atm K-1
mol-1
8.314 x 107 erg K-1
mol-1
82.1 cm3 atm K-1
mol-1
8.314 Joule K-1
mol-1
62.3 dm3 mm Hg K-1
mol-1
1.987 cal K-1
mol-1

9. 9
Dalton's Law of Partial Pressures
The total pressure of a mixture of gases is equal to the sum of the
partial pressures of all the gases present.
Ptotal = P1 + P2 + P3 +----- (V and T are constant)
Where,
P1, P2, P3 = partial pressures of three gases 1, 2, 3,….
PV = n R T
P1 = n1 (
RT
V
), P2 = n2(
RT
V
) , P3 = n3(
RT
V
)
 Pt = (n1 + n2 + n3) (
RT
V
)
Pt = (ntotal) (
RT
V
)

10. 10

11. Graham's Law of Diffusion
Under the same conditions of temperature and pressure, the rates
of diffusion of different gases are inversely proportional to the square
roots of their molecular masses.
r1
r2
=
𝑀2
𝑀1
(P, T constant)

12. 12
 Diffusion
Diffusion is mixing of gas molecules by random motion under conditions where
molecular collisions occur.
 Effusion
Effusion is escape of a gas through the pinhole without molecular collisions.
Dalton's Law when applied to effusion of a gas is called the Dalton's Law of
effusion expressed mathematically as
Effusion rate of gas1
Effusion rate of gas2
=
𝑀2
𝑀1
(P, T constant)

13. Assumptions of the Kinetic Theory of Gases
1. A gas consists of extremely small discrete particles called molecules.
2. Gas molecules are in constant random motion with high velocities.
3. The gas molecules can move freely, independent of each other.
4. All collisions are perfectly elastic. Hence, there is no loss of the kinetic
energy of molecule during a collision.
5. The pressure of a gas is caused by the hits recorded by molecules on the
walls of the container.
6. The average kinetic energy of the gas molecules is directly proportional
to absolute temperature.
Based on the fundamental concept that a gas is made of a large
number in perpetual motion.

14. Derivation of Kinetic gas equation
Let consider a certain mass of gas enclosed in a cubic box.
1) The velocity of single molecule along X, Y, Z axes.
2) Time between two collisions of Face A =
2𝑙
𝑣𝑥
s
3) The change of momentum for face A = mvx-(-mvx) = 2mvx
4) Change of momentum per second for Face A =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚
𝑡𝑖𝑚𝑒
= 2mvx x
𝑣𝑥
2𝑙
=
𝑚𝑣𝑥
2
𝑙
5) The change of momentum on opposite faces A and B along X, Y and Z axes
=
2𝑚𝑣𝑥
2
𝑙
+
2𝑚𝑣𝑦
2
𝑙
+
2𝑚𝑣𝑧
2
𝑙
=
2𝑚
𝑙
(𝑣𝑥
2 + 𝑣𝑦2 + 𝑣𝑧
2) =
2𝑚𝑣2
𝑙
6) For nth molecules with different velocities (v1, v2, v3, …),
the overall change of momentum per second on all faces of the box
=
2𝑚
𝑙
x (
𝑣1
2
+ 𝑣2
2
+ 𝑣3
2
𝑛
) =
2𝑚𝑛𝑢2
𝑙
(u = root mean square velocity)
7) Force = total change in momentum per second
Force =
2𝑚𝑛𝑢2
𝑙
, A= 6l2
Pressure =
𝐹𝑜𝑟𝑐𝑒
𝑎𝑟𝑒𝑎
, P=
2𝑚𝑛𝑢2
𝑙
×
1
6l2 =
𝑚𝑛𝑢2
3𝑙3 =
𝑚𝑛𝑢2
3𝑉
Therefore, PV =
𝟏
𝟑
mnu2
2 2 2 2
  
x y z
v v v v

15. Kinetic gas equation in terms of Kinetic energy
If ‘n’ be the number of molecule in a given mass of gas, where ‘e’ is the average kinetic energy of a single
molecule. According to kinetic gas equation,
PV =
1
3
mnu2 =
2
3
n x
1
2
𝑚𝑢2 =
2
3
𝑁 x e ( ·.· e =
1
2
𝑚𝑢2 )
Where ‘e’ is the average kinetic energy of a single molecule.
PV =
2
3
𝑛e
PV =
2
3
𝐸 (·.· ne = E) … (1)
Where ‘E’ is the total kinetic energy of all the ‘n’ molecules. The equation (1) may be called kinetic gas
equation in terms of kinetic energy.
Ideal gas equation is
PV = nRT (n = number of moles) … (2)
From equations (1) and (2)
2
3
𝐸 = nRT … (3)
The kinetic energy of one mole of a gas,
E =
3𝑅𝑇
2
… (4)
Since the number of gas molecules in one mole of a gas in N0 (Avogadro number), the average kinetic energy of
a single molecule is
e =
𝐸
𝑁0
the average kinetic energy of a single molecule, e =
3𝑅𝑇
2𝑁0

16. Deduction of Gas laws from Kinetic Gas Equation
Boyle’s Law
According to the kinetic theory, there is
a direct proportionality between absolute
temperature and average kinetic energy of the
molecules (
1
2
𝑚𝑢2 ) i.e.,
1
2
𝑚𝑢2 ∝T (or)
1
2
𝑚𝑢2 = kT (or)
3
2
x
1
3
𝑚𝑢2 = kT (or)
1
3
𝑚𝑢2 =
3
2
kT
Substitute the above value in the kinetic gas
equation PV ,
1
3
𝑚𝑢2 , we have
PV =
2
3
kT
The product PV, therefore, will have a constant
value at a constant temperature.
Charles’ Law
PV =
2
3
kT (or) V =
2
3
x
𝑘
𝑝
𝑇
At constant pressure ,V = k’T
where (k’ =
2
3
x
𝑘
𝑝
)
(or) V ∝ T
This is, at constant temperature, volume of a
gas is proportional to Kelvin temperature.

17. Avogadro's Law
If equal volume of two gases be
considered at the same pressure,
PV =
1
3
𝑚1𝑛1𝑢1
2
…. Kinetic equation as applied
to 1st gas
PV =
1
3
𝑚2𝑛2𝑢2
2
…. Kinetic equation as applied
to 2nd gas
⸫
1
3
𝑚1𝑛1𝑢1
2
=
1
3
𝑚2𝑛2𝑢2
2
…… (1)
When the temperature (T) of both the gases in the
same, their mean kinetic per molecules will also
be the same
i.e.
1
3
𝑚1𝑢1
2
=
1
3
𝑚2𝑢2
2
..…. (2)
Dividing (1) and (2), we have 𝑛1 = 𝑛2 or
Under the same condition of temperature and
pressure, equal volume of two gases contains the
same number of molecules.
Graham's Law of Diffusion
If m1 and m2 are the massed and u1 and
u2 are the velocities of gases 1 and 2, the at the
same pressure and volume
1
3
𝑚1𝑛1𝑢1
2
=
1
3
𝑚2𝑛2𝑢2
2
𝑚1𝑛1𝑢1
2
= 𝑚2𝑛2𝑢2
2
(
𝑢1
𝑢2
)2 =
𝑀1
𝑀2
(M1= m1n1, M2= m2n2)
𝑢1
𝑢2
=
𝑀2
𝑀1
The rate of diffusion (r) is proportional to the
velocity of molecules (u), therefore,
Rate of diffusion of gas 1
Rate of diffusion of gas 2
=
𝑟1
𝑟2
=
𝑀2
𝑀1

18. Different kinds of velocities
Average Velocity
Let’s there be ‘n’ molecules of a gas
having individual velocities
𝑣1, 𝑣2, 𝑣3, … , 𝑣𝑛. The ordinary average
velocity is the arithmetic of the various
velocities of the molecules.
𝑣 =
𝑣1+ 𝑣2+𝑣3+⋯+𝑣𝑛
𝑛
From Maxwell equation it has been
established that the average velocity 𝑣 is
given by the expression
𝑣 =
8𝑅𝑇
𝜋𝑀
Substituting the values R, T,𝜋 and M in
this expression, the average value can be
calculated.
Root Mean Square Velocity
If 𝑣1 + 𝑣2 + 𝑣3 … . +𝑣𝑛 are the velocity of n molecules
in a gas u2, the mean of square of all velocities is
u2 =
𝑣1
2+𝑣2
2+𝑣3
2+⋯+𝑣𝑛
2
𝑛
Taking the root
u =
𝑣1
2+𝑣2
2+𝑣3
2+⋯+𝑣𝑛
2
𝑛
is the Root Mean Velocity or
RMS velocity. It is denoted by u. The value of the
RMS of velocity u, at a given temperature can be
calculated from the kinetic gas equation.
u =
3𝑅𝑇
𝑀

19. Most Probable Velocity
As already stated, the most probable velocity is possessed by the largest number of molecules in
a gas. According to the calculations made by Maxwell, the most probably velocity, 𝑣𝑚𝑝 , is given by
the expression.
𝑣𝑚𝑝 =
2𝑅𝑇
𝑀
Relation between Average Velocity, RMS Velocity and Most Probable Velocity
∴
𝑣
𝒖
=
8𝑅𝑇
𝜋𝑀
×
𝑀
3𝑅𝑇
=
8
3𝜋
= 0.9213
𝑣 = u × 0.9213
That is, Average velocity = 0.9213 × RMS velocity
∴
𝑣𝑚𝑝
𝒖
=
2𝑅𝑇
𝑀
×
𝑀
3𝑅𝑇
=
2
3
= 0.8165
𝑣𝑚𝑝= u × 0.8165
That is, Most Probable Velocity = 0.8165 × RMS velocity

20. 20