How many liters of hydrogen are needed to react completely with 100 L of nitrogen gas at 1000K and 2500 atm?

Question

How many liters of hydrogen are needed to react completely with 100 L of nitrogen gas at 1000K and 2500 atm?

I need a formula, and a brief explaination for this problem. Thanks!

Answer 1

Nitrogen is an inert gas so your word choice is puzzling. React?

You are seeking details to the Haber process of producing ammonia. Simply mixing the two gases will not cause a reaction. A catalyst is necessary.

Answer 2

N2 + 3H2 = 2NH3
No. of moles occupied by 100L of nitrogen gas at 1000K and
2500 atm is calculated using the ideal gas equation
PV = nRT
where P is the pressure of the gas,V is volume of the gas
n is no.of moles,R is gas constant,T is temperature
Given P=2500atm,T=1000K and V=100L
R=8.314 lit-atm/mol-K
therefore no.of moles of N2 = PV/RT
=2500x100/8.314x1000=30.06
1 mole of N2 reacts with 3 moles of H2 to produce 2 moles
of NH3
no.of moles of H2 required for 30.06 moles of N2 to produce
NH3 = 3x30.06/1=90.18