The number of atoms in 4.25 g of `NH_(3)` is approximately

Options

A. `1xx10^(23)`
B. `1.5xx10^(23)`
C. `2xx10^(23)`
D. `6xx10^(23)`

Explanation

To find the number of atoms in 4.25 g of \( NH_3 \) (ammonia), we can follow these steps:

### Step 1: Calculate the Molar Mass of \( NH_3 \)
The molar mass of ammonia (\( NH_3 \)) can be calculated as follows:
- Nitrogen (N) has an atomic mass of approximately 14 g/mol.
- Hydrogen (H) has an atomic mass of approximately 1 g/mol, and there are 3 hydrogen atoms in \( NH_3 \).

\[ \text{Molar mass of } NH_3 = 14 + (3 \times 1) = 14 + 3 = 17 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles of \( NH_3 \)
Using the given mass of ammonia (4.25 g), we can calculate the number of moles using the formula:

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{4.25 \text{ g}}{17 \text{ g/mol}} \]

Calculating this gives:

\[ \text{Number of moles} = \frac{4.25}{17} \approx 0.250 \text{ moles} \]

### Step 3: Calculate the Number of Molecules
To find the number of molecules, we use Avogadro's number, which is \( 6.02 \times 10^{23} \) molecules/mol:

\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]

Substituting the values:

\[ \text{Number of molecules} = 0.250 \text{ moles} \times 6.02 \times 10^{23} \text{ molecules/mol} \]

Calculating this gives:

\[ \text{Number of molecules} \approx 1.505 \times 10^{23} \text{ molecules} \]

### Step 4: Calculate the Number of Atoms
Each molecule of \( NH_3 \) contains 4 atoms (1 nitrogen and 3 hydrogen). Therefore, to find the total number of atoms, we multiply the number of molecules by the number of atoms per molecule:

\[ \text{Number of atoms} = \text{Number of molecules} \times 4 \]

Substituting the values:

\[ \text{Number of atoms} = 1.505 \times 10^{23} \text{ molecules} \times 4 \approx 6.02 \times 10^{23} \text{ atoms} \]

### Conclusion
The number of atoms in 4.25 g of \( NH_3 \) is approximately \( 6.02 \times 10^{23} \).

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