To determine how many grams of nitrogen ([tex]\(N_2\)[/tex]) are required to react with 6.25 moles of hydrogen ([tex]\(H_2\)[/tex]), we can follow these steps:
1. Understand the balanced chemical equation:
[tex]\[
N_2 + 3H_2 \rightarrow 2NH_3
\][/tex]
According to this equation, 1 mole of [tex]\(N_2\)[/tex] reacts with 3 moles of [tex]\(H_2\)[/tex].
2. Calculate the moles of [tex]\(N_2\)[/tex] needed:
Given that we have 6.25 moles of [tex]\(H_2\)[/tex], we can determine the moles of [tex]\(N_2\)[/tex] required using the stoichiometric ratio from the balanced equation:
[tex]\[
\text{Moles of } N_2 = \frac{\text{Moles of } H_2}{3}
\][/tex]
Substituting in the given amount of hydrogen:
[tex]\[
\text{Moles of } N_2 = \frac{6.25 \text{ moles } H_2}{3} = 2.0833333333333335 \text{ moles}
\][/tex]
3. Convert moles of [tex]\(N_2\)[/tex] to grams:
We use the molar mass of [tex]\(N_2\)[/tex] to convert the moles to grams. The molar mass of [tex]\(N_2\)[/tex] is 28.02 g/mol.
[tex]\[
\text{Grams of } N_2 = \text{Moles of } N_2 \times \text{Molar mass of } N_2
\][/tex]
Substituting the values:
[tex]\[
\text{Grams of } N_2 = 2.0833333333333335 \text{ moles} \times 28.02 \text{ g/mol} = 58.375 \text{ grams}
\][/tex]
Thus, you would need 58.375 grams of nitrogen ([tex]\(N_2\)[/tex]) to react with 6.25 moles of hydrogen ([tex]\(H_2\)[/tex]).
