Question

The action of bacteria on meat and fish produces a poisonous compound called cadaverine. As its name and origin imply, it stinks. It is $58.77$% $C$, $13.81$ % $H$ and $27.42$ % $N$. Its molar mass is $102$ g/mol. Determine the molecular formula of cadaverine.

• A. $C_6{H}_{16}N$
• B. $C_5{H}_{16}{N}_2$
• C. $C_5{H}_{14}{N}_2$
• D. $C_4{H}_{16}{N}_3$

Answer 1

The correct option is C $C_5{H}_{14}{N}_2$

$100$ g of cadaverine contains $58.77$ g of $C$, $13.81$ g of $H$ and $27.42$ g of $N$.
The molar masses of $C$, $H$ and $N$ are $12$ g/mol, $1$ g/mol and $14$ g/mol respectively.
The number of moles of $C$ present is $\frac{58.77}{12}=4.89$ mol
The number of moles of $H$ present is $\frac{13.81}{1}=13.81$ mol
The number of moles of $N$ present is $\frac{27.42}{14}=1.96$ mol
Hence, the molar ratio is $C:H:N=4.89:13.81:1.96$
This is approximately equal to $5:14:2$.
Hence, the empirical formula of cadaverine is $C_5{H}_{14}{N}_2$.
The empirical formula mass is $5\left(12\right)+14\left(1\right)+2\left(14\right)=60+14+28=102$ g/mol.
This is equal to the molar mass. Thus, the empirical formula and the molecular formula are same.