Urea is used as a source of nitrogen in fertilizer. The second step of the synthesis is heating the intermediate ammonium carbamate to produce urea shown in the equation below:
NH₂CO₂ $\rarr$ NH₄ O) NH₂ + H₂O
The reaction proceeds in 60% yield, on average, and the product is mixed with unreacted starting materials, which are readily separated from the product. They can then be recycled and undergo the process again. If one starts with 1 kg of ammonium carbamate, how many times will it have to be cycled through this reaction to give at least a 90% yield?

Question

Urea is used as a source of nitrogen in fertilizer. The second step of the synthesis is heating the intermediate ammonium carbamate to produce urea shown in the equation below:
NH₂CO₂

\rarr

NH₄ O) NH₂ + H₂O
The reaction proceeds in 60% yield, on average, and the product is mixed with unreacted starting materials, which are readily separated from the product. They can then be recycled and undergo the process again. If one starts with 1 kg of ammonium carbamate, how many times will it have to be cycled through this reaction to give at least a 90% yield?

Quizplus · Accepted Answer

To achieve at least a 90% yield starting from 1 kg of ammonium carbamate with an average yield of 60% per cycle, the material needs to be cycled through the reaction three times. After the first cycle, 60% yield gives 0.6 kg of urea. Recycling the unreacted material (40% of 1 kg = 0.4 kg) through a second cycle yields an additional 0.24 kg (60% of 0.4 kg), totaling 0.84 kg. Recycling the remaining unreacted material (40% of 0.4 kg = 0.16 kg) through a third cycle yields an additional 0.096 kg (60% of 0.16 kg), totaling 0.936 kg, which is over 90% of the initial 1 kg.

Urea Is Used as a Source of Nitrogen in Fertilizer →\rarr→

Urea Is Used as a Source of Nitrogen in Fertilizer $\rarr$