Question

The number of atoms present in $1.6\text{g}$ of methane is

• A. $6.02\times {10}^{23}$
• B. $3.01\times {10}^{24}$
• C. $3.01\times {10}^{23}$
• D. $6.02\times {10}^{24}$

Answer 1

The correct option is C

$3.01\times {10}^{23}$

Explanation:

Step 1: Analyzing the given data

Given mass of methane$\left({\mathrm{CH}}_4\right)$ $=1.6\text{g}$

Molar mass of methane$\left({\mathrm{CH}}_4\right)$ ${\text{=12.01 g mol}}^{\text{-1}}\text{+1.0079×4}\text{g}{\mathrm{mol}}^{\text{-1}}=16.0416\text{g}{\mathrm{mol}}^{\text{-1}}$

Step 2: Calculating the number of atoms

The number of molecules of methane can be calculated using given formula

$\text{Number of molecules=}\frac{\text{Given mass}}{\text{Molar mass}}\text{×Avogadro number}$

Since one methane molecule contains four atoms of hydrogen and one atom of carbon. So, total number of atom can be calculated as

$$\begin{gathered} \text{Number of atoms=5×}\frac{1.6\text{g}}{16.0416{\text{g mol}}^{-1}}{\text{×6.022×10}}^{23}{\text{mol}}^{\text{-1}} \\ =3.003{\times 10}^{23} \\ \simeq 3.01{\times 10}^{23} \end{gathered}$$

Hence, the number of atoms is $3.01\times {10}^{23}$.

Hence, option (C) is correct.