Question

Which of the following has maximum number of atoms?

• A. $18\mathrm{g}$ of ${\mathrm{H}}_2\mathrm{O}$
• B. $18\mathrm{g}$ of ${\mathrm{O}}_2$
• C. $18\mathrm{g}$ of ${\mathrm{CO}}_2$
• D. $18\mathrm{g}$ of ${\mathrm{CH}}_4$

Answer 1

The correct option is D

$18\mathrm{g}$ of ${\mathrm{CH}}_4$

The explanation for correct option:-

d) $18\mathrm{g}$ of ${\mathrm{CH}}_4$ :-

Step1: analyzing given quantities

• $1$mole of ${\mathrm{CH}}_4$ = $16$ $\mathrm{g}{\mathrm{mol}}^{-1}$
• $16$g ${\mathrm{CH}}_4$ = $1$ mol
• $18\mathrm{g}$ ${\mathrm{CH}}_4$ = $(1/16)\times 18$ = $1.125$mol

Step 2: calculating the no. of atoms

• $1$ mol of ${\mathrm{CH}}_4$ contains $6.022\times {10}^{23}$ molecules
• $1.125$mol of ${\mathrm{CH}}_4$ contains = $6.77\times {10}^{23}$molecules
• Number of atoms in a molecule of ${\mathrm{CH}}_4$ = $5$
• Number of atoms in $18\mathrm{g}$ of ${\mathrm{CH}}_4$ = $6.77\times {10}^{23}$$\times 5$ = $33.87\times {10}^{23}$ = $3.387\times {10}^{24}$ atoms

The explanation for incorrect options:-

a) $18\mathrm{g}$of${\mathrm{H}}_2\mathrm{O}$:-

Step1: analyzing given quantities

• $1$ mole of ${\mathrm{H}}_2\mathrm{O}$ = $18\mathrm{g}$
• $1$ mole of ${\mathrm{H}}_2\mathrm{O}$ contains $6.022\times {10}^{23}$molecules

Step 2: calculating the no. of atoms

• Number of atoms in a molecule of ${\mathrm{H}}_2\mathrm{O}$ = $3$
• Number of atoms in $6.022\times {10}^{23}$ molecules of ${\mathrm{H}}_2\mathrm{O}$ = $3\times 6.022\times {10}^{23}$ = $18.1$$\times {10}^{23}$ = $1.81\times {10}^{24}$ atoms
• Hence it is not the correct option.

b) $18$g of${\mathrm{O}}_2$:-

Step1: analyzing given quantities

• $1$ mol of ${\mathrm{O}}_2$ = $32$g
• $32$g ${\mathrm{O}}_2$ = $1$mol
• $18$g ${\mathrm{O}}_2$ = $0.56$mol

Step 2: calculating the no. of atoms

• $1$ mole of ${\mathrm{O}}_2$ contains $6.022\times {10}^{23}$molecules
• $0.56$mol of ${\mathrm{O}}_2$ contains = $6.022\times {10}^{23}$$\times 0.56$ = $3.37\times {10}^{23}$
• Number of moles in a molecule of ${\mathrm{O}}_2$ = $2$
• Number of atoms in $3.37\times {10}^{23}$molecules of ${\mathrm{O}}_2$ =$3.37\times {10}^{23}$$\times 2$ = $6.74$$\times {10}^{23}$atoms
• Hence it is not the correct option.

c) $18\mathrm{g}$ of${\mathrm{CO}}_2$:-

Step1: analyzing given quantities

• $1$mol of ${\mathrm{CO}}_2$ = $44$g
• $44$g ${\mathrm{CO}}_2$ = $1$mol
• $18\mathrm{g}$ of ${\mathrm{CO}}_2$= $0.41$mol

Step 2: calculating the no. of atoms

• $1$ mole of ${\mathrm{CO}}_2$ contains $6.022\times {10}^{23}$molecules
• $0.41$mol of ${\mathrm{CO}}_2$ = $6.022\times {10}^{23}$$\times 0.41$ = $2.47\times {10}^{23}$ molecules
• Number of atoms in a molecule of ${\mathrm{CO}}_2$ = $3$
• Number of atoms in $2.47\times {10}^{23}$molecules of ${\mathrm{CO}}_2$ = $3\times 2.47\times {10}^{23}$= $7.41\times {10}^{23}$ atoms
• Hence it is not the correct option.

Therefore the correct option is d) $18\mathrm{g}$ of ${\mathrm{CH}}_4$