Question

Suppose a chemical engineer studying a new catalyst for the Haber reaction finds that liters per second of dinitrogen are consumed when the reaction is run at and the dinitrogen is supplied at . 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 question is incomplete. Here is the complete 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.°C and 0.88 atm. Calculate the rate at which ammonia is being produced. Give your answer in kilogram per second. Be sure your answer has the correct number of significant digits.

Answer: Rate = 0.41 kg/s

Explanation: The balanced Haber reaction is

$N_{2}+3H_{2}\rightarrow2NH_{3}$

As all the components are gases, we can use Ideal Gas Law, which relates Pressure (P), Volume (V), Temperature (T) and Moles (n) in the following formula:

PV = nRT

where

R is gas constant and, in this case, is R = 0.082 L.atm.K⁻¹mol⁻¹

T is in Kelvin

Converting Celsius in Kelvin:

T = 273 + 172

T = 445 K

Calculating moles

$n=\frac{PV}{RT}$

$n=\frac{0.88(505)}{0.082(445)}$

n = 12.18 moles

According to the balanced equation, for 1 mol of dinitrogen gas consumed, 2 moles of ammonia is produced.

With 12.18 moles of dinitrogen, the reaction will result in

2(12.18) = 24.36 moles of ammonia

Molar mass of ammonia is M = 17.031 g/mol.

In 24.36 moles, there are

$m=n.M$

m = 24.36.17.031

m = 414.87 grams

Since it's asking in kilograms: m = 0.41 kg.

In the beginning, it is said that dinitrogen gas is consumed at a rate of liters per second. So, the production rate of ammonia will be 0.41 kg/s.