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Spectrometry using high-resolution mass spectrometers to find the accurate molecular weight of a compound is called HRMS.

In this method, the formula mass is calculated with accuracy up to 4 decimal places.

It is extensively used in drug analysis to find the exact chemical composition of drugs.

The mass spectrum of a compound gives the m/z value of the molecular ion which can be used to find the molecular mass.

The molecular mass of a compound can also be obtained by adding the exact masses of all the atoms present in the compound. Then, this molecular mass can be compared to the molecular mass from the mass spectrum to find the molecular formula of the unknown compound.

The exact mass of analgesic as obtained from the mass spectrum is 151.0640.

The exact masses of carbon, hydrogen, nitrogen, and oxygen are 12.0000, 1.00783, 14.0031, and 15.9949 respectively.

Therefore,

The exact mass of ${\mathrm{C}}_7{\mathrm{H}}_5{\mathrm{NO}}_3$can be given as:

$\begin{array}{c}{\mathrm{m}}_{{\mathrm{C}}_7{\mathrm{H}}_5{\mathrm{NO}}_3}=(7×12)+(5×1.00783)+(1×14.0031)+(3×15.9949)\\ =151.0270\end{array}$

The exact mass of ${\mathrm{C}}_8{\mathrm{H}}_9{\mathrm{NO}}_2$can be given as:

$\begin{array}{c}{\mathrm{m}}_{{\mathrm{C}}_8{\mathrm{H}}_9{\mathrm{NO}}_2}=(8×12)+(9×1.00783)+(1×14.0031)+(2×15.9949)\\ =151.0634\end{array}$

The exact mass of ${\text{C}}_{10}{\mathrm{H}}_{17}\mathrm{N}$can be given as:

$\begin{array}{c}{\mathrm{m}}_{{\mathrm{C}}_{10}{\mathrm{H}}_{17}\mathrm{N}}=(10×12)+(17×1.00783)+(1×14.0031)\\ =151.1362\end{array}$

The exact mass of X is closest to${\mathrm{C}}_8{\mathrm{H}}_9{\mathrm{NO}}_2$.

Hence, the molecular formula of analgesic is ${\mathrm{C}}_8{\mathrm{H}}_9{\mathrm{NO}}_2$.