Question

Urea \[(N{H_2}CON{H_2})\] is formed when \[C{O_2}\] reacts with \[N{H_3}\]
 \[C{O_2} + 2N{H_3} \to N{H_2}CON{H_2} + {H_2}O\]
 \[N{H_3}\] and \[C{O_2}\] are obtained in the following steps:
 \[
 I:{N_2} + 3{H_2}\xrightarrow{{90\% }}2N{H_3} \\
 II:CaC{O_3}\xrightarrow{{50\% }}CaO + C{O_2} \\
 \]
The amount of \[{N_2}\] and \[CaC{O_3}\] required to produce 60 kg of urea are X kg and Y kg respectively. The value of X +Y (nearest integer value) is:

Answer 1

Hint: Urea is an organic compound also known as carbamide. It is a waste compound of the living organism. It is the major compound of human urine. It can break the amino acid chain which can make proteins. This is known as carbamylation. Extra nitrogen is expelled from the body through urea.

Complete step by step solution:
The first organic compound which was synthesized in 1828 is urea or ammonium cyanate, the chemical formula of urea is, \[N{H_2}CON{H_2}\]. This organic compound was synthesized by the German chemist “Wohler”.
The formation reaction of urea is,
 \[C{O_2} + 2N{H_3} \to N{H_2}CON{H_2} + {H_2}O\]
For 60Kg urea according to the mole concept,
We know 1 mole of any substance is equal to its molecular weight. Therefore, 60 Kg or 6000grm urea has
 \[\dfrac{{6000}}{{60}}\]
= 100moles
Now according to the given equation of formation of urea, the number of moles of \[N{H_3}\] and \[C{O_2}\] required to prepare 100 moles of urea are 200 moles and 100 moles respectively.
Now let, to prepare 100 moles of \[C{O_2}\] the amount of \[CaC{O_3}\] required is x.
Now from the given reaction,
 \[II:CaC{O_3}\xrightarrow{{50\% }}CaO + C{O_2}\]
The yield is \[50\% \]. So, the value of moles of \[C{O_2}\] prepared from x is,
 \[\dfrac{x}{{100}} \times 50\]. Now to prepare 60kg of urea, the amount of \[C{O_2}\] required is 100 moles,
Therefore, the value of x is,
 \[
\Rightarrow \dfrac{x}{{100}} \times 50 = 100 \\
\Rightarrow \dfrac{x}{{100}} = \dfrac{{100}}{{50}} \\
\Rightarrow x = 2 \times 100 \\
\Rightarrow x = 200 \\
 \]
And in the case of ammonia formation reaction,
 \[I:{N_2} + 3{H_2}\xrightarrow{{90\% }}2N{H_3}\], from this reaction, it is clear that 2 moles of ammonia forms from one-mole nitrogen. Let the number of moles required to prepare 200 moles of carbon dioxide the number of moles required is, Y. the yield of this reaction is \[90\% \].
Therefore, the value of Y should be,
 \[
\Rightarrow \dfrac{Y}{{2 \times 100}} \times 90 = 200 \\
\Rightarrow \dfrac{Y}{{2 \times 100}} = \dfrac{{200}}{{90}} \\
\Rightarrow Y = \dfrac{{20 \times 100 \times 2}}{9} \\
\Rightarrow Y = 444.4 \\
 \]
Therefore, the value of \[\left( {X + Y} \right)\] is,
 \[\left( {X + Y} \right) = 444.4 + 200\]
= 644.4

Note: Urea is also used in many skin conditions like dry or rough, some diseases like, corns callus. Also, for some nail problems like ingrown nails. It is also used to remove the dead tissues from the wound to help to heal. Urea is one of the most important nitrogenous fertilizer in the market. It is a white crystalline organic compound. It is a water-soluble compound.