Chapter 10, Problem 10.35P

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

a. ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}$

b. ${\text{C}}_{40}{\text{H}}_{56}$

c. ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{O}}_{\text{2}}$

d. ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{Br}$

e. ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{ClO}$

f. ${\text{C}}_{\text{7}}{\text{H}}_{\text{11}}\text{N}$

g. ${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}\text{BrN}$

h. ${\text{C}}_{\text{10}}{\text{H}}_{\text{18}}\text{ClNO}$

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 10.35P

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,

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

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.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(6\right)+2\right)-8}{2}\\ & =& \frac{14-8}{2}\\ & =& 3\end{array}$

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

(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 10.35P

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,

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

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.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(40\right)+2\right)-56}{2}\\ & =& \frac{82-56}{2}\\ & =& 13\end{array}$

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

(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 10.35P

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,

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

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.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(10\right)+2\right)-16}{2}\\ & =& \frac{22-16}{2}\\ & =& 3\end{array}$

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

(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 10.35P

The number of degree of unsaturation for ${\text{C}}_{\text{8}}{\text{H}}_{\text{9}}\text{Br}$ is $3$.

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,

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

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.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(8\right)+2\right)-10}{2}\\ & =& \frac{18-10}{2}\\ & =& 4\end{array}$

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 ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}{\text{O}}_{\text{2}}$ is $3$.

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,

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

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 10.35P

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 $9$. 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,

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

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.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(8\right)+2\right)-10}{2}\\ & =& \frac{18-10}{2}\\ & =& 4\end{array}$

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

(f)

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 10.35P

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 $11$. If nitrogen atom is present in molecular formula than replace nitrogen and remove hydrogen for each nitrogen atom. Therefore, the molecular formula becomes ${\text{C}}_7{\text{H}}_{10}$.

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.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(7\right)+2\right)-10}{2}\\ & =& \frac{16-10}{2}\\ & =& 3\end{array}$

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

(g)

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 10.35P

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 $8$. If halogen atom is present in molecular formula than replace halogen and add hydrogen. If nitrogen atom is present in molecular formula than replace nitrogen and remove hydrogen for each nitrogen atom. Therefore, the molecular formula becomes ${\text{C}}_4{\text{H}}_8$.

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.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(4\right)+2\right)-8}{2}\\ & =& \frac{10-8}{2}\\ & =& 1\end{array}$

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 $1$.

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,

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

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 10.35P

The number of degree of unsaturation for ${\text{C}}_{\text{10}}{\text{H}}_{\text{18}}\text{ClNO}$ is $2$.

Explanation of Solution

The given molecular formula is ${\text{C}}_{\text{10}}{\text{H}}_{\text{18}}\text{ClNO}$.

The number of carbon and hydrogen atoms present in ${\text{C}}_{\text{10}}{\text{H}}_{\text{18}}\text{ClNO}$ are $10$ and $18$. If halogen atom is present in molecular formula than replace halogen and add hydrogen. If nitrogen atom is present in molecular formula than replace nitrogen and remove hydrogen for each nitrogen atom. Therefore, the molecular formula becomes ${\text{C}}_{10}{\text{H}}_{18}$.

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.

$\begin{array}{rll}\text{DU}& =& \frac{\left(2n+2\right)-x}{2}\\ & =& \frac{\left(2\left(10\right)+2\right)-18}{2}\\ & =& \frac{22-18}{2}\\ & =& 2\end{array}$

Therefore, the number of degree of unsaturation for ${\text{C}}_{\text{10}}{\text{H}}_{\text{18}}\text{ClNO}$ is $2$.

Conclusion

The number of degree of unsaturation for ${\text{C}}_{\text{10}}{\text{H}}_{\text{18}}\text{ClNO}$ is $2$.