Chapter 12, Problem 12.35P

Interpretation Introduction

(a)

Interpretation: The number of rings and number of pi bonds in A is to be determined. And one possible structure is to be drawn.

Concept introduction: Degree of unsaturation is used to determine the total number of rings and pi bonds present in compound by just looking at the molecular formula. It does not specify the total number of rings and total number of pi bonds individually.

Answer to Problem 12.35P

The number of pi bonds and number of rings in A is one. The possible structure is given in Figure 1.

Explanation of Solution

For compound A:

Before hydrogenation, the molecular formula is ${\text{C}}_5{\text{H}}_8$.

The maximum number of $\text{H's}$ possible for $n\text{C's}$ is $2n+2$.

The maximum number of $\text{H's}$ possible for $5\text{C's}$ is $2\left(5\right)+2=12$.

The number of $\text{H's}$ fewer than the maximum is calculated by formula,

$\text{Fewer}\text{than}\text{maximum}\text{H's}=\text{Maximum}\text{H's}-\text{Actual}\text{H's}$

Substitute the values of maximum number of $\text{H's}$ possible and actual $\text{H's}$ in the above formula.

$\begin{array}{rll}\text{Fewer}\text{than}\text{maximum}\text{H's}& =& 12\text{H's}-8\text{H's}\\ & =& 4\text{H's}\end{array}$

The degree of unsaturation is calculated by the formula,

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{\text{H's}\text{fewer}\text{than}\text{the}\text{maximum}}{\text{2H's}\text{removed}\text{for}\text{each}\text{degree}\text{of}\text{saturation}}\\ & =& \frac{4}{2}\\ & =& 2\end{array}$

Hence, the degree of unsaturation before hydrogenation is two.

After hydrogenation, the molecular formula is ${\text{C}}_5{\text{H}}_{\text{10}}$.

The maximum number of $\text{H's}$ possible for $n\text{C's}$ is $2n+2$.

The maximum number of $\text{H's}$ possible for $5\text{C's}$ is $2\left(5\right)+2=12$.

The number $\text{H's}$ fewer than the maximum is calculated by formula,

$\text{Maximum}\text{H's}-\text{Actual}\text{H's}=\text{Fewer}\text{than}\text{maximum}\text{H's}$

Substitute the values of maximum number of $\text{H's}$ possible and actual $\text{H's}$ in the above formula.

$\begin{array}{rll}\text{Fewer}\text{than}\text{maximum}\text{H's}& =& 12\text{H's}-10\text{H's}\\ & =& 2\text{H's}\end{array}$

The degree of unsaturation is calculated by the formula,

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{\text{H's}\text{fewer}\text{than}\text{the}\text{maximum}}{\text{2H's}\text{removed}\text{for}\text{each}\text{degree}\text{of}\text{saturation}}\\ & =& \frac{2}{2}\\ & =& 1\end{array}$

Hence, the degree of unsaturation after hydrogenation is one.

The number of pi bonds in A is calculated by the formula,

$\text{Number}\text{of}\pi \text{bonds}=\left(\begin{array}{l}\text{Degree}\text{of}\text{unsaturation}\text{before}\text{hydrogenation}-\\ \text{Degree}\text{of}\text{unsaturation}\text{after}\text{hydrogenation}\end{array}\right)$

Substitute the values of degree of unsaturation before hydrogenation and degree of unsaturation after hydrogenation in the above formula.

$\begin{array}{rll}\text{Number}\text{of}\pi \text{bonds}& =& 2-1\\ & =& 1\end{array}$

Hence, the number of pi bonds is one.

Number of rings is calculated by the formula,

$\text{Degree}\text{of}\text{unsaturation}=\text{Number}\text{of}\text{π}\text{bonds}+\text{Number}\text{of}\text{rings}$

Substitute the values of degree of unsaturation and number of pi bonds in the above formula.

$\begin{array}{rll}2& =& 1+\text{Number}\text{of}\text{rings}\\ \text{Number}\text{of}\text{rings}& =& 2-1\\ & =& 1\end{array}$

Hence, the number of rings is one.

The possible structure for A is,

Figure 1

Conclusion

The number of pi bonds and number of rings in A is one. The possible structure is given in Figure 1.

Interpretation Introduction

(b)

Interpretation: The number of rings and number of pi bonds in B is to be determined. And one possible structure is to be drawn.

Concept introduction: Degree of unsaturation is used to determine the total number of rings and pi bonds present in compound by just looking at the molecular formula. It does not specify the total number of rings and total number of pi bonds individually.

Answer to Problem 12.35P

The number of pi bonds and number of rings in B is one and two respectively. The possible structure is given in Figure 2.

Explanation of Solution

For compound B:

Before hydrogenation, the molecular formula is ${\text{C}}_{10}{\text{H}}_{16}$.

The maximum number of $\text{H's}$ possible for $n\text{C's}$ is $2n+2$.

The maximum number of $\text{H's}$ possible for $10\text{C's}$ is $2\left(10\right)+2=22$.

The number of $\text{H's}$ fewer than the maximum is calculated by formula,

$\text{Fewer}\text{than}\text{maximum}\text{H's}=\text{Maximum}\text{H's}-\text{Actual}\text{H's}$

Substitute the values of maximum number of $\text{H's}$ possible and actual $\text{H's}$ in the above formula.

$\begin{array}{rll}\text{Fewer}\text{than}\text{maximum}\text{H's}& =& 22\text{H's}-16\text{H's}\\ & =& 6\text{H's}\end{array}$

The degree of unsaturation is calculated by the formula,

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{\text{H's}\text{fewer}\text{than}\text{the}\text{maximum}}{\text{2H's}\text{removed}\text{for}\text{each}\text{degree}\text{of}\text{saturation}}\\ & =& \frac{6}{2}\\ & =& 3\end{array}$

Hence, the degree of unsaturation before hydrogenation is three.

After hydrogenation, the molecular formula is ${\text{C}}_{10}{\text{H}}_{\text{18}}$.

The maximum number of $\text{H's}$ possible for $n\text{C's}$ is $2n+2$.

The maximum number of $\text{H's}$ possible for $10\text{C's}$ is $2\left(10\right)+2=22$.

The number $\text{H's}$ fewer than the maximum is calculated by formula,

$\text{Maximum}\text{H's}-\text{Actual}\text{H's}=\text{Fewer}\text{than}\text{maximum}\text{H's}$

Substitute the values of maximum number of $\text{H's}$ possible and actual $\text{H's}$ in the above formula.

$\begin{array}{rll}\text{Fewer}\text{than}\text{maximum}\text{H's}& =& 22\text{H's}-18\text{H's}\\ & =& 4\text{H's}\end{array}$

The degree of unsaturation is calculated by the formula,

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{\text{H's}\text{fewer}\text{than}\text{the}\text{maximum}}{\text{2H's}\text{removed}\text{for}\text{each}\text{degree}\text{of}\text{saturation}}\\ & =& \frac{4}{2}\\ & =& 2\end{array}$

Hence, the degree of unsaturation after hydrogenation is two.

The number of pi bonds in A is calculated by the formula,

$\text{Number}\text{of}\pi \text{bonds}=\left(\begin{array}{l}\text{Degree}\text{of}\text{unsaturation}\text{before}\text{hydrogenation}-\\ \text{Degree}\text{of}\text{unsaturation}\text{after}\text{hydrogenation}\end{array}\right)$

Substitute the values of degree of unsaturation before hydrogenation and degree of unsaturation after hydrogenation in the above formula.

$\begin{array}{rll}\text{Number}\text{of}\pi \text{bonds}& =& 3-2\\ & =& 1\end{array}$

Hence, the number of pi bonds is one.

Number of rings is calculated by the formula,

$\text{Degree}\text{of}\text{unsaturation}=\text{Number}\text{of}\text{π}\text{bonds}+\text{Number}\text{of}\text{rings}$

Substitute the values of degree of unsaturation and number of pi bonds in the above formula.

$\begin{array}{rll}3& =& 1+\text{Number}\text{of}\text{rings}\\ \text{Number}\text{of}\text{rings}& =& 3-1\\ & =& 2\end{array}$

Hence, the number of rings is two.

The possible structure for B is,

Figure 2

Conclusion

The number of pi bonds and number of rings in B is one and two respectively. The possible structure is given in Figure 2.

Interpretation Introduction

(c)

Interpretation: The number of rings and number of pi bonds in B is to be determined. And one possible structure is to be drawn.

Concept introduction: Degree of unsaturation is used to determine the total number of rings and pi bonds present in compound by just looking at the molecular formula. It does not specify the total number of rings and total number of pi bonds individually.

Answer to Problem 12.35P

The number of pi bonds and number of rings in C is four and one respectively. The possible structure is given in Figure 3.

Explanation of Solution

For compound C:

Before hydrogenation, the molecular formula is ${\text{C}}_8{\text{H}}_8$.

The maximum number of $\text{H's}$ possible for $n\text{C's}$ is $2n+2$.

The maximum number of $\text{H's}$ possible for $8\text{C's}$ is $2\left(8\right)+2=18$.

The number of $\text{H's}$ fewer than the maximum is calculated by formula,

$\text{Fewer}\text{than}\text{maximum}\text{H's}=\text{Maximum}\text{H's}-\text{Actual}\text{H's}$

Substitute the values of maximum number of $\text{H's}$ possible and actual $\text{H's}$ in the above formula.

$\begin{array}{rll}\text{Fewer}\text{than}\text{maximum}\text{H's}& =& 18\text{H's}-8\text{H's}\\ & =& 10\text{H's}\end{array}$

The degree of unsaturation is calculated by the formula,

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{\text{H's}\text{fewer}\text{than}\text{the}\text{maximum}}{\text{2H's}\text{removed}\text{for}\text{each}\text{degree}\text{of}\text{saturation}}\\ & =& \frac{10}{2}\\ & =& 5\end{array}$

Hence, the degree of unsaturation before hydrogenation is five.

After hydrogenation, the molecular formula is ${\text{C}}_8{\text{H}}_{\text{16}}$.

The maximum number of $\text{H's}$ possible for $n\text{C's}$ is $2n+2$.

The maximum number of $\text{H's}$ possible for $8\text{C's}$ is $2\left(8\right)+2=18$.

The number $\text{H's}$ fewer than the maximum is calculated by formula,

$\text{Maximum}\text{H's}-\text{Actual}\text{H's}=\text{Fewer}\text{than}\text{maximum}\text{H's}$

Substitute the values of maximum number of $\text{H's}$ possible and actual $\text{H's}$ in the above formula.

$\begin{array}{rll}\text{Fewer}\text{than}\text{maximum}\text{H's}& =& 18\text{H's}-16\text{H's}\\ & =& 2\text{H's}\end{array}$

The degree of unsaturation is calculated by the formula,

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}& =& \frac{\text{H's}\text{fewer}\text{than}\text{the}\text{maximum}}{\text{2H's}\text{removed}\text{for}\text{each}\text{degree}\text{of}\text{saturation}}\\ & =& \frac{2}{2}\\ & =& 1\end{array}$

Hence, the degree of unsaturation after hydrogenation is one.

The number of pi bonds in A is calculated by the formula,

$\text{Number}\text{of}\pi \text{bonds}=\left(\begin{array}{l}\text{Degree}\text{of}\text{unsaturation}\text{before}\text{hydrogenation}-\\ \text{Degree}\text{of}\text{unsaturation}\text{after}\text{hydrogenation}\end{array}\right)$

Substitute the values of degree of unsaturation before hydrogenation and degree of unsaturation after hydrogenation in the above formula.

$\begin{array}{rll}\text{Number}\text{of}\pi \text{bonds}& =& 5-1\\ & =& 4\end{array}$

Hence, the number of pi bonds is four.

Number of rings is calculated by the formula,

$\text{Degree}\text{of}\text{unsaturation}=\text{Number}\text{of}\text{π}\text{bonds}+\text{Number}\text{of}\text{rings}$

Substitute the values of degree of unsaturation and number of pi bonds in the above formula.

$\begin{array}{rll}5& =& 4+\text{Number}\text{of}\text{rings}\\ \text{Number}\text{of}\text{rings}& =& 5-4\\ & =& 1\end{array}$

Hence, the number of rings is one.

The possible structure for C is,

Figure 3

Conclusion

The number of pi bonds and number of rings in C is four and one respectively. The possible structure is given in Figure 3.