Name: Properties and Examples of Gases
Uploaded: 2019-07-19
Duration: 3 min 58 s
Description: The invisible and yet crucial state of matter is the gaseous state. It plays a vital role in sustaining life on Earth. Learn about its unique properties in this

Question

What is an ideal (or perfect) gas? Under what conditions of pressure and temperature can gas be assumed as an ideal gas? Determine the gas constant for one gram-molecule of a gas.

Accepted Answer

In practice, it is observed that gases do not obey strictly Boyle’s law, Charles' law and the law of pressure under all conditions of temperature and pressure. They obey these laws only ‘approximately’ and the deviations from the laws are different for different gases.

The experiments performed on different gases show that as the pressure is decreased, different gases become more and more similar in behaviour and also more and more obedient to the gas laws. So, we can imagine a gas whose properties are similar to the properties of a real gas at infinitely low pressure. Such an imaginary gas is called ‘perfect gas’ or ‘ideal gas’.

According to the definition, the following properties are imagined in a perfect gas:

$1 .$ It strictly obeys Boyle’s law, Charles’ law and the law of pressure under all conditions of temperature and pressure.

$2 .$ Its pressure coefficient and volume coefficient are exactly equal to each other.

$3 .$ Its molecules are infinitesimally small.

$4 .$ There is no force of attraction between its molecules.

There is a relation between the pressure, volume and temperature of a given mass of a gas. This relation is called ‘perfect gas equation’.

Suppose, initially the pressure, volume and absolute temperature of a given mass of a gas are $P_{1}$ , $V_{1}$ and $T_{1}$ respectively and they finally change to $P_{2}$ , $V_{2}$ and $T_{2}$ respectively. We can divide this change into two parts:

$(1)$ Suppose the temperature of the gas is kept constant at $T_{1}$ and the pressure is changed from $P_{1}$ to $P_{2}$ . If in this process the volume changes from $V_{1}$ to $V^{'}$ then by Boyle’s law, we have $P_{2} V^{'} = P_{1} V_{1}$ or

$V^{'} = \frac{P_{1} V_{1}}{P_{2}} . . . . . (i)$

$(2)$ Now, suppose the pressure of the gas is kept constant at $P_{2}$ and its absolute temperature is changed from $T_{1}$ to $T_{2}$ . If in this process the volume of the gas changes from $V^{'}$ to $V_{2}$ , then by Charles’ law, we have,

$\frac{V^{'}}{T_{1}} = \frac{V_{2}}{T_{2}}$ or

$V^{'} = \frac{T_{1} V_{2}}{T_{2}} . . . . . (i i)$

Comparing the two equations,

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$ or

$\frac{P V}{T} = r$ (constant) or

$P V = r T$

This is the perfect gas equation. The value of the gas-constant $r$ depends upon the nature and the mass of the gas. Its value is different for different masses of the same gas or for different gases of the same mass. It is also called ‘specific gas constant’.

However, if we take $1$ gram-molecule (1 mole) of a gas, the value of gas-constant will be the same for all gases. Then it is called ‘universal gas constant’ and is represented by $R$ . Hence, for $1$ mole of gas, the gas equation takes the following form:

$P V = R T$ .

What is an ideal (or perfect) gas? Under what conditions of pressure and temperature can gas be assumed as an ideal gas? Determine the gas constant for one gram-molecule of a gas.

Important Questions on Kinetic Theory of Gases

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