Q.12-22E - Organic Chemistry (Mcmurry)

Question

Question: By knowing the natural abundances of minor isotopes, it’s possible to

calculate the relative heights of and M +1 peaks. If ¹³C has a natural

abundance of 1.10%, what are the relative heights of the and

M +1 peaks in the mass spectrum of benzene, C₆H₆?

Step-by-Step Solution

Answer

Answer

For benzene, the relative height of (M+1) is 6.66 % of the height of M⁺.

Step 1: Isotopic peaks in Molecular ion region

Molecules in nature do not occur as isotopically pure species. All atoms have heavier isotopes that occur in characteristic natural abundance. Molecular ion peaks of significant intensity, and due to presence of these heavier isotopes, it also appears in the mass spectra.

Step 2: Calculate Relative heights of the M + and M + 1 peaks in the mass spectrum of benzene,C 6 H 6.

The contribution of M +1 peak from ¹³C is 1.10%, and the natural abundance   ¹²C is 98.90%. The ratio of the height of the  ¹³C  peak to the height of  ¹²C  peak for one carbon atom compound is calculated as shown below.

  $$\begin{gathered} \text{Relative height of peak =}\frac{{\text{\% of natural abundance of }}^{13}\text{C}}{{\text{\% of natural abundance of }}^{12}\text{C}}\text{×100\%} \\ =\frac{1.110}{98.90}\times 100\% \\ =1.11\% \end{gathered}$$       

Benzene has six carbon atoms. For six carbon compounds, the ratio of the height of the ¹³C peak to the height of the ¹²C peak is calculated as shown below.

$$\begin{gathered} \text{Relative height of peak =}\frac{{\text{\% of natural abundance of }}^{13}\text{C}}{{\text{\% of natural abundance of }}^{12}\text{C}}\text{×100\%} \\ =6\times \frac{1.110}{98.90}\times 100\% \\ =6.66\% \end{gathered}$$

                                     

 

For benzene, the relative height of (M+1) is 6.66 % of the height of M⁺ peak.