Question

Which of the given sets of temperature and pressure will cause gas to exhibit the greatest deviation from ideal gas behaviour?
 (A) ${100^ \circ }C$ and $4atm$
(B) ${100^ \circ }C$ and $2atm$
(C) $ - {100^ \circ }C$ and $4atm$
(D) ${0^ \circ }C$ and $2atm$

Answer 1

Hint: In order to solve this question, we should first understand the Van der Waals equation. In the year $1873$ A.D. Van der Waals made some changes with the ideal law of gas equation in order to explain the behaviour of the real gases in which he considered the volume of the gas molecules and also the forces of attraction between the gas molecules.

Complete Step by Step Solution:
The ideal gas behaviour is a theory which expects the gases to act in a particular way and assume that the gases have very negligible or no space at all and they also have no intermolecular force of attraction among them.

Van der Waals did some changes with the ideal law of gas equation and the outcome of it is as follows:
$\left( {P + \dfrac{a}{{{v^2}}}} \right)\left( {v - b} \right) = RT$
If there are $n$ moles of the gas, then the equation will be as follows:
$\left( {P + \dfrac{{a{n^2}}}{{{v^2}}}} \right)\left( {v - nb} \right) = nRT$

Here, the constants $a$ and $b$ represent the scale of intermolecular attraction and the excluded volume respectively. If the value of $a$ is more, then the molecular attraction is more and the gas can be compressed easily. The value of the constant $b$ is used to represent the excluded volume that is occupied by gas particles.

Gases deviate from ideal gas behaviour to real gas according to the above equation at low temperature and high pressure. Among the given sets of temperature and pressure, $ - {100^ \circ }C$ and $4atm$ will cause gas to exhibit the greatest deviation from ideal gas behaviour
Therefore, the correct answer is option C.

Note: It is important to note that if the value of $a$ is more, then the molecular attraction is more and the gas can be compressed easily. The value of the constant $b$ is used to represent the excluded volume that is occupied by gas particles.