Question

Which of the following contains maximum number of molecules?

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

Answer 1

The correct option is C

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

Step 1: Understanding the molecules

Molecules: When two or more atoms get chemically bonded due to some attractive forces, then a molecule is formed. The number of molecules in a particular amount of substance can be determined by multiplying the number of moles with Avogadro's Number.

Step 2: Finding the number of molecules for each substance

Option A: 1 g ${\mathrm{CO}}_2$

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{molecules}\mathrm{in}1\mathrm{g}{\mathrm{CO}}_2& =& \frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molar}\mathrm{mass}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& \frac{1\mathrm{g}}{44\mathrm{g}/\mathrm{mol}}\times 6.022\times {10}^{23}\\ & =& 1.36\times {10}^{22}\mathrm{molecules}\end{array}$

Option B: 1 g ${\mathrm{N}}_2$

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{molecules}\mathrm{in}1\mathrm{g}{\mathrm{N}}_2& =& \frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molar}\mathrm{mass}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& \frac{1\mathrm{g}}{14\mathrm{g}/\mathrm{mol}}\times 6.022\times {10}^{23}\\ & =& 4.30\times {10}^{22}\mathrm{molecules}\end{array}$

Option C: 1 g ${\mathrm{H}}_2$

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{molecules}\mathrm{in}1\mathrm{g}{\mathrm{H}}_2& =& \frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molar}\mathrm{mass}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& \frac{1\mathrm{g}}{2\mathrm{g}/\mathrm{mol}}\times 6.022\times {10}^{23}\\ & =& 3.011\times {10}^{23}\mathrm{molecules}\end{array}$

Option D: 1 g ${\mathrm{CH}}_4$

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{molecules}\mathrm{in}1\mathrm{g}{\mathrm{CH}}_4& =& \frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molar}\mathrm{mass}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& \frac{1\mathrm{g}}{16\mathrm{g}/\mathrm{mol}}\times 6.022\times {10}^{23}\\ & =& 3.76\times {10}^{22}\mathrm{molecules}\end{array}$

Step-3: Finding the maximum number

From the above, the maximum number of molecules are present in 1 g of ${\mathrm{H}}_2$.

Hence, Option C is the correct answer.