Question

Which of the following contains maximum number of molecules?

• A. $1\mathrm{g}{\mathrm{CO}}_2$
• B. $1\mathrm{g}{\mathrm{N}}_2$
• C. $1\mathrm{g}{\mathrm{H}}_2$
• D. $1\mathrm{g}{\mathrm{CH}}_4$

Answer 1

The correct option is C

$1\mathrm{g}{\mathrm{H}}_2$

The explanation for the correct option:

(C) $1\mathrm{g}{\mathrm{H}}_2$

Step 1: Calculation of the number of moles

• Number of moles ($\mathrm{n}$) $=\frac{\mathrm{w}}{\mathrm{M}}$

Where,

$\mathrm{w}$ is the given weight of the compound in grams

$\mathrm{M}$ is the molar mass of the compound

• Number of moles in $1\mathrm{g}{\mathrm{H}}_2$ $=\frac{1}{2}$

$=0.5\mathrm{mol}$

• Therefore, it has the maximum number of molecules.

Step 2: Calculation of the number of molecules

• Number of molecules in $1\mathrm{g}{\mathrm{H}}_2$ $=\mathrm{n}\times {\mathrm{N}}_{\mathrm{A}}$

Where,

${\mathrm{N}}_{\mathrm{A}}$ is Avogadro's number which is equal to $6.022\times {10}^{23}$

• Number of molecules in $1\mathrm{g}{\mathrm{H}}_2$ $=0.5\times 6.022\times {10}^{23}$

$=3.011\times {10}^{23}$ molecules

The explanation for the incorrect options:

(A) $1\mathrm{g}{\mathrm{CO}}_2$

Step 1: Calculation of the number of moles

• Number of moles ($\mathrm{n}$) $=\frac{\mathrm{w}}{\mathrm{M}}$

Where,

$\mathrm{w}$ is the given weight of the compound in grams

$\mathrm{M}$ is the molar mass of the compound

• Number of moles in $1\mathrm{g}{\mathrm{CO}}_2$ $=\frac{1}{44}$

$=0.0227\mathrm{mol}$

Step 2: Calculation of the number of molecules

• Number of molecules in $1\mathrm{g}{\mathrm{CO}}_2$ $=\mathrm{n}\times {\mathrm{N}}_{\mathrm{A}}$

Where,

${\mathrm{N}}_{\mathrm{A}}$ is Avogadro's number which is equal to $6.022\times {10}^{23}$

• Number of molecules in $1\mathrm{g}{\mathrm{CO}}_2$ $=0.0227\times 6.022\times {10}^{23}$

$=0.136\times {10}^{23}$ molecules

• Therefore, it has a lesser number of molecules than ${\mathrm{H}}_2$.

(B) $1\mathrm{g}{\mathrm{N}}_2$

Step 1: Calculation of the number of moles

• Number of moles ($\mathrm{n}$) $=\frac{\mathrm{w}}{\mathrm{M}}$

Where,

$\mathrm{w}$ is the given weight of the compound in grams

$\mathrm{M}$ is the molar mass of the compound

• Number of moles in $1\mathrm{g}{\mathrm{N}}_2$ $=\frac{1}{28}$

$=0.0357\mathrm{mol}$

Step 2: Calculation of the number of molecules

• Number of molecules in $1\mathrm{g}{\mathrm{N}}_2$ $=\mathrm{n}\times {\mathrm{N}}_{\mathrm{A}}$

Where,

${\mathrm{N}}_{\mathrm{A}}$ is Avogadro's number which is equal to $6.022\times {10}^{23}$

• Number of molecules in $1\mathrm{g}{\mathrm{N}}_2$ $=0.0357\times 6.022\times {10}^{23}$

$=0.215\times {10}^{23}$ molecules

• Therefore, it has a lesser number of molecules than ${\mathrm{H}}_2$.

(D) $1\mathrm{g}{\mathrm{CH}}_4$

Step 1: Calculation of the number of moles

• Number of moles ($\mathrm{n}$) $=\frac{\mathrm{w}}{\mathrm{M}}$

Where,

$\mathrm{w}$ is the given weight of the compound in grams

$\mathrm{M}$ is the molar mass of the compound

• Number of moles in $1\mathrm{g}{\mathrm{CH}}_4$ $=\frac{1}{16}$

$=0.0625\mathrm{mol}$

Step 2: Calculation of the number of molecules

• Number of molecules in $1\mathrm{g}{\mathrm{CH}}_4$ $=\mathrm{n}\times {\mathrm{N}}_{\mathrm{A}}$

Where,

${\mathrm{N}}_{\mathrm{A}}$ is Avogadro's number which is equal to $6.022\times {10}^{23}$

• Number of molecules in $1\mathrm{g}{\mathrm{CH}}_4$ $=0.0625\times 6.022\times {10}^{23}$

$=0.376\times {10}^{23}$ molecules

• Therefore, it has a lesser number of molecules than ${\mathrm{H}}_2$.

Hence, the correct option is (C) $1\mathrm{g}{\mathrm{H}}_2$.