Question

The value of van der Waal’s constant ‘a’ for the gases \[{{\text{O}}_{\text{2}}}\text{,}{{\text{N}}_{\text{2}}}\text{,N}{{\text{H}}_{\text{3}}}\] and \[\text{C}{{\text{H}}_{\text{4 }\!\!~\!\!\text{ }}}\] are \[\text{1}\text{.360, 1}\text{.390, 4}\text{.170 and 2}\text{.253 }\!\!~\!\!\text{ }{{\text{L}}^{\text{2}}}\text{ }\!\!~\!\!\text{ atm }\!\!~\!\!\text{ mo}{{\text{l}}^{\text{-2}}}\text{ }\!\!~\!\!\text{ }\]respectively. The gas which can most easily be liquefied is
A \[{{\text{O}}_{\text{2}}}\]
B \[{{\text{N}}_{\text{2}}}\]
C \[\text{N}{{\text{H}}_{\text{3}}}\]
D \[\text{C}{{\text{H}}_{\text{4 }\!\!~\!\!\text{ }}}\]

Answer 1

Hint: van der Waal’s equation is used to describe the real nature of any gas. Ideal gas is considered to be never liquified but real gas can be liquified. At low pressures, the equation is a decent approximation for real gases and is precise for an ideal gas. Also known as the ideal gas law and ideal gas equation.

Complete step-by-step answer:The ideal gas law states that PV = nRT, where n is the number of moles, P is the pressure, V is the volume, T is the temperature, and R is the constant of all gases. The Van der Waals equation of state for real gases do not adhere to the ideal gas law. The following describes how to derive the van der Waals Equation.
The volume of a real gas is calculated using the van der Waals equation as (\[{{V}_{m}}\text{ }-\text{ }b\]), where b is the volume occupied per mole.
$\begin{array}{*{35}{l}}
   P({{V}_{m}}-b)=nRT \\
\end{array}$

Intermolecular attraction caused P to change as seen below.
$\begin{array}{*{35}{l}}
   (P+\frac{a}{V_{m}^{2}})({{V}_{m}}-b)=RT \\
\end{array}$
$\begin{array}{*{35}{l}}
   (P+\frac{a{{n}^{2}}}{{{V}^{2}}})(V-nb)=nRT \\
\end{array}$

The intermolecular attractive forces can be measured indirectly using Van der Waal's constant, "a." Strong intermolecular forces of attraction exist in ammonia. Other gases lack intermolecular hydrogen bonding.
As a result, ammonia has a higher value of van der Waal's constant "a" than other gases.
Ammonia may therefore be liquefied the most easily.

Option ‘C’ is correct

Note: The van der Waal’s equation for real gas roughly describes how real fluids behave above their critical temperatures and, at low temperatures, is qualitatively reasonable for low-pressure gaseous forms. When the value of a and b is very small so that we can neglect these correction term, then that gas behaves as an ideal gas.