To determine the mass of hydrogen (H₂) used in the reaction, we can start by analyzing the balanced chemical equation:
\[ \text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3 \]
From the equation, we see that 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia.
Step 1: Calculate the moles of nitrogen (N₂).
The molar mass of nitrogen (N₂) is approximately: \[ 14.01 , \text{g/mol} \times 2 = 28.02 , \text{g/mol} \]
Now, we can convert the mass of nitrogen to moles: \[ \text{Moles of N}_2 = \frac{10.0 , \text{g}}{28.02 , \text{g/mol}} \approx 0.356 , \text{mol} \]
Step 2: Use the stoichiometry of the reaction to find the moles of hydrogen (H₂) required.
According to the balanced equation, 1 mole of N₂ reacts with 3 moles of H₂. Therefore, the number of moles of hydrogen needed is: \[ \text{Moles of H}_2 = 3 \times \text{Moles of N}_2 = 3 \times 0.356 , \text{mol} \approx 1.067 , \text{mol} \]
Step 3: Calculate the mass of hydrogen used.
The molar mass of hydrogen (H₂) is: \[ 1.008 , \text{g/mol} \times 2 = 2.016 , \text{g/mol} \]
Now we can calculate the mass of hydrogen: \[ \text{Mass of H}_2 = \text{Moles of H}_2 \times \text{Molar mass of H}_2 = 1.067 , \text{mol} \times 2.016 , \text{g/mol} \approx 2.15 , \text{g} \]
Conclusion: The mass of hydrogen used in the reaction is approximately 2.15 grams.
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