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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
[tex]N_{2}+3H_{2}\rightarrow2NH_{3}[/tex]
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
[tex]n=\frac{PV}{RT}[/tex]
[tex]n=\frac{0.88(505)}{0.082(445)}[/tex]
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
[tex]m=n.M[/tex]
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.
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