Question

Question: Propose structures for compounds that fit the following mass-spectral data:

(a) A hydrocarbon with ${\mathbf{M}}^{\mathbf{+}}\mathbf{=}\mathbf{132}$

(b) A hydrocarbon with ${\mathbf{M}}^{\mathbf{+}}\mathbf{=}\mathbf{166}$

(c) A hydrocarbon with ${\mathbf{M}}^{\mathbf{+}}\mathbf{=}\mathbf{84}$

Short answer

Possible structures of molecule:

a)

${\mathrm{C}}_{10}{\mathrm{H}}_{12}$

b)

${\mathrm{C}}_{12}{\mathrm{H}}_{22}$

c)

${\mathrm{C}}_6{\mathrm{H}}_{12}$

Step-by-step solution

Molecular mass

Molecular mass of a substance is the sum of atomic masses of all its atoms in a molecule.

Calculation of molecular formula

• These molecules have only hydrogen and carbon.

• Molecular mass of carbon is 12 and molecular mass of hydrogen is 1.

• Sum of molecular mass of C and H is$12+1=13$

• Now divide the given molecular mass by 13.

• The quotient indicates the number of carbon and number of hydrogen is equal to the quotient plus the remainder.

Molecular formula of given molecules

(a) A hydrocarbon with molecular weight 132:

• Given by: $\frac{132}{13}=10\frac{2}{13}$

• This indicates that there are 10 carbon and 12 hydrogens.

• So, the formula is${\mathrm{C}}_{10}{\mathrm{H}}_{12}$

  
  

  
  

  
  

(b) A hydrocarbon with molecular weight 166:

• Given by: $\frac{166}{13}=12\frac{10}{13}$

• This indicates that there are 12 carbon and 22 hydrogen.

• So, the formula is ${\mathrm{C}}_{12}{\mathrm{H}}_{22}$

  
  

  
  

  
  

Here one more structure is possible with formula ${\mathrm{C}}_{13}{\mathrm{H}}_{10}$.

(c) A hydrocarbon with molecular weight 84:

• Given by: $\frac{84}{13}=6\frac{6}{13}$

• This indicates that there are 10 carbon and 12 hydrogen.

• So, the formula is${\mathrm{C}}_6{\mathrm{H}}_{12}$