Question

An organic compound made of C, H and N contains 20% nitrogen. Its minimum molecular weight is:
A.70
B.140
C.100
D.65

Answer 1

Hint: We know that the minimum molecular weight will be the total mass of element whose percentage is given, which can be calculated using formula given below:
${\text{minimum molecular weight = }}\dfrac{{100}}{{{\text{percentage of element given}}}} \times {\text{atomic mass of same element}}$
Given:
Percentage of nitrogen = 20 %

Complete step by step answer:
Now, let us assume the total molecular weight to be ‘x’, so 20 % of x will give me the atomic weight of Nitrogen.
Therefore, 20% of x = atomic weight of nitrogen
In numerical values, we can express above statement as:
\[20\% \times x = 14\]
Solving further, we get:
\[\dfrac{{20}}{{100}} \times x = 14\]
Taking all numbers to right side of equal to sign, and finding value of x, we get:
\[x = \dfrac{{14 \times 100}}{{20}}\]
Simplifying, we get value of x to be:
\[\therefore x = 70\]
Thus the correct option is (A) 70.

Additional information: We know in this question, we have Carbon (atomic weight = 12), we have Hydrogen (atomic weight = 1), and Nitrogen (atomic weight = 14).
The total molecular weight of any compound is the sum of individual atomic masses of all elements in the compound.

Note:
Alternate method:
We directly know the formula stated in hint to get, minimum molecular weight, which can be given below:
${\text{minimum molecular weight = }}\dfrac{{100}}{{{\text{percentage of element given}}}} \times {\text{atomic mass of same element}}$
Now, we also know Percentage of Nitrogen = 20 %
Atomic mass of Nitrogen = 14
Substitute these values into above equation, we get:
${\text{minimum molecular weight = }}\dfrac{{100}}{{20}} \times 14$
Now, on simplification, we get final value:
$\therefore {\text{minimum molecular weight = 70}}$
Thus option (A) 70 is the correct option.