To solve this problem, we need to determine how much hydrogen (H2) is required to react with the given amount of nitrogen (N2) based on the chemical equation:
\[ \text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3 \]
From the balanced equation, we see that 1 mole of N2 reacts with 3 moles of H2 to produce 2 moles of NH3.
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Calculate moles of nitrogen:
- The molar mass of N2 (nitrogen) is approximately 28.02 g/mol.
- The number of moles of nitrogen in 10.0 grams can be calculated as follows: \[ \text{moles of N}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{10.0 , \text{g}}{28.02 , \text{g/mol}} \approx 0.357 , \text{moles of N}_2 \]
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Calculate moles of hydrogen needed:
- From the balanced equation, 1 mole of N2 requires 3 moles of H2. Therefore, the amount of H2 required is: \[ \text{moles of H}_2 = 3 \times \text{moles of N}_2 = 3 \times 0.357 , \text{moles} \approx 1.071 , \text{moles of H}_2 \]
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Convert moles of hydrogen to grams:
- The molar mass of H2 (hydrogen) is about 2.02 g/mol.
- The mass of H2 needed can be calculated as: \[ \text{mass of H}_2 = \text{moles of H}_2 \times \text{molar mass of H}_2 = 1.071 , \text{moles} \times 2.02 , \text{g/mol} \approx 2.16 , \text{g of H}_2 \]
Based on the calculations, the closest answer would be approximated to 2.0 grams of H2.
Thus, the answer is: B. 2.0 g of H2.