Question

Which of the following contains the largest number of atoms?

• A. $11\mathrm{g}\mathrm{of}{\mathrm{CO}}_2$
• B. $4\mathrm{g}\mathrm{of}{\mathrm{H}}_2$
• C. $5\mathrm{g}\mathrm{of}{\mathrm{NH}}_3$
• D. $8\mathrm{g}\mathrm{of}{\mathrm{SO}}_2$

Answer 1

The correct option is B

$4\mathrm{g}\mathrm{of}{\mathrm{H}}_2$

The explanation for the correct option:

(B) $4\mathrm{g}\mathrm{of}{\mathrm{H}}_2$

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 $4\mathrm{g}\mathrm{of}{\mathrm{H}}_2$ $=\frac{4}{2}\mathrm{mol}$

$=2\mathrm{mol}$

Step 2: Calculation of the number of molecules

• Number of molecules $=\mathrm{n}\times {\mathrm{N}}_{\mathrm{A}}$

Where,

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

• Number of molecules in $4\mathrm{g}\mathrm{of}{\mathrm{H}}_2$ $=2\times 6.022\times {10}^{23}$molecules

$=12.044\times {10}^{23}$ molecules

Step 3: Calculation of the number of atoms

• Number of atoms in one molecule of Hydrogen gas $=2$atoms
• Number of atoms in $12.044\times {10}^{23}$ molecules of Hydrogen gas $=2\times 12.044\times {10}^{23}\mathrm{atoms}$

$=24.088\times {10}^{23}$ atoms

• Therefore, it has the maximum number of atoms and is the correct answer.

The explanation for the incorrect options:

(A) $11\mathrm{g}\mathrm{of}{\mathrm{CO}}_2$

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 $11\mathrm{g}\mathrm{of}{\mathrm{CO}}_2$ $=\frac{11}{44}\mathrm{mol}$

$=0.25\mathrm{mol}$

Step 2: Calculation of the number of molecules

• Number of molecules $=\mathrm{n}\times {\mathrm{N}}_{\mathrm{A}}$

Where,

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

• Number of molecules in $11\mathrm{g}{\mathrm{CO}}_2$ $=0.25\times 6.022\times {10}^{23}$molecules

$=1.505\times {10}^{23}$ molecules

Step 3: Calculation of the number of atoms

• Number of atoms in one molecule of Carbon dioxide $=3$atoms
• Number of atoms in $1.505\times {10}^{23}$ molecules of Carbon dioxide $=3\times 1.505\times {10}^{23}\mathrm{atoms}$

$=4.516\times {10}^{23}$ atoms

• Therefore, it does not have the maximum number of atoms and is the incorrect answer.

(C) $5\mathrm{g}\mathrm{of}{\mathrm{NH}}_3$

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 $5\mathrm{g}\mathrm{of}{\mathrm{NH}}_3$ $=\frac{5}{17}$

$=0.2941\mathrm{mol}$

Step 2: Calculation of the number of molecules

• Number of molecules $=\mathrm{n}\times {\mathrm{N}}_{\mathrm{A}}$

Where,

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

• Number of molecules in $5\mathrm{g}{\mathrm{NH}}_3$ $=0.2941\times 6.022\times {10}^{23}$molecules

$=1.771\times {10}^{23}$ molecules

Step 3: Calculation of the number of atoms

• Number of atoms in one molecule of Ammonia $=4$atoms
• Number of atoms in $1.771\times {10}^{23}$ molecules of Ammonia $=4\times 1.771\times {10}^{23}$atoms

$=7.084\times {10}^{23}$ atoms

• Therefore, it does not have the maximum number of atoms and is the incorrect answer.

(D) $8\mathrm{g}\mathrm{of}{\mathrm{SO}}_2$

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 $8\mathrm{g}\mathrm{of}{\mathrm{SO}}_2$ $=\frac{8}{64}$

$=0.125\mathrm{mol}$

Step 2: Calculation of the number of molecules

• Number of molecules $=\mathrm{n}\times {\mathrm{N}}_{\mathrm{A}}$
• Where,${\mathrm{N}}_{\mathrm{A}}$ is Avogadro's number which is equal to $6.022\times {10}^{23}\mathrm{molecules}$
• Number of molecules in $8\mathrm{g}{\mathrm{SO}}_2$ $=0.125\times 6.022\times {10}^{23}\mathrm{molecules}$

$=0.752\times {10}^{23}$ molecules

Step 3: Calculation of the number of atoms

• Number of atoms in one molecule of Sulphur dioxide $=3\mathrm{atoms}$
• Number of atoms in $0.752\times {10}^{23}$ molecules of Sulphur dioxide $=3\times 0.752\times {10}^{23}\mathrm{atoms}$

$=2.258\times {10}^{23}$ atoms

• Therefore, it does not have the maximum number of atoms and is the incorrect answer.

Hence, the correct option is (B) $4\mathrm{g}\mathrm{of}{\mathrm{H}}_2$.