To calculate the number of moles of hydrazine (N₂H₄) burned, we need to follow these steps:
1. Find the molar mass of hydrazine (N₂H₄):
- The molecular formula for hydrazine is N₂H₄, which means it contains 2 nitrogen (N) atoms and 4 hydrogen (H) atoms.
- The atomic mass of nitrogen (N) is approximately 14.01 g/mol.
- The atomic mass of hydrogen (H) is approximately 1.008 g/mol.
- Therefore, the molar mass of hydrazine (N₂H₄) can be calculated as:
[tex]\[
\text{Molar mass of N₂H₄} = (2 \times 14.01\, \text{g/mol}) + (4 \times 1.008\, \text{g/mol})
= 28.02\, \text{g/mol} + 4.032\, \text{g/mol}
= 32.052\, \text{g/mol}
\][/tex]
2. Use the mass of the sample to calculate the number of moles:
- We have a 1.000 g sample of hydrazine.
- The number of moles (n) is given by the formula:
[tex]\[
n = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
- Plugging in the values:
[tex]\[
n = \frac{1.000\, \text{g}}{32.0452\, \text{g/mol}}
\][/tex]
3. Perform the calculation:
After dividing the mass of the sample by the molar mass, we get:
[tex]\[
n \approx 0.0312\, \text{mol}
\][/tex]
Thus, the number of moles of hydrazine (N₂H₄) burned is approximately [tex]\( \boxed{0.0312}\)[/tex] moles.
