Ammonia is used for fertilizer production and has been critical to successful agriculture. A steady-state chemical process is used to convert nitrogen (N2) and hydrogen (H2) to ammonia (NH3). The reaction is N2 +3H2->2NH3 One of the inlet streams to the reactor contains 95% nitrogen and the balance helium, on a molar basis, and flows at a rate of 200 lbmol/hr. A second stream of pure hydrogen (density = 0.08 lbm/ft3) enters the reactor at a rate of 80,000 ft3/hr. A single stream leaves the reactor. If all of the nitrogen is converted in the reaction, what is the molar flow rate of hydrogen in the exiting stream?

The molar flow rate of hydrogen in the exiting stream = 2604.6 lbmol/hr.

Explanation:

First off, the equation for the reaction

N₂ + 3H₂ > 2NH₃

But before the reaction, we find out the amount of each reactant coming into the reaction.

For Nitrogen,

Nitrogen is contained in a 200 lbmol/hr stream with helium, but Nitrogen has a molar percentage of 95%.

Hence molar flowrate of Nitrogen in steam 1 = 0.95 × 200 = 190 lbmol/hr

Then for Hydrogen,

Hydrogen is contained in a second stream with a volumetric flowrate of 80000 ft³/hr with a density of 0.08 lbm/ft³.

Mass flowrate = density × volumetric flowrate = 80000 × 0.08 = 6400 lbm/hr

Molar flow rate = (Mass flowrate)/(Molar mass)

Molar mass of Hydrogen = 2.016 lbm/lbmol

Molar flowrate of Hydrogen = 6400/2.016 = 3174.6 lbmol/hr.

Back to the stoichiometric balance for the reaction

N₂ + 3H₂ > 2NH₃

Nitrogen is said to be totally used up in this reaction, that is, Nitrogen is the limiting reagent. The limiting reagent determines the amount of product (Ammonia) that'll be formed and the amount of other reactants (Hydrogen) that will be required for the reaction.

1 mole of Nitrogen requires 3 moles of Hydrogen

190 lbmol/hr of Nitrogen will require (190×3/1) lbmol/hr of Hydrogen, That is, 570 lbmol/hr.

Molar flowrate of Hydrogen coming into the reaction = 3174.6 lbmol/hr

Amount of Hydrogen that is used up = 570 lbmol/hr

Molar flowrate of unreacted Hydrogen exiting the reaction = 3174.6 - 570 = 2604.6 lbmol/hr.

Hence, the molar flow rate of hydrogen in the exiting stream is 2604.6 lbmol/hr.

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