Q12-12-14 - Organic Chemistry (Mcmurry)

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 \({{\bf{M}}^ + }{\rm{ =  84}}\)         

 

Step-by-Step Solution

Answer

a.

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

b.

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

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

c.

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

Step 1: Molecular mass

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

Step 2: 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.

Step 3: 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 \({C_6}H{}_{12}\)

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