Q18E - Organic Chemistry (Mcmurry)

Question

In light of the nitrogen rule mentioned in Problem 12-17, what is the molecular formula of pyridine, M⁺=79?

Step-by-Step Solution

Answer

The molecular formula of pyridine, M⁺= 79 is ${\mathrm{C}}_5{\mathrm{H}}_5\mathrm{N}$.

Step 1: Nitrogen rule

According to nitrogen rule an organic compound having odd molar mass contain odd number of nitrogen atoms and compound having even molar mass contain even number of nitrogen atoms.

Step 2: Calculate molecular formula of pyridine, M + = 79

As we have M⁺= 79 is an odd number, pyridine contains an odd number of Nitrogen atom. If pyridine contain one nitrogen atom (atomic weight = 14) the remaining atoms would have formula weight of 65, corresponding to $-{\mathrm{C}}_5{\mathrm{H}}_5$. ${\mathrm{C}}_5{\mathrm{H}}_5\mathrm{N}$is, in fact the molecular formula of pyridine.

According to rule of 13, divide 79 by 13

                          $\frac{79}{13}=13\begin{array}{c}6\\ \overline{)\begin{array}{l}79\\ \underset{\_}{-78}\\ 1\\ \end{array}}\end{array}$ 

The remainder is 1. The basic C-H formula is: ${\mathrm{C}}_{\mathrm{n}}{\mathrm{H}}_{(\mathrm{n}+\mathrm{r})}$

Here n=6 and r=1

                        

                               ${\mathrm{C}}_6{\mathrm{H}}_{(6+1)}={\mathrm{C}}_6{\mathrm{H}}_7$

As, molecular formula is odd it also contain odd nitrogen atom in it.

Thus,

As, ${\mathrm{C}}_5{\mathrm{H}}_5=(12\times 5)+(1\times 5)$

                 = 60 + 5

                  =65

By adding one odd number of nitrogen atom we have,${\mathrm{C}}_5{\mathrm{H}}_5\mathrm{N}=60+5+14=79$.