In the Haber reaction, patented by German chemist Fritz Haber in 1908, dinitrogen gas combines with dihydrogen gas to produce gaseous ammonia. This reaction is now the first step taken to make most of the world's fertilizer. Suppose a chemical engineer studying a new catalyst for the Haber reaction finds that 505 liters per second of dinitrogen are consumed when the reaction is run at 172°C and 0.88atm. Calculate the rate at which ammonia is being produced.

24 mol/s

Explanation:

Step 1: Write tha balanced equation for the Haber process

N₂ + 3 H₂ ⇄ 2 NH₃

Step 2: Convert 172 °C to Kelvin

We will use the following expression.

K = °C + 273.15

K = 172°C + 273.15 = 445 K

Step 3: Calculate the moles of N₂ consumed per second

We will use the ideal gas equation.

P × V = n × R × T

n = P × V/R × T

n = 0.88 atm × 505 L/(0.0821 atm.L/mol.K) × 445 K

n = 12 mol

Step 4: Calculate the rate at which ammonia is being produced

12 moles of N₂ are consumed per second. Given the molar ratio of N₂ to NH₃ is 1:2, the rate of production of ammonia is:

12 mol N₂/s × 2 mol NH₃/ 1 mol N₂ = 24 mol NH₃/s