Question

If \[1{\text{L}}\]of \[{{\text{O}}_2}\] at \[{15^ \circ }{\text{C}}\]and \[750{\text{mm}}\] pressure contains N molecules, the number of molecules in \[2{\text{L}}\] of \[{\text{S}}{{\text{O}}_2}\]under the same conditions of temperature and pressure will be:
A. \[\dfrac{{\text{N}}}{2}\]
B. \[{\text{N}}\]
C. \[2{\text{N}}\]
D. \[4{\text{N}}\]

Answer 1

Hint: Avogadro’s law is the basis for finding the number of molecules in a specific volume of a gas. If the amount of a gas in a container is increased, the volume is increased. If the amount of a gas is decreased, the volume is decreased.
Given data:
Volume of \[{{\text{O}}_2}\],\[{{\text{V}}_1} = 1{\text{L}}\]
Volume of \[{\text{S}}{{\text{O}}_2}\],${{\text{V}}_2} = 2{\text{L}}$
Temperature, \[{\text{T}} = {15^ \circ }{\text{C}}\]
Pressure,\[{\text{P}} = 750{\text{mm}}\]
Number of molecules of \[{{\text{O}}_2}\], \[{{\text{n}}_1} = {\text{N}}\]
Number of molecules of \[{\text{S}}{{\text{O}}_2}\], \[{{\text{n}}_2} = ?\]\[\]

Complete step by step solution:
Avogadro’s law states that at same temperature and pressure conditions, equal volumes of gases contain equal numbers of molecules. For example, when we increase the amount of gas, the volume of the balloon increases likewise. It can be expressed as
\[{\text{V}}\alpha {\text{n}}\]
Or \[\dfrac{{\text{V}}}{{\text{n}}} = {\text{k}}\]
\[{\text{V}} \to \]Volume of gas
\[{\text{n}} \to \]number of molecules in a gas
\[{\text{k}} \to \]a constant
The equation can also be written as
\[\dfrac{{{{\text{V}}_1}}}{{{{\text{n}}_1}}} = \dfrac{{{{\text{V}}_2}}}{{{{\text{n}}_2}}}\]
Substituting the values of volume and number of molecules of each gas, we get
\[\dfrac{1}{2} = \dfrac{{\text{N}}}{{{{\text{n}}_2}}}\]\[ \Leftrightarrow {{\text{n}}_2} = 2{\text{N}}\]
Therefore number of molecules in \[{\text{S}}{{\text{O}}_2}\]is double of the number of molecules in \[{{\text{O}}_2}\]
Hence the option C is correct.
Additional information:
This law offered a rational explanation of Gay-Lussac’s law of combining volumes of gases. It indicated the diatomic nature of elemental gases, such as hydrogen, chlorine, and oxygen. It provided a method for determining the molecular weights of gases of known molecular weight.

Note: Avogadro’s law afforded a firm foundation for the development of kinetic molecular theory. Avogadro number is an absolute number which indicates the number of particles in one mole of a substance. The value of Avogadro number is \[6.022 \times {10^{23}}\].