Chapter 10, Problem 10.2P

How many degrees of unsaturation are present in each compound?

a. ${\text{C}}_{\text{6}}{\text{H}}_{\text{6}}$

b. ${\text{C}}_8{\text{H}}_{18}$

c. ${\text{C}}_7{\text{H}}_8\text{O}$

d. ${\text{C}}_7{\text{H}}_{11}\text{Br}$

e. ${\text{C}}_5{\text{H}}_{\text{9}}\text{N}$

Interpretation Introduction

(a)

Interpretation: The number of degree of unsaturation for the given molecular formula is to be calculated.

Concept introduction: The formula to calculate the number of degree of unsaturation is,

$\text{DU}=\frac{\left(2n+2\right)-x}{2}$

Where,

• $n$ is the number of carbon atom given in molecular formula.

• $x$ is the number of hydrogen atom given in molecular formula.

Answer to Problem 10.2P

The number of degree of unsaturation for ${\text{C}}_{\text{6}}{\text{H}}_6$ is $4$.

Explanation of Solution

The given molecular formula is ${\text{C}}_{\text{6}}{\text{H}}_6$.

The number of carbon and hydrogen atoms present in ${\text{C}}_{\text{6}}{\text{H}}_6$ are six and six.

The formula to calculate the number of degree of unsaturation is,

$\text{DU}=\frac{\left(2n+2\right)-x}{2}$

Where,

• $n$ is the number of carbon atom given in molecular formula.

• $x$ is the number of hydrogen atom given in molecular formula.

Substitute the value of $n$ and $x$ in the given formula.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(6\right)+2\right)-6}{2}\\ & =& \frac{14-6}{2}\\ & =& 4\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_{\text{6}}{\text{H}}_6$ is $4$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_{\text{6}}{\text{H}}_6$ is $3$.

Interpretation Introduction

(b)

Interpretation: The number of degree of unsaturation for the given molecular formula is to be calculated.

Concept introduction: The formula to calculate the number of degree of unsaturation is,

$\text{DU}=\frac{\left(2n+2\right)-x}{2}$

Where,

• $n$ is the number of carbon atom given in molecular formula.

• $x$ is the number of hydrogen atom given in molecular formula.

Answer to Problem 10.2P

The number of degree of unsaturation for ${\text{C}}_8{\text{H}}_{18}$ is $0$.

Explanation of Solution

The given molecular formula is ${\text{C}}_8{\text{H}}_{18}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_8{\text{H}}_{18}$ are $8$ and $18$.

The formula to calculate the number of degree of unsaturation is,

$\text{DU}=\frac{\left(2n+2\right)-x}{2}$

Where,

• $n$ is the number of carbon atom given in molecular formula.

• $x$ is the number of hydrogen atom given in molecular formula.

Substitute the value of $n$ and $x$ in the given formula.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(8\right)+2\right)-18}{2}\\ & =& \frac{18-18}{2}\\ & =& 0\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_8{\text{H}}_{18}$ is $0$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_8{\text{H}}_{18}$ is $0$.

Interpretation Introduction

(c)

Interpretation: The number of degree of unsaturation for the given molecular formula is to be calculated.

Concept introduction: The formula to calculate the number of degree of unsaturation is,

$\text{DU}=\frac{\left(2n+2\right)-x}{2}$

Where,

• $n$ is the number of carbon atom given in molecular formula.

• $x$ is the number of hydrogen atom given in molecular formula.

Answer to Problem 10.2P

The number of degree of unsaturation for ${\text{C}}_7{\text{H}}_8\text{O}$ is $4$.

Explanation of Solution

The given molecular formula is ${\text{C}}_7{\text{H}}_8\text{O}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_7{\text{H}}_8\text{O}$ are $7$ and $8$.

The formula to calculate the number of degree of unsaturation is,

$\text{DU}=\frac{\left(2n+2\right)-x}{2}$

Where,

• $n$ is the number of carbon atom given in molecular formula.

• $x$ is the number of hydrogen atom given in molecular formula.

Substitute the value of $n$ and $x$ in the given formula.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(7\right)+2\right)-8}{2}\\ & =& \frac{16-8}{2}\\ & =& 4\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_7{\text{H}}_8\text{O}$ is $4$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_7{\text{H}}_8\text{O}$ is $4$.

Interpretation Introduction

(d)

Interpretation: The number of degree of unsaturation for the given molecular formula is to be calculated.

Concept introduction: The formula to calculate the number of degree of unsaturation is,

$\text{DU}=\frac{\left(2n+2\right)-x}{2}$

Where,

• $n$ is the number of carbon atom given in molecular formula.

• $x$ is the number of hydrogen atom given in molecular formula.

Answer to Problem 10.2P

The number of degree of unsaturation for ${\text{C}}_7{\text{H}}_{11}\text{Br}$ is $2$.

Explanation of Solution

The given molecular formula is ${\text{C}}_7{\text{H}}_{11}\text{Br}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_7{\text{H}}_{11}\text{Br}$ are $7$ and $11$.

If halogen atom is present in molecular formula than replace halogen and add hydrogen. Therefore, the molecular formula becomes ${\text{C}}_7{\text{H}}_{12}$.

The formula to calculate the number of degree of unsaturation is,

$\text{DU}=\frac{\left(2n+2\right)-x}{2}$

Where,

• $n$ is the number of carbon atom given in molecular formula.

• $x$ is the number of hydrogen atom given in molecular formula.

Substitute the value of $n$ and $x$ in the given formula.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(7\right)+2\right)-12}{2}\\ & =& \frac{16-12}{2}\\ & =& 2\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_7{\text{H}}_{11}\text{Br}$ is $2$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_7{\text{H}}_{11}\text{Br}$ is $2$.

Interpretation Introduction

(e)

Interpretation: The number of degree of unsaturation for given molecular formula is to be calculated.

Concept introduction: The formula to calculate the number of degree of unsaturation is,

$\text{DU}=\frac{\left(2n+2\right)-x}{2}$

Where,

• $n$ is the number of carbon atom given in molecular formula.

• $x$ is the number of hydrogen atom given in molecular formula.

Answer to Problem 10.2P

The number of degree of unsaturation for ${\text{C}}_5{\text{H}}_{\text{9}}\text{N}$ is $2$.

Explanation of Solution

The given molecular formula is ${\text{C}}_5{\text{H}}_{\text{9}}\text{N}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_5{\text{H}}_{\text{9}}\text{N}$ are $5$ and $9$. If nitrogen atom is present in molecular formula than replace nitrogen and remove hydrogen for each nitrogen atom. Therefore, the molecular formula becomes ${\text{C}}_7{\text{H}}_8$.

The formula to calculate the number of degree of unsaturation is,

$\text{DU}=\frac{\left(2n+2\right)-x}{2}$

Where,

• $n$ is the number of carbon atom given in molecular formula.

• $x$ is the number of hydrogen atom given in molecular formula.

Substitute the value of $n$ and $x$ in the given formula.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(5\right)+2\right)-2}{2}\\ & =& \frac{12-8}{2}\\ & =& 2\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_5{\text{H}}_{\text{9}}\text{N}$ is $2$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_5{\text{H}}_{\text{9}}\text{N}$ is $2$.