Total number of atoms present in 34 g of `NH_3` is

Options

A. `4xx10^23`
B. `4.8xx10^21`
C. `2xx10^23`
D. `48xx10^23`

Explanation

To find the total number of atoms present in 34 g of ammonia (NH₃), we can follow these steps:

### Step 1: Calculate the molar mass of NH₃
The molar mass of ammonia (NH₃) can be calculated as follows:
- Nitrogen (N) has a molar mass of approximately 14 g/mol.
- Hydrogen (H) has a molar mass of approximately 1 g/mol, and there are three hydrogen atoms in NH₃.

Thus, the molar mass of NH₃ = 14 g/mol (N) + 3 × 1 g/mol (H) = 14 g/mol + 3 g/mol = 17 g/mol.

### Step 2: Calculate the number of moles of NH₃ in 34 g
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Substituting the values:
\[ \text{Number of moles} = \frac{34 \text{ g}}{17 \text{ g/mol}} = 2 \text{ moles} \]

### Step 3: Calculate the number of molecules of NH₃
Using Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol), we can find the number of molecules:
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of molecules} = 2 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \]
\[ \text{Number of molecules} = 12.044 \times 10^{23} \text{ molecules} \]

### Step 4: Calculate the total number of atoms in NH₃
Each molecule of NH₃ contains 4 atoms (1 nitrogen atom and 3 hydrogen atoms). Therefore, to find the total number of atoms, we multiply the number of molecules by the number of atoms per molecule:
\[ \text{Total number of atoms} = \text{Number of molecules} \times \text{Number of atoms per molecule} \]
\[ \text{Total number of atoms} = 12.044 \times 10^{23} \text{ molecules} \times 4 \text{ atoms/molecule} \]
\[ \text{Total number of atoms} = 48.176 \times 10^{23} \text{ atoms} \]

### Final Answer
The total number of atoms present in 34 g of NH₃ is approximately \(4.82 \times 10^{24}\) atoms.

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