Question

A gas such as carbon monoxide would be most likely to obey the ideal gas law at :
(A) High temperatures and high pressure
(B) Low temperature and low pressure
(C) High temperatures and low pressure
(D) Low temperatures and high pressure

Answer 1

Hint:In order to solve these types of questions we need to study the conditions very carefully so the condition at which the volume is very large and the terms \[\dfrac{a}{{{V^2}}}\] and can be neglected.The van der waals equation reduces to ideal gas equation $PV = nRT$

Complete step-by-step answer:For solving this question we need to know that the gas such as carbon monoxide would most likely to obey the ideal gas under some conditions which we will be studying now:So for ideal gas:
$PV = nRT$
Where:
P is the pressure
V is the volume
n are the number of moles
R is the gas constant
T is the temperature
So we should know that the real gas can behave as an ideal gas if the volume of the molecule is negligible. This will happen when the number of molecules per unit volume is very small.
From ideal gas equation,
$PV = nRT$
Or by exchanging these terms we can get:
$\dfrac{V}{n} = \dfrac{{RT}}{P}$
So the term $\dfrac{V}{n}$ is large if $T$ is very large and $P$ is very small Under these conditions, the volume $V$ is very large and the terms $\dfrac{a}{{{V^2}}}$ and can be neglected.So the correct option is high temperature and low pressure.

Therefore (C) option is correct.

Note:It should be known that the ideal gas is non-existing so we only can transform any gas close to the ideal gas not we can make it fully ideal.So for above question the van der waals equation will be $PV = nRT$