Caffeine has a molecular mass of `194`. If it contains `28.9%` by mass of nitrogen, Calculate number of atoms of nitrogen in one molecule of caffeine ?

Options

A. 4
B. 6
C. 2
D. 3

Answer

To solve the problem of calculating the number of nitrogen atoms in one molecule of caffeine, we can follow these steps:

### Step 1: Calculate the mass of nitrogen in caffeine
Given:
- Molecular mass of caffeine = 194 g/mol
- Percentage of nitrogen by mass = 28.9%

To find the mass of nitrogen in 194 g of caffeine, we use the formula:
\[ \text{Mass of Nitrogen} = \left( \frac{\text{Percentage of Nitrogen}}{100} \right) \times \text{Molecular Mass of Caffeine} \]
Substituting the values:
\[ \text{Mass of Nitrogen} = \left( \frac{28.9}{100} \right) \times 194 = 56.06 \, \text{g} \]

### Step 2: Calculate the number of moles of nitrogen
Next, we need to find the number of moles of nitrogen. We use the formula:
\[ \text{Number of moles} = \frac{\text{Mass of Nitrogen}}{\text{Atomic Mass of Nitrogen}} \]
The atomic mass of nitrogen (N) is approximately 14 g/mol. Thus:
\[ \text{Number of moles of Nitrogen} = \frac{56.06 \, \text{g}}{14 \, \text{g/mol}} \approx 4.004 \, \text{moles} \]

### Step 3: Determine the number of nitrogen atoms in one molecule of caffeine
Since we have calculated the number of moles of nitrogen, we can find the number of nitrogen atoms in one molecule of caffeine.

In one mole of any substance, there are Avogadro's number of entities (atoms, molecules, etc.), which is approximately \(6.022 \times 10^{23}\).

To find the number of nitrogen atoms in one molecule of caffeine, we can assume that the number of nitrogen atoms is equal to the number of moles of nitrogen calculated, as we are looking for the number of nitrogen atoms in a single molecule.

Since we found that there are approximately 4 moles of nitrogen in the caffeine molecule, we conclude that:
\[ \text{Number of Nitrogen Atoms in one molecule of caffeine} = 4 \]

### Final Answer:
Therefore, there are **4 atoms of nitrogen** in one molecule of caffeine.

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