4th Lecture on States of Matter Chemistry Part II 11th Standard by Rizwana Mohammed

1. The Malegaon High School & Jr. College
Malegaon, (Nashik), 423203
4th Lecture on States of Matter
Chemistry Part II, 11th Science
By
Rizwana Mohammad

2. Relation between molar mass and density of a gas:
We know, n =
m
M
…1
m = mass of a gas, M = molar s of a gas.
We know V = k4n …2
Therefore substituting eqn 1 in 2
V = k4
m
M
Therefore M = k4
m
M
But
m
V
= d
Therefore M = k4d
Therefore M ∝ d
Therefore the density of a gas is directly proportional to its molar
volume.
Ideal gas: A gas that follows strictly all the gas laws is an ideal gas.

3. Derivation of ideal gas equation:
The three gas laws, Boyle’s law, Charles’ law and Avogadro’s law are
combined mathematically is called ideal gas equation.
1. At constant T and n, V ∝ Τ1
P (Boyle’s law)
2. At constant P and n, V ∝ T (Charles’ law)
3. At constant P and T, V ∝ n (Avogadro’s law)
Combining all 3 laws
V ∝
nT
P
Therefore V = R(
nT
P
)
Therefore PV = nRT
This equation is ideal gas equation.
R is gas constant
Units of R:
R = 8.314 JK-1 mol-1
R = 0.0821 dm3 atm K-1 mol-1
R = 1.987 ≅ 2 Cal K-1 mol-1

4. Expression for molar mass:
We know ideal gas equation
PV = nRT
n =
PV
RT
n =
m
M
Therefore
m
M
=
PV
RT
Therefore M =
mRT
PV
Combined gas law:
PV = nRT
Therefore
PV
T
= nR = constant
P1
V1
T1
=
P2
V2
T2
The ideal gas equation used in this form is called combined gas law.

5. Relation between density, molar mass and pressure:
We know PV = nRT
n
V
=
P
RT
n =
m
M
m
MV
=
P
RT
Therefore
d
M
=
P
RT
…1
m
V
= d = density of gas, from eqn 1
Therefore M =
dRT
P
From eqn 1, , Boyle's law can be stated in terms of density as: at constant
temperature, pressure of a given mass of gas is directly proportional to its density.
Dalton's law of partial pressure:
This law is applicable for those gases which do not react chemically on mixing. The
pressure exerted by an individual gas in a mixture of two or more gases is called
partial pressure.
Dalton's law of partial pressure is stated as, “The total pressure of a mixture of two
or more non reactive gases is the sum of the partial pressures of the individual gases
in the mixture.”
Mathematically,
PTotal = P1 + P2 + P3 + ………(at constant V and T)

6. Partial pressure and mole fraction:
We know PV = nRT
P =
nRT
V
(V and T are constant)
Therefore P ∝ n
The pressure of an individual gas in a mixture of gases is proportional to its
amount in that mixture.
The partial pressure of individual gases can be written in terms of ideal gas
equation as:
P1 = n1(
RT
V
), P2 = n2(
RT
V
), P3 = n3(
RT
V
), ………..and so on …1
Therefore
Ptotal = n1
RT
V
+ n2(
RT
V
) + n3(
RT
V
)………
=
RT
V
(n1 + n2+ n3 …….)
=
RT
V
nTotal
Mole fraction of any individual gas in the mixture is given by
X1 =
n1
n1
+n2
+n3
+⋯.
=
n1
nTotal
…2
From eqn 1 and 2
n1 =
P1
( ൗRT
V)
…3 and nTotal =
PTotal
( ൗRT
V)
…4

7. Combining eqn 3 and 4
n1
nTotal
= X1 =
ൗ
P1
( ൗRT
V)
ൗ
PTotal
( ൗRT
V)
=
P1
PTotal
…5
Therefore it follows that
P1 = X1 Ptotal …6
Similarly,
P2 = X2 Ptotal, P3 = X3 Ptotal, P4 = X4 Ptotal, …..and so on
“Thus partial pressure of a gas is obtained by multiplying the total pressure
of mixture by mole fraction of that gas.”