Question

Indeed, the cyanate ion is $ CN{O^ - } $ .
Explanation:
The reaction you are describing is called Wohler synthesis.
The idea here is that you decompose ammonium cyanate, $ N{H_4}CNO $ by heating, forming ammonia, $ N{H_3} $ and cyanic acid, $ HCN $
These two compounds will then react to form urea, $ CO{\left( {N{H_2}} \right)_2} $ .
So, how do you know what the formula of the cyanate ion present in the ammonium cyanate is? Look at the chemical formula of urea.

Answer 1

Hint: Given that the reaction described is Wohler synthesis. In this reaction, the ammonium cyanate will convert into urea, by slowly evaporating the water solution of ammonium cyanate. Based on the law of conservation of mass, the atoms in the urea should be equal to atoms of ammonium ion and cyanate ion.

Complete answer:
Ammonium cyanate is a chemical compound with the molecular formula of $ N{H_4}CNO $ . On heating, ammonium cyanate leads to the formation of ammonia, and cyanic acid. Later, these two compounds react to form urea.
The molecular formula of urea is $ CO{\left( {N{H_2}} \right)_2} $
It has four atoms of hydrogen, two atoms of nitrogen, one atom of oxygen, and one atom of carbon.
From the given explanation, urea is the only decomposition product of ammonium cyanate.
As ammonium ions have one nitrogen atom, and four hydrogen atoms.
Thus, cyanate ions must consist of one nitrogen atom, one oxygen atom, and one carbon atom.
The molecular formula of cyanate ion is $ CN{O^ - } $
From the law of conservation of mass, the atoms in ammonium ions and atoms in cyanate ions must be equal to atoms in urea.
The reaction involved will be as follows:
 $ N{H_4}CNO\xrightarrow{\Delta }N{H_3} + HCN \to CO{\left( {N{H_2}} \right)_2} $ .

Note:
According to the law of conservation of mass, the atoms in the reactants side should be equal to the atoms in the product side. So many reactions obey this law as there will be no side products in so many chemical reactions. Based on this law only, the formula of cyanate ions is determined.