Find percentage nitrogen by mass in Histamine?

Options

A. (a) 37.84
B. (b) 45.42
C. (c) 25.38
D. (d) 49.85

Explanation

To find the percentage of nitrogen by mass in histamine, we can follow these steps:

### Step 1: Determine the Molecular Formula of Histamine
Histamine has a molecular formula of C₄H₉N₃. This means it contains:
- 4 Carbon (C) atoms
- 9 Hydrogen (H) atoms
- 3 Nitrogen (N) atoms

### Step 2: Calculate the Molar Mass of Histamine
To find the molar mass of histamine, we need to sum the atomic masses of all the atoms in the molecular formula:
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Hydrogen (H) = 1 g/mol
- Atomic mass of Nitrogen (N) = 14 g/mol

Calculating the total molar mass:
- Molar mass of C₄ = 4 × 12 g/mol = 48 g/mol
- Molar mass of H₉ = 9 × 1 g/mol = 9 g/mol
- Molar mass of N₃ = 3 × 14 g/mol = 42 g/mol

Total molar mass of histamine = 48 g/mol + 9 g/mol + 42 g/mol = 99 g/mol

### Step 3: Calculate the Total Mass of Nitrogen in Histamine
Since there are 3 nitrogen atoms in histamine, the total mass of nitrogen is:
- Total mass of N = 3 × 14 g/mol = 42 g/mol

### Step 4: Calculate the Percentage of Nitrogen by Mass
The percentage of nitrogen by mass in histamine can be calculated using the formula:
\[ \text{Percentage of Nitrogen} = \left( \frac{\text{Total mass of Nitrogen}}{\text{Total molar mass of Histamine}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage of Nitrogen} = \left( \frac{42 \, \text{g/mol}}{99 \, \text{g/mol}} \right) \times 100 \approx 42.42\% \]

### Final Answer
The percentage of nitrogen by mass in histamine is approximately **42.42%**.

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