Gaseous State

Question 1

Basic assumptions of the kinetic theory as applied to an ideal gas

Answer 1

• The particles (atoms or molecules) of an ideal gas have negligible volume compared to the volume of the container (total volume occupied by the gas)
  
  • There are negligible intermolecular forces between the particles of an ideal gas
  • The collisions between particles of an ideal gas are perfectly elastic i.e. There is no loss of kinetic energy during collision
  • The particles of an ideal gas behave as rigid spheres

Question 2

Ideal gas equation

Answer 2

pV=nRT
p: pressure, pascal, Pa
V: volume, cubic metres, m^3
n: amount of gas, mol
R: molar gas constant, 8.31 J K^-1 mol^-1
T: temperature, Kelvin, K

Question 3

gas laws

Answer 3

Boyle’s law: V 1/p
(constant n, T)
* Charles’ law: V  T (constant n, p)
* Avogadro’s law: V  n (constant p, T)

Question 4

Avogadro’s law

Answer 4

Avogadro’s law states that equal volumes of all gases under the same conditions of temperature
and pressure contain equal number of molecules.
* It follows from Avogadro’s law that the volume occupied by one mole of molecules must be the
same for all gases.
* The volume occupied by one mole of a gas is termed the molar volume of the gas.
* Molar volume of an ideal gas at s.t.p. (273 K and 1 bar) = 22.7 dm3 mol−1
* Molar volume of an ideal gas at r.t.p. (293 K and 1 atm) = 24.0 dm3 mol−1

Question 5

Partial pressure of gas

Answer 5

• In a mixture of gases that do not react with each other, each gas behaved as if it were the only gas present. For such a mixture, each gas exerts its own pressure (independent of the other gases present) known as its partial pressure
  
  • impt: The partial pressure of a gas in a mixture of non-reacting gases is the pressure the gas would exert if it alone were to occupy the container under the same physical conditions

Question 6

Dalton’s law of partial pressure

Answer 6

• States that in a mixture of non-reacting gases, the total pressure of the mixture is equal to the sum of partial pressures of all the individual gases in the mixture

Question 7

Mole fraction

Answer 7

• The mole fraction of a component A, Xa, in a mixture is the ratio of the number of moles of A to the total number of moles of all components present in the mixture

Question 8

Partial pressure

Answer 8

• The partial pressure of a gas A in a mixture of non-reacting gases is the product of the mole fraction of A in the mixture and the total pressure of the mixture

Question 9

Ideal gas VS real gas

Answer 9

The molecules have negligible volume so
that gas particles can move anywhere in the
container. VS
The molecules have a certain size and
volume. Hence the gas particles cannot just
move anywhere in the container because
they cannot move into a volume occupied by
the other gas molecules.

There are no forces of attraction between
the molecules. VS
There are forces of attraction between the
molecules. The forces of attraction of some
gases are greater than others, e.g. there are
greater attractive forces between NH3
molecules (due to hydrogen bonding) than
between H2 molecules (due to instantaneous
dipole–induced dipole interaction) at the
same temperature and pressure.

An ideal gas obeys the gas laws and the
ideal gas equation perfectly under all
conditions. VS
A real gas approaches ideality (obeys gas
laws) under the conditions of:
(i) low pressure
(ii) high temperature

Question 10

Real gas and non-ideal behaviour

Answer 10

In practice, a real gas behaves most like an ideal gas and obeys the ideal gas equation closely, under
the following conditions.
Low Pressure:
- The gas molecules are far apart and can be
considered to have negligible volume
compared to the volume of the container.
- The intermolecular attractive forces
between the widely spaced gas molecules
are negligible.
High temperature:
- At high temperature, the gas molecules
possess sufficiently high kinetic energy to
overcome the intermolecular attractive
forces. Hence the intermolecular attractive
forces can be considered negligible.

In practice, a real gas behaves least like an ideal gas under the following conditions:
High Pressure:
- The gas molecules are closer together and
the gas occupies a smaller volume. As such
the gas molecules have significant volume
compared to the volume of the container
- In addition, the intermolecular attractive
forces between the closely spaced gas
molecules are significant.
Low Temperature:
- At low temperature, the gas molecules
possess less kinetic energy and hence
the intermolecular attractive forces are
significant.

Question 11

Type and magnitude of intermolecular forces

Answer 11

Gases with stronger intermolecular forces of attraction tend to deviate more from ideal behaviour.
In general, strength of hydrogen bonding > strength of permanent dipole-permanent dipole > strength
of instantaneous dipole-induced dipole interactions.

NH3 has hydrogen bonding between its molecules compared to the weaker instantaneous dipole-
induced dipole interactions between H2 and N2 molecules. Therefore, NH3 molecules deviate most from

the ideal gas condition.
Note: Between steam, H2O, and NH3 gas, steam has more extensive hydrogen bonding than NH3 gas
therefore steam deviates more from ideal gas condition.

Question 12

Size of electron cloud

Answer 12

Gases with larger electron cloud tend to deviate more from ideal behaviour.
Both N2 and H2 molecules are non-polar. N2 molecules have a larger electron cloud size than H2

molecules. Therefore, N2 has a more polarisable electron cloud and stronger instantaneous dipole-
induced dipole interactions between molecules. This leads to N2 molecules having more significant

intermolecular forces of attraction and volume than H2 molecules. N2 molecules take up more
significant volume as compared to the volume of the container.