Question

Which of the following contains the greatest number of atoms?

• A. $1\mathrm{g}\mathrm{of}\mathrm{Butane}$
• B. $1\mathrm{g}\mathrm{of}\mathrm{Nitrogen}$
• C. $1\mathrm{g}\mathrm{of}\mathrm{Silver}$
• D. $1\mathrm{g}\mathrm{of}\mathrm{water}$

Answer 1

The correct option is A

$1\mathrm{g}\mathrm{of}\mathrm{Butane}$

The explanation for the correct option:

(A) $1\mathrm{g}\mathrm{of}\mathrm{Butane}$

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 $1\mathrm{g}\mathrm{of}\mathrm{Butane}$ $=\frac{1}{58}\mathrm{mol}$

$=0.0172\mathrm{mol}$

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 $6.022\times {10}^{23}$

• Number of molecules in $1\mathrm{g}\mathrm{of}{\mathrm{C}}_4{\mathrm{H}}_{10}$ $=0.0172\times 6.022\times {10}^{23}\mathrm{molecules}$

$=0.1035\times {10}^{23}$ molecules

Step 3: Calculation of the number of atoms

• Number of atoms in one molecule of Butane $=14$
• Number of atoms in $0.1035\times {10}^{23}$ molecules of Butane $=14\times 0.1035\times {10}^{23}$atoms

$=1.45\times {10}^{23}$ atoms

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

The explanation for the incorrect options:

(B) $1\mathrm{g}\mathrm{of}\mathrm{Nitrogen}$

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 $1\mathrm{g}\mathrm{of}\mathrm{Nitrogen}$ $=\frac{1}{28}\mathrm{mol}$

$=0.0357\mathrm{mol}$

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

$=0.2149\times {10}^{23}$ molecules

Step 3: Calculation of the number of atoms

• Number of atoms in one molecule of Nitrogen $=2\mathrm{u}$
• Number of atoms in $0.2149\times {10}^{23}$ molecules of Nitrogen $=2\times 0.2149\times {10}^{23}$atoms

$=0.43\times {10}^{23}$ atoms

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

(C) $1\mathrm{g}\mathrm{of}\mathrm{Silver}$

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 $1\mathrm{g}\mathrm{of}\mathrm{Silver}$ $=\frac{1}{108}\mathrm{mol}$

$=0.0092\mathrm{mol}$

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 $1\mathrm{g}\mathrm{Ag}$ $=0.0092\times 6.022\times {10}^{23}$molecules

$=0.0554\times {10}^{23}$ molecules

Step 3: Calculation of the number of atoms

• Number of atoms in one molecule of Silver $=1\mathrm{u}$
• Number of atoms in $0.0554\times {10}^{23}$ molecules of Silver $=1\times 0.0554\times {10}^{23}$atoms

$=0.054\times {10}^{23}$ atoms

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

(D) $1\mathrm{g}\mathrm{of}\mathrm{water}$

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 $1\mathrm{g}\mathrm{of}\mathrm{water}$ $=\frac{1}{18}\mathrm{mol}$

$=0.055\mathrm{mol}$

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 $1\mathrm{g}{\mathrm{H}}_2\mathrm{O}$ $=0.055\times 6.022\times {10}^{23}$molecules

$=0.3312\times {10}^{23}$ molecules

Step 3: Calculation of the number of atoms

• Number of atoms in one molecule of Water $=3\mathrm{u}$
• Number of atoms in $0.3312\times {10}^{23}$ molecules of Nitrogen $=3\times 0.3312\times {10}^{23}$atoms

$=0.993\times {10}^{23}$ atoms

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

Hence, the correct option is (A) $1\mathrm{g}\mathrm{of}\mathrm{Butane}$.