Fritz Haber, a German chemist, discovered a way to synthesize ammonia gas (NH3) by combining hydrogen and nitrogen gases according to the following equation: 3H2(g) + N2(g) → 2NH3(g)

What volume of nitrogen is needed to produce 250.0 L of ammonia gas at STP?
L
What volume of hydrogen is needed to produce 2.50 mol NH3 at STP?
L

Volume of nitrogen needed  = 125.5 L

Volume of hydrogen needed = 84.05 L

Explanation:

Given data:

Volume of ammonia produced = 250.0 L

Volume of nitrogen needed = ?

Solution:

Chemical equation:

N₂ + 3H₂  →    2NH₃

Number of moles of ammonia:

PV = nRT

1 atm× 250.0 L = n × 0.0821 amt.L/mol.K × 273K

250.0 atm.L = n × 22.41 amt.L/mol

n = 250.0 atm.L /22.41 amt.L/mol

n = 11.2 mol

Now we will compare the moles of ammonia with nitrogen.

             NH₃          :           N₂

               2             :            1

             11.2            :         1/2×11.2 = 5.6 mol

Volume of nitrogen needed:

PV = nRT

1 atm× V  = 5.6 mol × 0.0821 amt.L/mol.K × 273K

V  = 125.5amt.L/1 atm

V = 125.5 L

2nd)

Given data:

Number of moles of ammonia produced = 2.50 mol

Volume of hydrogen needed = ?

Solution:

Chemical equation:

N₂ + 3H₂  →    2NH₃

Now we will compare the moles of ammonia and hydrogen.

                     NH₃          :          H₂

                       2            :            3

                    2.50         :           3/2×2.50 = 3.75 mol    

Volume of hydrogen:

PV = nRT

1 atm × V = 3.75 mol × 0.0821 amt.L/mol.K × 273K

V = 84.05 amt.L/1 atm

V = 84.05 L

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