Chapter 10, Problem 10.37P

Calculate the number of degrees of unsaturation f or each molecular formula.

a. ${\text{C}}_3{\text{H}}_4$ c. ${\text{C}}_{40}{\text{H}}_{56}$ e. ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{O}}_{\text{2}}$ g. ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{ClO}$ i. ${\text{C}}_7{\text{H}}_{11}\text{N}$

b. ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}$ d. ${\text{C}}_{\text{8}}{\text{H}}_{\text{8}}\text{O}$ f. ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{Br}$ h. ${\text{C}}_{\text{7}}{\text{H}}_9\text{Br}$ j. ${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}\text{BrN}$

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,

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Answer to Problem 10.37P

The number of degree of unsaturation for ${\text{C}}_3{\text{H}}_4$ is $2$.

Explanation of Solution

The given molecular formula is ${\text{C}}_3{\text{H}}_4$.

The number of carbon and hydrogen atoms present in ${\text{C}}_3{\text{H}}_4$ are three and four.

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

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

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

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

Substitute all the values in the given formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}\\ & =& \frac{2\left(3\right)+2+0+0-4}{2}\\ & =& \frac{8-4}{2}\\ & =& 2\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_3{\text{H}}_4$ is $2$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_3{\text{H}}_4$ is $2$.

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,

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Answer to Problem 10.37P

The number of degree of unsaturation for ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}$ is $3$.

Explanation of Solution

The given molecular formula is ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}$ are six and eight.

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

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Substitute all the values in the given formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}\\ & =& \frac{2\left(6\right)+2+0-0-8}{2}\\ & =& \frac{14-8}{2}\\ & =& 3\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}$ is $3$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}$ is $3$.

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,

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Answer to Problem 10.37P

The number of degree of unsaturation for ${\text{C}}_{40}{\text{H}}_{56}$ is $13$.

Explanation of Solution

The given molecular formula is ${\text{C}}_{40}{\text{H}}_{56}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_{40}{\text{H}}_{56}$ are $40$ and $56$.

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

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Substitute all the values in the given formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}\\ & =& \frac{2\left(40\right)+2+0-0-56}{2}\\ & =& \frac{82-56}{2}\\ & =& 13\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_{40}{\text{H}}_{56}$ is $13$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_{40}{\text{H}}_{56}$ is $13$.

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,

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Answer to Problem 10.37P

The number of degree of unsaturation for ${\text{C}}_8{\text{H}}_8\text{O}$ is $5$.

Explanation of Solution

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

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

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

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

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

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

Substitute all the values in the given formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}\\ & =& \frac{2\left(8\right)+2+0+0-8}{2}\\ & =& \frac{18-8}{2}\\ & =& 5\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_8{\text{H}}_8\text{O}$ is $5$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_8{\text{H}}_8\text{O}$ is $5$.

Interpretation Introduction

(e)

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,

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Answer to Problem 10.37P

The number of degree of unsaturation for ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{O}}_{\text{2}}$ is $3$.

Explanation of Solution

The given molecular formula is ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{O}}_{\text{2}}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{O}}_{\text{2}}$ are $10$ and $16$.

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

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Substitute all the values in the given formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{2{\text{N}}_C+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}\\ & =& \frac{2\left(10\right)+2+0+0-16}{2}\\ & =& \frac{22-16}{2}\\ & =& 3\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{O}}_{\text{2}}$ is $3$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{O}}_{\text{2}}$ is $3$.

Interpretation Introduction

(f)

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,

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Answer to Problem 10.37P

The number of degree of unsaturation for ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{Br}$ is $4$.

Explanation of Solution

The given molecular formula is ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{Br}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{Br}$ are $8$ and $9$. If halogen atom is present in molecular formula than replace halogen and add hydrogen. Therefore, the molecular formula becomes ${\text{C}}_{\text{8}}{\text{H}}_{10}$.

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

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Substitute all the values in the given formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}\\ & =& \frac{2\left(8\right)+2+0-1-9}{2}\\ & =& \frac{18-10}{2}\\ & =& 4\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{Br}$ is $4$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{Br}$ is $4$.

Interpretation Introduction

(g)

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,

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Answer to Problem 10.37P

The number of degree of unsaturation for ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{ClO}$ is $4$.

Explanation of Solution

The given molecular formula is ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{ClO}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{ClO}$ are $8$ and $9$.

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

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Substitute all the values in the given formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}\\ & =& \frac{2\left(8\right)+2+0-1-9}{2}\\ & =& \frac{18-10}{2}\\ & =& 4\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{ClO}$ is $4$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{ClO}$ is $4$.

Interpretation Introduction

(h)

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,

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Answer to Problem 10.37P

The number of degree of unsaturation for ${\text{C}}_{\text{7}}{\text{H}}_9\text{Br}$ is $3$.

Explanation of Solution

The given molecular formula is ${\text{C}}_{\text{7}}{\text{H}}_9\text{Br}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_{\text{7}}{\text{H}}_9\text{Br}$ are $7$ and $9$. If halogen atom is present in molecular formula than replace halogen and add hydrogen. Therefore, the molecular formula becomes ${\text{C}}_7{\text{H}}_{10}$.

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

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Substitute all the values in the given formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}\\ & =& \frac{2\left(7\right)+2+0-1-9}{2}\\ & =& \frac{16-10}{2}\\ & =& 3\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_{\text{7}}{\text{H}}_9\text{Br}$ is $3$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_{\text{7}}{\text{H}}_9\text{Br}$ is $3$.

Interpretation Introduction

(i)

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,

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Answer to Problem 10.37P

The number of degree of unsaturation for ${\text{C}}_{\text{7}}{\text{H}}_{\text{11}}\text{N}$ is $3$.

Explanation of Solution

The given molecular formula is ${\text{C}}_{\text{7}}{\text{H}}_{\text{11}}\text{N}$.

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

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

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Substitute all the values in the given formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}\\ & =& \frac{2\left(7\right)+2+1-11}{2}\\ & =& \frac{16-10}{2}\\ & =& 3\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_{\text{7}}{\text{H}}_{\text{11}}\text{N}$ is $3$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_{\text{7}}{\text{H}}_{\text{11}}\text{N}$ is $3$.

Interpretation Introduction

(j)

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,

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Answer to Problem 10.37P

The number of degree of unsaturation for ${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}\text{BrN}$ is $1$.

Explanation of Solution

The given molecular formula is ${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}\text{BrN}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}\text{BrN}$ are $4$ and $8$.

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

$\text{Degree}\text{of}\text{unsaturation}=\frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}$

Where,

• ${\text{N}}_C$ is the number of carbon atoms.

• ${\text{N}}_{\text{N}}$ is the number of nitrogen atoms.

• ${\text{N}}_{\text{X}}$ is the number of halogen atoms.

• ${\text{N}}_{\text{H}}$ is the number of hydrogen atoms.

Substitute all the values in the given formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{2{\text{N}}_{\text{C}}+2+{\text{N}}_{\text{N}}-{\text{N}}_{\text{X}}-{\text{N}}_{\text{H}}}{2}\\ & =& \frac{2\left(4\right)+2+1-1-8}{2}\\ & =& \frac{10-8}{2}\\ & =& 1\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}\text{BrN}$ is $1$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}\text{BrN}$ is $1$.