percentage of nitrogen by mass in `N_(2)H_(4)`?

Answer

To find the percentage of nitrogen by mass in hydrazine (N₂H₄), we can follow these steps:

### Step 1: Calculate the molar mass of N₂H₄
- The molecular formula of hydrazine is N₂H₄, which consists of:
- 2 nitrogen (N) atoms
- 4 hydrogen (H) atoms

- The atomic mass of nitrogen (N) is approximately 14 g/mol.
- The atomic mass of hydrogen (H) is approximately 1 g/mol.

**Calculation:**
\[ \text{Molar mass of N}_2\text{H}_4 = (2 \times \text{Atomic mass of N}) + (4 \times \text{Atomic mass of H}) \]
\[ = (2 \times 14) + (4 \times 1) \]
\[ = 28 + 4 = 32 \text{ g/mol} \]

### Step 2: Calculate the total mass of nitrogen in N₂H₄
- Since there are 2 nitrogen atoms in N₂H₄:
\[ \text{Mass of nitrogen} = 2 \times \text{Atomic mass of N} = 2 \times 14 = 28 \text{ g} \]

### Step 3: Calculate the percentage of nitrogen by mass in N₂H₄
- The formula for mass percentage is:
\[ \text{Mass percentage of nitrogen} = \left( \frac{\text{Mass of nitrogen}}{\text{Molar mass of N}_2\text{H}_4} \right) \times 100 \]

**Calculation:**
\[ \text{Mass percentage of nitrogen} = \left( \frac{28}{32} \right) \times 100 \]
\[ = 0.875 \times 100 = 87.5\% \]

### Final Answer:
The percentage of nitrogen by mass in N₂H₄ is **87.5%**.

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