Kinetic Theory Concept Page - 1

Definition

Ideal gas equation

The ideal gas equation is
PV=nRT$PV=nRT$
Assumptions:
(1) the gas consists of a large number of molecules, which are in random motion and obey Newton's laws of motion; (2) the volume of the molecules is negligibly small compared to the volume occupied by the gas; and (3) no forces act on the molecules except during elastic collisions of negligible duration.

Definition

Absolute Zero temperature

The Kelvin scale is an absolute, thermodynamic temperature scale using its null point as absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics.

Definition

Charle's law

When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be directly related.
V∝T$V\propto T$

Definition

Limitation of Charles' Law

• The ideal gas laws make some assumptions that are not necessarily true always. So from here we conclude that they have certain limitations also.

• The ideal gas equation is usually derived from the kinetic theory of gases, which presumes that molecules occupy negligible volume, do not attract each other and undergo elastic collisions (no loss of kinetic energy).

• But in reality gases made up of polar molecules (for example, water) deviate more from this ideality and hence Charles's Law is less accurate in describing the behavior of these gases.

Limitations : 

• This law implies theoretically that as a temperature reaches absolute zero temperature, the gas should shrink down to zero volume. This is not physically correct, since in fact all gases turn into liquids at a low enough temperature, and Charles's law is not applicable at low temperatures for this reason.
• We assume that gas particles are not attracted to each other. But in reality gas particles are attracted to each other. As kinetic energy decreases as a gas is cooled, the particles will eventually move slowly enough that there attractive forces cause them to condense. The gas law no longer applies here because the substance is no longer remains a gas.

Law

Verification of Boyle's Law

Experiment: By using a simple U-tube apparatus, Boyles Law can be verified as shown in the figure. The U tube is a glass tube closed on one end (left side) and left open to the atmosphere on the other side. It is filled with mercury in such a way that some air or any other gas used for the experiment is trapped in the closed end of the U tube. The height of the mercury column AB (height h in the the figure) along with the atmospheric pressure PA gives the pressure of the trapped gas in mm of mercury.  

Law

Limitation of ideal gas equation

Following are the assumptions of ideal gas equation-
1. A gas consists of a large number of particles those are rigid and perfectly elastic.
2. All particles (molecules) of the same gas are identical in shape, mass and size.
3. Molecules are always in a state of random motion.
4. Due to random motion molecules collides with each other and with wall elastically and between two successive collisions travels in a straight line with constant velocity.
5. The collision takes place in very small time compared with free path between two successive collisions.

Diagram

Charles' Law Graph

Charles Law states that Pressure remaining constant, the volume of a given mass of gas is directly proportional to the absolute temperature. This is referred to as the law of volumes.V∝T$V\propto T$;  [pressure remaining constant]
It can also be stated as VT=${\displaystyle \frac{V}{T}}=$ a constant.
The graph of the volume plotted against temperature would be a straight line (shown as the solid line in the figure).

Diagram

Boyle's Law graph

Boyles Law states that Temperature remaining constant, the pressure of a given mass of gas is inversely proportional to its volume. In mathematical language
we express the same as follows:P∝1V$P\propto {\displaystyle \frac{1}{V}}$; [Temperature remaining constant]
It can also be stated as, PV=$PV=$ a constant.
A sample graph of the pressure and the volume of a given mass of gas is shown in the figure.

Example

Solve problem on ideal gas equation

Example: One mole of ideal gas is filled in a closed container of volume 1 m3${}^3$ at a temperature 300K then find the pressure exerted by it on the wall of the container.

Solution:
As,  pV = nRT
p×1=1×25/3×300$p\times 1=1\times 25/3\times 300$
p=2500$p=2500$ pa

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