Chapter 4, Problem 4.1P

Interpretation Introduction

Interpretation: The number of hydrogen atoms in the saturated hydrocarbons that contain $\text{23,}\text{25,}\text{and}\text{27}$ carbon atoms is to be calculated.

Concept introduction: The aliphatic hydrocarbons that have only $\text{C}-\text{C}$ and $\text{C}-\text{H}$ bonds are called alkanes. They are classified as acyclic or cyclic. The acyclic alkanes are known as saturated hydrocarbons. The general molecular formula of acyclic alkanes is ${\text{C}}_n{\text{H}}_{2n+2}$.

Answer to Problem 4.1P

The number of $\text{H}$ atoms present in the saturated hydrocarbons of sex pheromone that contain $\text{23,}\text{25,}\text{and}\text{27}$ carbon atoms are $\text{48,}\text{52,}\text{and}\text{56}$ respectively.

Explanation of Solution

The given hydrocarbons of sex pheromone are saturated acyclic alkanes.

The aliphatic hydrocarbons that have only $\text{C}-\text{C}$ and $\text{C}-\text{H}$ sigma bonds are called alkanes. They are classified as acyclic or cyclic. The acyclic alkanes are known as saturated hydrocarbons.

The general molecular formula of acyclic alkanes is ${\text{C}}_n{\text{H}}_{2n+2}$.

Where,

•  n is an integer, that represents number of carbon atoms.

For the hydrocarbon of sex pheromone that contains $\text{23}$ carbon atoms:

Substitute the value of number of carbon atoms $\left(n\right)$ in general molecular formula of acyclic alkanes.

$\begin{array}{l}{\text{C}}_{23}{\text{H}}_{\left(2\times 23\right)+2}\\ {\text{C}}_{23}{\text{H}}_{48}\end{array}$

Thus, the molecular formula of hydrocarbon that contains $\text{23}$ carbon atoms is ${\text{C}}_{23}{\text{H}}_{48}$.

Hence, the number of hydrogen atoms is $48$.

For the hydrocarbon of sex pheromone that contains $\text{25}$ carbon atoms:

Substitute the value of number of carbon atoms $\left(n\right)$ in general molecular formula of acyclic alkanes.

$\begin{array}{l}={\text{C}}_{25}{\text{H}}_{\left(2\times 25\right)+2}\\ ={\text{C}}_{25}{\text{H}}_{52}\end{array}$

Thus, the molecular formula of hydrocarbon that contains $\text{25}$ carbon atoms is ${\text{C}}_{25}{\text{H}}_{52}$.

Hence, the number of hydrogen atoms is $52$.

For the hydrocarbon of sex pheromone that contains $\text{27}$ carbon atoms:

Substitute the value of number of carbon atoms $\left(n\right)$ in general molecular formula of acyclic alkanes.

$\begin{array}{l}={\text{C}}_{27}{\text{H}}_{\left(2\times 27\right)+2}\\ ={\text{C}}_{27}{\text{H}}_{56}\end{array}$

Thus, the molecular formula of hydrocarbon that contains $\text{27}$ carbon atoms is ${\text{C}}_{27}{\text{H}}_{56}$.

Hence, the number of hydrogen atoms is $56$.

Conclusion

The number of $\text{H}$ atoms in hydrocarbons of sex pheromone that contain $\text{23,}\text{25,}\text{and}\text{27}$ carbon atoms are $\text{48,}\text{52,}\text{and}\text{56}$ respectively.