To determine the mass of hydrogen (H₂) used in the reaction, we can follow these steps:
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Calculate the moles of nitrogen (N₂) used:
- The molar mass of nitrogen (N₂) is approximately 28.02 g/mol (14.01 g/mol for each nitrogen atom).
- The number of moles of N₂ in 10.0 grams is calculated as follows: \[ \text{moles of N₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{10.0 \text{ g}}{28.02 \text{ g/mol}} \approx 0.357 \text{ moles of N₂} \]
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Using the stoichiometry of the balanced equation:
- The balanced equation is: \[ N₂ + 3H₂ → 2NH₃ \]
- From the equation, 1 mole of N₂ reacts with 3 moles of H₂.
- Therefore, moles of H₂ needed for the reaction can be calculated as: \[ \text{moles of H₂} = 3 \times \text{moles of N₂} = 3 \times 0.357 \text{ moles} \approx 1.071 \text{ moles of H₂} \]
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Calculate the mass of hydrogen used:
- The molar mass of hydrogen (H₂) is approximately 2.02 g/mol.
- The mass of H₂ used in the reaction is: \[ \text{mass of H₂} = \text{moles of H₂} \times \text{molar mass of H₂} = 1.071 \text{ moles} \times 2.02 \text{ g/mol} \approx 2.16 \text{ g} \]
Given the closest answer option to our calculation:
C. 2.0 g of H₂ is the correct answer.