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

Options

A. (a)4
B. (b)6
C. (c )2
D. (d)3

Explanation

To determine the number of nitrogen atoms in one molecule of caffeine, follow these steps:

### Step 1: Calculate the mass of nitrogen in one mole of caffeine.
Given that caffeine has a molecular weight of 194 g/mol and contains 28.9% nitrogen by mass, we can calculate the mass of nitrogen in one mole of caffeine.

\[ \text{Mass of nitrogen} = \text{Molecular weight of caffeine} \times \left(\frac{\text{Percentage of nitrogen}}{100}\right) \]

\[ \text{Mass of nitrogen} = 194 \, \text{g/mol} \times \left(\frac{28.9}{100}\right) = 56.06 \, \text{g} \]

### Step 2: Calculate the number of moles of nitrogen.
Next, we need to find out how many moles of nitrogen are present in the calculated mass. The atomic weight of nitrogen (N) is approximately 14 g/mol.

\[ \text{Number of moles of nitrogen} = \frac{\text{Mass of nitrogen}}{\text{Atomic weight of nitrogen}} = \frac{56.06 \, \text{g}}{14 \, \text{g/mol}} \approx 4.00 \, \text{moles} \]

### Step 3: Determine the number of nitrogen atoms in one molecule of caffeine.
Since we have found that there are approximately 4 moles of nitrogen in one mole of caffeine, and knowing that one mole of any substance contains Avogadro's number of molecules (approximately \(6.022 \times 10^{23}\)), we can conclude that:

\[ \text{Number of nitrogen atoms in one molecule of caffeine} = 4 \]

### Final Answer:
Thus, the number of nitrogen atoms in one molecule of caffeine is **4**.

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