Question

In using a mass spectrometer, a chemist sees a peak at a mass of 30.0106. Of the ¹²C₂¹H₆, ¹²C¹H₂ ¹⁶O and ¹⁴N¹⁶O, which is responsible for this peak? Pertinent masses are ¹H,1.007825; ¹⁶O,15.994915; and ¹⁴N,14.003074.

Short answer

Thecompound responsible for the peak is¹²C₂¹H₆

Step-by-step solution

Definition

The lmolar mass of a materia is defined as the mass of the substancecontained in one moleof the substance, and it is equal to the total massof the component atoms. It may be stated mathematically as follows:
Molar mass =$\frac{Weighting}{numberofmoles}$

Determination molecular mass

A peak will appear on the mass spectrometerat the place that corresponds to the molecular massof the chemical being studied. We can establish which component is responsible for a peak at 30.0106 by using the molar masses of the constituent elements to calculate the molecular mass of the complete molecule.

$$\begin{gathered} {}^{12}C_2{}^{1}H_6 \\ \left(2\times 12.01\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\right)+\left(6\times 1.007825\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\right)=30.07\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right. \\ {}^{12}C_2{}^{1}H_6{}^{16}O \\ \left(12.01\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\right)+\left(2\times 1.007825\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\right)+\left(15.994915\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\right)=30.02\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right. \\ {}^{1}N{}^{16}O \\ \left(14.003074\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\right)+\left(15.994915\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\right)=29.99\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right. \end{gathered}$$

Therefore the responsible compound is ¹²C₂¹H₆.