Assumptions in an ideal gas | Elaboration |
Molecules have 0 volume. | In the equation, V is the volume available for molecules to move around. The gas molecules don't occupy any space at all. |
Intermolecular attraction is 0. | P is the pressure created by free molecules colliding with the walls of the container. There're no intermolecular forces to affect the speed of molecules and hence the impact of molecules with the walls of the container. |
In
an ideal gas, the volume of gas molecules is negligible and the
intermolecular attraction is negligible...
Here's a question from a past Physics paper.
(Phy Nov
2009) An ideal gas occupies a container of volume 4.5 x 103
cm3
at a pressure of 2.5 x 105
Pa and a temperature of 290 K.
(a) Show that the number of atoms of gas in the container is 2.8 x 1023. (b) Atoms of a real gas each have a diameter of 1.2 x 10-10 m. (i) Estimate the volume occupied by 2.8 x 1023 atoms of this gas. (ii) Suggest whether the real gas does approximate to an ideal gas. |
(a) PV = nRT
Number of moles of gas, n
= PV/RT
= (2.5 x 105 Pa)(4.5 x 103 cm3)/(8.31 J K–1 mol–1)(290 K)
= (2.5 x 105 Pa)(4.5 x 10-3 m3)/(8.31 J K–1 mol–1)(290 K)
Number of atoms
= number of moles, n x Avogadro's constant
= (2.5 x 105 Pa)(4.5 x 10-3 m3)/(8.31 J K–1 mol–1)(290 K) x 6.02 × 1023 mol–1
= 0.467 mol x 6.02 × 1023 mol–1
= 2.8 x 1023
(b) (i) Volume of atom
= 4Ï€r3/3
= 4Ï€(1.2 x 10-10 m)3/3
Volume of 2.8 x 1023 atoms
= 2.8 x 1023 x 4Ï€(1.2 x 10-10 m)3/3
= 2.0 x 10-6 m3
(ii) Volume of atoms / volume of gas
= 2.0 x 10-6 m3 / 4.5 x 10-3 m3
= 0.00045
The volume of the atoms is a very small fraction of the volume of the gas. The real gas does approximates the ideal gas.
Gases
deviate from ideal behavior at low pressures and low temperatures...
For a real gas, PV/nRT = 1 at very low pressures such as 1 atm. For many real gases, PV/nRT decreases rapidly to a minimum below 1 as pressure is increased. Thereafter, PV/nRT increases from below 1 to above 1.
Pressure | Value of PV/nRT | Explanation |
At very low pressure of 1 atm | Close to 1 | Molecules
are far apart enough such that:
|
When pressure increases from 1 atm | Decreases rapidly below 1 | Molecules
are closer such that they are able to exert attractive
intermolecular van der Waals forces.
|
As pressure increases further | Increases from below 1 to above 1 | Molecules
are so close that their electron clouds begin to intrude into one
another's territory. Molecules begin to repel one another.
|
At high temperatures, molecules collide with the walls of container at high speeds with little effect by intermolecular van der Waals forces. At low temperatures close to the temperature at which the gas changes to liquid/solid, intermolecular van der Waals forces are significant. For each temperature, the change in PV/nRT with pressure follows the above description.
At
high pressures and low temperatures, the volume of molecules compared
to the gas becomes significant and the intermolecular van der Waals
forces become significant enough to affect the pressure...
To account for the deviation from ideal gas behavior, van der Waals made the following corrections to P and V in PV = nRT.
- The
ideal gas volume available for molecules to move through is changed
to V – nb where n = number of moles and b = constant that's
related to the volume of molecules.
- Molecules
may collide and stick to one another (inelastic collision) due to
intermolecular forces. The probability of two molecules being at the
same place is proportional to n/V x n/V = n2/V2.
The reduction in pressure due to inelastic collisions is
proportional to n2/V2.
The ideal gas pressure is then changed to (P + an2/V2)
where a = constant.
Let's again write down the ideal gas equation PV = nRT ==> P = nRT/V.
If we put in the correction due to the volume of molecules, we get:
P
= nRT(V – nb)
Next, we account for the reduction in pressure due to the inelastic collisions and we get:
P
= nRT/(V – nb) – an2/V2
There's no need to memorize this intimidating equation. You just need to understand why gases deviate from the ideal behavior which is already tough enough.
(Chem Jun 2004) (i) When an evacuated glass bulb of volume 63.8 cm3 is filled with a gas at 24 ºC and 99.5 kPa, the mass increases by 0.103 g. Deduce whether the gas is ammonia, nitrogen or argon. (ii) Explain why ammonia is most likely of these three gases to deviate from ideal gas behavior. |
(i) PV = nRT
Number of moles of the gas, n
= PV/RT
= (99.5 x kPa)(63.8 cm3)/(8.31 J K–1 mol–1)(24 + 273.15)
= (99.5 x 103 Pa)(63.8 x 10-6 m3)/(8.31 J K–1 mol–1)(24 + 273.15 K)
= 0.002571 mol
Ammonia: mass increase = 0.002571 mol x (14.01 + 3.01) g/mol = 0.0438 g
Nitrogen: mass increase = 0.002571 mol x (14.01 + 14.01) g/mol = 0.0720 g
Argon: mass increase = 0.002571 mol x 39.95 g/mol = 1.03 g
The gas is argon.
(ii) The ammonia molecule consists of an electronegative nitrogen atom with a lone pair of electrons bonded to three hydrogen atoms. Ammonia therefore consists of polar molecules. Nitrogen consists of non-polar molecules and argon consists of atoms. The van der Waals forces between the polar ammonia molecules is the greatest. This van der Waals forces between ammonia molecules would greatly affect the speeds at which the molecules impact the walls of the container. Therefore, ammonia is mostly likely to deviate from ideal gas behavior.
Try these questions.
- (Chem
2011) At room temperature and pressure, chlorine does not behave as
an ideal gas. At which temperature and pressure would the behavior
of chlorine become more ideal?
Pressure / kPa | Temperature / K | |
A | 50 | 200 |
B | 50 | 400 |
C | 200 | 200 |
D | 200 | 400 |
- (Chem
Nov 2006) For an ideal gas, the plot of pV against p is a straight
line. For a real gas, such a plot shows a deviation from ideal
behavior. The plots of pV against three real gases ammonia, hydrogen
and nitrogen are shown below.
What are the identities of X-Z?
- (Chem
2004/2013) (a) State two assumptions of ideal gas behavior. (b) (i)
State the conditions of temperature and pressure under which real
gases behave least like an ideal gas. (ii) Explain why real gases do
not behave ideally under these conditions. (c) Explain the meanings
of the terms p, V and T in the ideal gas equation. Give units for
each to correspond with the value of R in the Data Booklet.
- (Chem
Jun 2011) Place ammonia, neon and nitrogen in decreasing order of
ideal behavior. Explain your answer.
- (Chem
Nov 2009) Suggest one reason why CO2
does not behave as an ideal gas.
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