Question

Nitrogen (N), Phosphorus (P) and Potassium (K) are the main nutrients in plant fertilizers. According to an industry convention, the numbers on the label refer to the mass $\%$ of N, ${{P}_{2}}O$ and ${{K}_{2}}O$ in that order. What is N:P:K ratio of a 28 : 14.2: 4.7 fertilizer in terms of moles of each elements and expressing it as x:y:1.0 is:
A.1 : 0.66 : 1.0
B. 20 : 0.66 : 1.0
C. 8.4 : 1.3 : 1.0
D. 16.8 : 1.3 : 1.0

Answer 1

Use the concept of stoichiometry and the condition given in the question to derive a ratio. On simplifying this ratio to decimal places, the final answer can be obtained.

Complete answer:
In order to answer our question, we need to understand the concept of stoichiometry, moles and molar mass. Now, matter is made up of particles mainly atoms. Now, every substance has different masses, when the same volume of it is taken. So, we calculate the number of moles to get an idea about the concentration of the substance. One mole of any substance is the mass that is contained by approximately $6.022\times {{10}^{23}}$ particles inside it. This is also called the Avogadro’s number. Two elements which have the same number of atoms, i.e Avogadro's number will have the same i.e concentration of one mole, but their masses will be completely different.
So, the mass that corresponds to 1 mole of the substance is called its molar mass and the molar mass is different for different elements. Now, let us come to our question. We have been given with the following molecules and the data obtained are:
Molar mass of ${{N}_{2}}$ is 28
Molar mass of ${{P}_{2}}O$ is 78, and
Molar mass of ${{K}_{2}}O$ is 94
Now, according to the condition that is given in the question, we can write the ratio as:
$\dfrac{28}{28}:\dfrac{14.2}{78}:\dfrac{4.7}{94}$
On simplification, we get the final answer as $1:0.66:1.0$ and this gives the final answer as option A.

Note: It is to be noted that in order to find out the molar mass of a compound, the molar masses of the elements present in it are added. For diatomic molecules, the molar mass of the element is multiplied by 2. For example, calculating the molar mass of ${{H}_{2}}O$ , we have $(2\times 1)+16g\,mo{{l}^{-1}}$ .