Question

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

(a) A hydrocarbon with\({{\bf{M}}^ + }{\rm{ = }}{\bf{132}}\)

(b) A hydrocarbon with\({{\bf{M}}^ + }{\rm{ = }}{\bf{1}}66\)

(c) A hydrocarbon with\({{\bf{M}}^ + }{\rm{ = 84}}\)

Short answer

a.

\({C_{10}}H{}_{12}\)

b.

\({C_{12}}H{}_{22}\)

\({C_{12}}H{}_{22}\)

c.

\({C_6}H{}_{12}\)

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 12hydrogens.
• So, the formula is \({C_{10}}H{}_{12}\)

\({C_{10}}H{}_{12}\)

(b) A hydrocarbon with molecular weight 166:

• Given by: \(\frac{{166}}{{13}} = 12\frac{{10}}{{13}}\)\(\begin{array}{l}\frac{{84}}{{13}} = 6\frac{6}{{13}}\\{C_6}H{}_{12}\end{array}\)
• This indicates that there are 12 carbon and 22 hydrogen.
• So, the formula is \({C_{12}}H{}_{22}\)

\({C_{12}}H{}_{22}\)

Here one more structure is possible with formula\({C_{13}}H{}_{10}\).

\({C_{13}}H{}_{10}\)

(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 \({C_6}H{}_{12}\)

\({C_6}H{}_{12}\)