Answer
427.5k+ views
Hint: To find the nitrogen content in the compound, we can use the following formula
\[\% N = \dfrac{{{\text{Weight of N in the compound}}}}{{{\text{Molecular weight of the compound}}}} \times 100\]
Atomic weight of nitrogen is $14gmmo{l^{ - 1}}$.
Complete step by step solution:
We will find the % nitrogen in all the compounds. In order to find this, we will first find the molecular weight of all the given compounds. Finally from the %N composition, we will be able to predict the cheapest fertilizer.
Molecular weight of ${(N{H_2})_2}CO$ = 2(Atomic weight of N) + 4 (Atomic weight of H) + Atomic weight of C + Atomic weight of O
Molecular weight of ${(N{H_2})_2}CO$ = 2(14) + 4(1) + 12 + 16 = 60$gmmo{l^{ - 1}}$
Molecular weight of $N{H_3}$ = Atomic weight of N + 3(Atomic weight of H)
Molecular weight of $N{H_3}$ = 14 + 3(1) = 17$gmmo{l^{ - 1}}$
Molecular weight of $N{H_4}N{O_3}$ = 2(Atomic weight of N) + 4(Atomic weight of H) + 3(Atomic weight of O)
Molecular weight of $N{H_4}N{O_3}$ = 2(14) + 4(1) + 3(16) = 80 $gmmo{l^{ - 1}}$
Molecular weight of $HNC{(N{H_3})_2}$ = 3(Atomic weight of N) + 7(Atomic weight of H) + Atomic weight of C
Molecular weight of $HNC{(N{H_3})_2}$ = 3(14) + 7(1) + 12 = 61$gmmo{l^{ - 1}}$
Now, we will find the %Nitrogen in all the given compounds using the below given formula.
\[\% N = \dfrac{{{\text{Weight of N in the compound}}}}{{{\text{Molecular weight of the compound}}}} \times 100{\text{ }}....{\text{(1)}}\]
For Urea:
We know that the weight of N in the compound is $28gmmo{l^{ - 1}}$. So, we can write the equation (1) as
\[\% N = \dfrac{{28}}{{60}} \times 100 = 46.66\% \]
For Ammonia:
Here, the weight of N in the compound is $14gmmo{l^{ - 1}}$. So, we can write the equation (1) as
\[\% N = \dfrac{{14}}{{17}} \times 100 = 82.35\% \]
For Ammonium nitrate:
In this compound, the total weight of N in the compound is 28$gmmo{l^{ - 1}}$. So, we can write the equation (1) as
\[\% N = \dfrac{{28}}{{80}} \times 100 = 35\% \]
For Guanidine:
Here, the weight of N in the compound is 42$gmmo{l^{ - 1}}$. So, we can write the equation (1) as
\[\% N = \dfrac{{42}}{{61}} \times 100 = 68.85\% \]
So, from the above results we can say that ammonium nitrate has the least % of nitrogen in its structure. So, as the prices are set according to the nitrogen content, it will be the least expensive amongst all.
Therefore, the correct answer is (C).
Note: Note that the % nitrogen content is not dependent on the weight of the sample. So, no matter the weight of the sample, % nitrogen will remain the same in all samples with different weights of the same compound.
\[\% N = \dfrac{{{\text{Weight of N in the compound}}}}{{{\text{Molecular weight of the compound}}}} \times 100\]
Atomic weight of nitrogen is $14gmmo{l^{ - 1}}$.
Complete step by step solution:
We will find the % nitrogen in all the compounds. In order to find this, we will first find the molecular weight of all the given compounds. Finally from the %N composition, we will be able to predict the cheapest fertilizer.
Molecular weight of ${(N{H_2})_2}CO$ = 2(Atomic weight of N) + 4 (Atomic weight of H) + Atomic weight of C + Atomic weight of O
Molecular weight of ${(N{H_2})_2}CO$ = 2(14) + 4(1) + 12 + 16 = 60$gmmo{l^{ - 1}}$
Molecular weight of $N{H_3}$ = Atomic weight of N + 3(Atomic weight of H)
Molecular weight of $N{H_3}$ = 14 + 3(1) = 17$gmmo{l^{ - 1}}$
Molecular weight of $N{H_4}N{O_3}$ = 2(Atomic weight of N) + 4(Atomic weight of H) + 3(Atomic weight of O)
Molecular weight of $N{H_4}N{O_3}$ = 2(14) + 4(1) + 3(16) = 80 $gmmo{l^{ - 1}}$
Molecular weight of $HNC{(N{H_3})_2}$ = 3(Atomic weight of N) + 7(Atomic weight of H) + Atomic weight of C
Molecular weight of $HNC{(N{H_3})_2}$ = 3(14) + 7(1) + 12 = 61$gmmo{l^{ - 1}}$
Now, we will find the %Nitrogen in all the given compounds using the below given formula.
\[\% N = \dfrac{{{\text{Weight of N in the compound}}}}{{{\text{Molecular weight of the compound}}}} \times 100{\text{ }}....{\text{(1)}}\]
For Urea:
We know that the weight of N in the compound is $28gmmo{l^{ - 1}}$. So, we can write the equation (1) as
\[\% N = \dfrac{{28}}{{60}} \times 100 = 46.66\% \]
For Ammonia:
Here, the weight of N in the compound is $14gmmo{l^{ - 1}}$. So, we can write the equation (1) as
\[\% N = \dfrac{{14}}{{17}} \times 100 = 82.35\% \]
For Ammonium nitrate:
In this compound, the total weight of N in the compound is 28$gmmo{l^{ - 1}}$. So, we can write the equation (1) as
\[\% N = \dfrac{{28}}{{80}} \times 100 = 35\% \]
For Guanidine:
Here, the weight of N in the compound is 42$gmmo{l^{ - 1}}$. So, we can write the equation (1) as
\[\% N = \dfrac{{42}}{{61}} \times 100 = 68.85\% \]
So, from the above results we can say that ammonium nitrate has the least % of nitrogen in its structure. So, as the prices are set according to the nitrogen content, it will be the least expensive amongst all.
Therefore, the correct answer is (C).
Note: Note that the % nitrogen content is not dependent on the weight of the sample. So, no matter the weight of the sample, % nitrogen will remain the same in all samples with different weights of the same compound.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)