Question

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 oC and 0.88 atm. Calculate the rate at which ammonia is being produced. Give your answer in kilograms per second. Be sure your answer has the correct number of significant digits.

Answer 1

The rate at which ammonia is being produced is 0.41 kg/sec.

Step-by-step explanation:

`N_2+3H_2\rightarrow 2NH_3` Haber reaction

Volume of dinitrogen consumed in a second = 505 L

Temperature at which reaction is carried out,T= 172°C = 445.15 K

Pressure at which reaction is carried out, P = 0.88 atm

Let the moles of dinitrogen be n.

Using an Ideal gas equation:

`PV=nRT`

`n=(PV)/(RT)=(0.88 atm* 505 L)/(0.0821 atm l/mol K* 445.15 K)=12.1597 mol`

According to reaction , 1 mol of ditnitrogen gas produces 2 moles of ammonia.

Then 12.1597 mol of dinitrogen will produce :

`(2)/(1)* 12.1597 mol=24.3194 mol` of ammonia

Mass of 24.3194 moles of ammonia =24.3194 mol × 17 g/mol

=413.43 g=0.41343 kg ≈ 0.41 kg

505 L of dinitrogen are consumed in 1 second to produce 0.41 kg of ammonia in 1 second. So the rate at which ammonia is being produced is 0.41 kg/sec.