91Ó°ÊÓ

The mass of a compound is calculated with the individual mass.High-resolution mass spectrometers are known to provide the exact mass of any element up to four decimal places.

The exact masses of the most abundant isotopes of the elements C, H, O, N are given below:

Table of exact mass of C, H, N, and O

The high-resolution mass spectrum provides the exact mass to be 153.0680.

The two possible molecular formulas are: ${\text{C}}_{\text{8}}{\text{H}}_{\text{11}}{\text{NO}}_{\text{2}}$and ${\mathrm{C}}_7{\mathrm{H}}_{11}{\mathrm{N}}_3\mathrm{O}$

The exact mass of the molecular formula ${\text{C}}_{\text{8}}{\text{H}}_{\text{11}}{\text{NO}}_{\text{2}}$is:

$\begin{array}{c}{\text{M}}_{{\text{C}}_{\text{8}}{\text{H}}_{\text{11}}{\text{NO}}_{\text{2}}}\text{ = }\left({\text{8 ×â¶Ä‰M}}_{\text{C}}\right)\text{ + }\left({\text{11 ×â¶Ä‰M}}_{\text{H}}\right)\text{ + }\left({\text{1× M}}_{\text{N}}\right)\text{ + }\left({\text{2 ×â¶Ä‰M}}_{\text{O}}\right)\\ =\text{ }\left(\text{8 ×â¶Ä‰}12.0000\right)\text{ + }\left(\text{11 ×â¶Ä‰}1.00783\right)\text{ + }\left(\text{1× }14.0031\right)\text{ + }\left(\text{2 ×â¶Ä‰}15.9949\right)\\ =\text{ }96\text{ }+\text{ }11.08613\text{ }+\text{ }14.0031\text{ }+\text{ }31.9898\\ =\text{ }153.07903\end{array}$

The exact mass of the molecular formula ${\mathrm{C}}_7{\mathrm{H}}_{11}{\mathrm{N}}_3\mathrm{O}$ is:

$\begin{array}{c}{\text{M}}_{{\text{C}}_{\text{7}}{\text{H}}_{\text{11}}{\text{N}}_{\text{3}}\text{O}}\text{ = }\left(7{\text{ ×â¶Ä‰M}}_{\text{C}}\right)\text{ + }\left({\text{11 ×â¶Ä‰M}}_{\text{H}}\right)\text{ + }\left({\text{3× M}}_{\text{N}}\right)\text{ + }\left(1{\text{ ×â¶Ä‰M}}_{\text{O}}\right)\\ =\text{ }\left(7\text{ ×â¶Ä‰}12.0000\right)\text{ + }\left(\text{11 ×â¶Ä‰}1.00783\right)\text{ + }\left(\text{2× }14.0031\right)\text{ + }\left(1\text{ ×â¶Ä‰}15.9949\right)\\ =\text{ }84\text{ }+\text{ }11.08613\text{ }+\text{ }28.0062\text{ }+\text{ }15.9949\\ =\text{ }139.08723\end{array}$

From the two values, it can be observed that the exact mass of ${\text{C}}_{\text{8}}{\text{H}}_{\text{11}}{\text{NO}}_{\text{2}}$is similar to that obtained from the spectrum. Hence, the formula for dopamine is ${\text{C}}_{\text{8}}{\text{H}}_{\text{11}}{\text{NO}}_{\text{2}}$.