Hydrazine (N2H4) reacts with oxygen to produce water and nitrogen gas according to the equation: N2H4 + O2 → N2 + 2 H2O. How many grams of hydrazine (N2H4) are needed to produce 96.0 g of water (H2O)?

• A. 96.0 g
• B. 42.0 g
• C. 48.0 g
• D. 21.0 g

Answer: (B)

Verified step by step guidance

1. Write the balanced chemical equation for the reaction: \(\mathrm{N_2H_4 + O_2 \rightarrow N_2 + 2 H_2O}\).
2. Calculate the molar mass of water (\(\mathrm{H_2O}\)) by adding the atomic masses of hydrogen and oxygen: \$2 \times 1.008 + 16.00$ g/mol.
3. Convert the given mass of water (96.0 g) to moles using the formula: \(\text{moles of } H_2O = \frac{\text{mass of } H_2O}{\text{molar mass of } H_2O}\).
4. Use the stoichiometric ratio from the balanced equation to find moles of hydrazine (\(\mathrm{N_2H_4}\)) needed. According to the equation, 1 mole of \(\mathrm{N_2H_4}\) produces 2 moles of \(\mathrm{H_2O}\), so: \(\text{moles of } N_2H_4 = \frac{1}{2} \times \text{moles of } H_2O\).
5. Calculate the molar mass of hydrazine (\(\mathrm{N_2H_4}\)) by adding atomic masses: \$2 \times 14.01 + 4 \times 1.008\( g/mol, then convert moles of hydrazine to grams using: \)\text{mass of } N_2H_4 = \text{moles of } N_2H_4 \times \text{molar mass of } N_2H_4$.