Question

Which has the maximum number of molecules?
$\begin{align}
  & \text{A}\text{. 7g }{{\text{N}}_{2}} \\
 & \text{B}\text{. 2g }{{\text{H}}_{2}} \\
 & \text{C}\text{. 16g N}{{\text{O}}_{2}} \\
 & \text{D}\text{. 16g }{{\text{O}}_{2}} \\
\end{align}$

Answer 1

Hint: Different gases with the same number of moles have the same no. of molecules which is equal to the Avagadro's number i.e. $6.022\text{ }\cdot \text{ 1}{{\text{0}}^{23}}$. Whereas a number of moles are equal to the mass of the substance divided by the molar mass of the substance.

Complete Step-by-Step Answer:
-To calculate the number of molecules of a substance, we have to calculate the number of moles of the molecule.
-We know that number of moles is equal to the mass of a substance divided by the molar mass of a substance, so the number of moles of 7g nitrogen is:
-Given, the mass of nitrogen = 7g
The molar mass of nitrogen = \[14\text{ }\cdot \text{ 2 = 28}\]
Number of moles = \[\dfrac{7}{28}\text{ = }\dfrac{1}{4}\]
-Now, similarly, we will calculate the number of molecules of hydrogen
-Given, the mass of hydrogen = 2g and molar mass of 2 molecules of hydrogen = 2
$\begin{align}
  & \text{No}\text{. of moles = }\dfrac{\text{Mass}}{\text{Molar mass}} \\
 & =\text{ }\dfrac{2}{2}\text{ = 1} \\
\end{align}$
-A number of moles of nitrogen dioxide are:
-Given, Mass of Nitrogen dioxide = 16g
The molar mass of nitrogen dioxide
$\begin{align}
  & =\text{ 14 + }\left( 2\text{ }\cdot \text{ 16} \right) \\
 & =\text{ 14 + 32} \\
 & \text{= 46} \\
\end{align}$
Number of moles = $\dfrac{\text{16}}{46}\text{ = }\dfrac{8}{23}\text{ = 0}\text{.34}$
-Now, a number of moles of oxygen are:
Given, the mass of oxygen = 16g
The molar mass of oxygen = 32
The number of moles = $\dfrac{16}{32}\text{ = }\dfrac{1}{2}$
-Now, we know that no. of moles of a substance is directly proportional to the no. of molecules of a substance.
-From the above calculation, we can write the increasing order of the number of moles i.e.
$\text{7g }{{\text{N}}_{2}}\text{ }$˂ $\text{16g N}{{\text{O}}_{2}}$˂ $16\text{g }{{\text{O}}_{2}}$˂ $\text{2g }{{\text{H}}_{2}}$
Therefore, $\text{2g }{{\text{H}}_{2}}$has the maximum number of molecules.

Note: The term mole concept was given by Wilhelm Ostwald. There is a very important mole concept in studying the smallest particles such as atoms with large units. Moreover, to convert moles into molecules we can multiply moles by the Avagadro's number.