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 112. liters per second of dinitroge are consumed when the reaction is run at 17.2°C and 0.88atm.
Required:
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

Answer: Rate = 0.14 kg/s

Explanation: The Haber reaction is demonstrated below in the balanced equation

$N_{2}+3H_{2}$ → $2NH_{3}$

To determine the rate of ammonia production, we need to determine the amount of nitrogen gas is being consumed.

As it is a gas, we can find moles by using Ideal Gas Law, whose formula is

PV = nRT

P is pressure

V is volume

n is moles

R is universal gas constant

T is temperature in Kelvin (K)

For the nitrogen gas, temperature will be

T = 273 + 17.2

T = 290.2 K

Solving for moles:

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

$n=\frac{0.88(112)}{0.082(290.2)}$

n = 4.14 moles

In the Haber reaction, it is consumed 4.14 moles per second of nitrogen gas.

From the balanced equation, we know 1 mol of nitrogen gas produces 2 moles of ammonia, so

$n_{NH_{3}}$ = 2(4.14)

$n_{NH_{3}}$ = 8.48 moles

Number of moles (n) is mass in grams divided by molar mass of the compound:

$n=\frac{m}{M}$

Molar mass of ammonia is M = 17.031 u, so mass produced is

m = n.M

m = 8.48(17.031)

m = 144.42 g

In kilograms, m = 0.14 kg

When consuming N₂ at a rate of 4.14 moles/s, it will be produced ammonia at a rate of 0.14 kg/s