Question

50 kg ${N_2}$ and 10 kg ${H_2}$ are mixed to produce $N{H_3}$. Calculate the ammonia gas formed. Identify the limiting reactant.

Answer 1

Hint:. The reaction for ammonia formation is -
${N_2} + 3{H_2} \to 2N{H_3}$
From this, by converting mass into moles; we can find the moles of ammonia formed.
Further, the limiting reagent is the reactant which is present in smaller quantities and the quantity of product is determined from it. So, the reactant which will decide the formation of the product will be the limiting reactant.

Complete step by step answer:
We know the reaction for formation of ammonia can be written as -
${N_2} + 3{H_2} \to 2N{H_3}$
This means one mole of Nitrogen reacts with three moles of hydrogen to give ammonia gas.
We have the mass of ${N_2}$= 50 kg = 50000 g
Mass of ${H_2}$= 10 kg = 10000 g
First, we will find moles of nitrogen and hydrogen.
Moles of ${N_2}$= $\dfrac{{Given{\text{ mass of }}{N_2}}}{{Molar{\text{ mass of }}{N_2}}}$
Moles of ${N_2}$= $\dfrac{{50000}}{{28}}$
Moles of ${N_2}$= $17.86 \times {10^2}$moles

Moles of ${H_2}$= $\dfrac{{Given{\text{ mass of }}{{\text{H}}_2}}}{{Molar{\text{ mass of }}{{\text{H}}_2}}}$
Moles of ${H_2}$= $\dfrac{{10000}}{2}$
Moles of ${H_2}$= 5000 moles

We have 1 mole of Nitrogen that reacts with three moles of hydrogen to give ammonia gas.
So, the number of moles of hydrogen required to react with $17.86 \times {10^2}$ moles of nitrogen = $3 \times 17.86 \times {10^2}$
Number of moles of hydrogen required to react with $17.86 \times {10^2}$ moles of nitrogen = $5.36 \times {10^3}$ moles
But we have 5000 moles. So, the hydrogen is limiting reactant because it is deciding the amount of product formed.
So, the amount of ammonia formation will be decided by hydrogen.
We have that the three moles of hydrogen give two moles of ammonia.
So, 1 mole of hydrogen will give = $\dfrac{2}{3}$

So, 5000 moles of hydrogen will give = $\dfrac{2}{3} \times 5000$
So, 5000 moles of hydrogen will give = $3.33 \times {10^3}$ moles
So, the total amount of ammonia gas formed is $3.33 \times {10^3}$ moles and hydrogen is the limiting reactant.

Note: It must be noted that the number of moles of a molecule can be found by dividing the given mass of molecule with the molar mass of molecule. The molar mass of nitrogen is 28 and not 14 because it exists as ${N_2}$. It has two atoms. Similarly, the molar mass of hydrogen is 2 and not 1 because it exists as ${H_2}$.