To find the quantity of hydrogen (H2) that participated in the reaction, we can use the mole concept and stoichiometry based on the balanced equation:
\[ N_2 + 3H_2 \rightarrow 2NH_3 \]
First, we need to determine the number of moles of nitrogen (N2) that reacted. The molar mass of nitrogen (N2) is approximately 28.02 g/mol (since each nitrogen atom has a molar mass of about 14.01 g).
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Calculate the moles of nitrogen (N2): \[ \text{Moles of } N_2 = \frac{\text{mass of } N_2}{\text{molar mass of } N_2} = \frac{10.0 , \text{g}}{28.02 , \text{g/mol}} \approx 0.357 , \text{mol} , N_2 \]
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Using the balanced equation, determine the moles of hydrogen (H2) required: According to the equation, 1 mole of N2 reacts with 3 moles of H2. Therefore, the moles of H2 needed can be calculated as follows: \[ \text{Moles of } H_2 = 3 \times \text{moles of } N_2 = 3 \times 0.357 , \text{mol} \approx 1.071 , \text{mol} , H_2 \]
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Now, calculate the mass of hydrogen (H2) that corresponds to these moles: The molar mass of hydrogen (H2) is approximately 2.02 g/mol. \[ \text{Mass of } H_2 = \text{moles of } H_2 \times \text{molar mass of } H_2 = 1.071 , \text{mol} \times 2.02 , \text{g/mol} \approx 2.16 , \text{g} , H_2 \]
However, since the product is 12.0 g of NH3, we can also verify how much H2 is actually consumed by using the moles of ammonia produced.
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Calculate moles of ammonia produced: The molar mass of ammonia (NH3) is approximately 17.03 g/mol: \[ \text{Moles of } NH_3 = \frac{12.0 , \text{g}}{17.03 , \text{g/mol}} \approx 0.705 , \text{mol} , NH_3 \]
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Using the balanced equation, determine the moles of H2 that correspond to the produced NH3: Since 2 moles of NH3 are produced from 3 moles of H2: \[ \text{Moles of } H_2 \text{ required} = 3 \times \frac{0.705}{2} = 1.0575 , \text{mol} , H_2 \]
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Calculate the mass of hydrogen (H2) again: \[ \text{Mass of } H_2 = 1.0575 , \text{mol} \times 2.02 , \text{g/mol} \approx 2.14 , \text{g} , H_2 \]
It appears that there may be inconsistencies in the existing choices since the calculated value aligns with none of them. However, based on reasoning with the stoichiometry derived, approximately 2.14 g of hydrogen would have been consumed in the reaction, reflecting its use in producing the stated mass of ammonia.
Given the provided answer choices: A. 12 g of H2 B. 2.9 g of H2 C. 3.0 g of H2 D. 10 g of H2
The answer would be closest to B. 2.9 g of H2.