In the ammonia production process given by the reaction 3H₂(g) + N₂(g) → 2NH₃(g), when 7.00 g of hydrogen react with 70.0 g of nitrogen, hydrogen is considered the limiting reactant because <u>7.5 moles of hydrogen would be needed to consume the available nitrogen</u> (option 1).
The reaction is the following:
3H₂(g) + N₂(g) → 2NH₃(g) (1)
To know why hydrogen is considered the limiting reactant, we need to calculate the number of moles of nitrogen and hydrogen with the following equation:
![n = \frac{m}{M}](https://tex.z-dn.net/?f=%20n%20%3D%20%5Cfrac%7Bm%7D%7BM%7D%20)
Where:
m: is the mass
M: is the molar mass
- For <em>hydrogen </em>we have:
![n_{H_{2}} = \frac{m}{M} = \frac{7.00 g}{2.016 g/mol} = 3.47 \:moles](https://tex.z-dn.net/?f=%20n_%7BH_%7B2%7D%7D%20%3D%20%5Cfrac%7Bm%7D%7BM%7D%20%3D%20%5Cfrac%7B7.00%20g%7D%7B2.016%20g%2Fmol%7D%20%3D%203.47%20%5C%3Amoles%20)
- And for <em>nitrogen</em>:
![n_{N_{2}} = \frac{m}{M} = \frac{70.0 g}{28.013 g/mol} = 2.50 \:moles](https://tex.z-dn.net/?f=%20n_%7BN_%7B2%7D%7D%20%3D%20%5Cfrac%7Bm%7D%7BM%7D%20%3D%20%5Cfrac%7B70.0%20g%7D%7B28.013%20g%2Fmol%7D%20%3D%202.50%20%5C%3Amoles%20)
We can see in reaction (1) that <u>3 moles of hydrogen</u> react with <u>1 mol of nitrogen</u>, so the number of hydrogen moles needed to react nitrogen is:
![n_{H_{2}} = \frac{3\:moles\:H_{2}}{1\:moles\:N_{2}}*n_{N_{2}} = \frac{3\:moles\:H_{2}}{1\:moles\:N_{2}}*2.50 \:moles = 7.50 \:moles](https://tex.z-dn.net/?f=%20n_%7BH_%7B2%7D%7D%20%3D%20%5Cfrac%7B3%5C%3Amoles%5C%3AH_%7B2%7D%7D%7B1%5C%3Amoles%5C%3AN_%7B2%7D%7D%2An_%7BN_%7B2%7D%7D%20%3D%20%5Cfrac%7B3%5C%3Amoles%5C%3AH_%7B2%7D%7D%7B1%5C%3Amoles%5C%3AN_%7B2%7D%7D%2A2.50%20%5C%3Amoles%20%3D%207.50%20%5C%3Amoles%20)
Since we have <u>3.47 moles of hydrogen</u> and we need <u>7.50 moles</u> to react with all the mass of nitrogen, the <em>limiting reactant</em> is <em>hydrogen</em>.
We can find the number of ammonia moles produced with the limiting reactant (hydrogen) konwing that <u>3 moles of hydrogen</u> produces <u>2 moles of ammonia</u>, so:
![n_{NH_{3}} = \frac{2\:moles\:NH_{3}}{3\:moles\:H_{2}}*n_{H_{2}} = \frac{2\:moles\:NH_{3}}{3\:moles\:H_{2}}*3.47 \:moles = 2.31 \:moles](https://tex.z-dn.net/?f=%20n_%7BNH_%7B3%7D%7D%20%3D%20%5Cfrac%7B2%5C%3Amoles%5C%3ANH_%7B3%7D%7D%7B3%5C%3Amoles%5C%3AH_%7B2%7D%7D%2An_%7BH_%7B2%7D%7D%20%3D%20%5Cfrac%7B2%5C%3Amoles%5C%3ANH_%7B3%7D%7D%7B3%5C%3Amoles%5C%3AH_%7B2%7D%7D%2A3.47%20%5C%3Amoles%20%3D%202.31%20%5C%3Amoles%20)
Hence, hydrogen would produce <u>2.31 moles of ammonia</u>.
Therefore, hydrogen is the limiting reactant because <u>7.5 moles of hydrogen would be needed to consume the available nitrogen</u> (option 1).
Find more about limiting reactants here:
brainly.com/question/2948214?referrer=searchResults
I hope it helps you!