Chapter 12, Problem 12.7P

Compound	Molecular formula before hydrogenation	Molecular formula after hydrogenation	Number of rings	Number of pi bonds
A	${\text{C}}_{\text{10}}{\text{H}}_{\text{12}}$	${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}$	?	?
B	?	${\text{C}}_4{\text{H}}_{\text{10}}$	$0$	$1$
C	${\text{C}}_6{\text{H}}_8$	?	$1$	?

Complete the missing information for compounds A, B, and C, each subjected to hydrogenation.

The number of rings and π bonds refers to the reactant (A, B, or C) prior to hydrogenation.

Expert Solution & Answer

Interpretation Introduction

Interpretation: The missing information in the given table is to be completed.

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 12.7P

The missing information about compounds A, B and C is completed in the table given below.

Compound	Molecular formula before hydrogenation	Molecular formula after hydrogenation	Number of rings	Number of pi bonds
A	${\text{C}}_{\text{10}}{\text{H}}_{\text{12}}$	${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}$	2	3
B	${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}$	${\text{C}}_4{\text{H}}_{\text{10}}$	0	1
C	${\text{C}}_6{\text{H}}_8$	${\text{C}}_6{\text{H}}_{12}$	1	2

Explanation of Solution

For compound A:

Before hydrogenation, the molecular formula is ${\text{C}}_{\text{10}}{\text{H}}_{\text{12}}$.

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.

$\begin{array}{rll}\text{Fewer}\text{than}\text{maximum}\text{H's}& =& 22\text{H's}-12\text{H's}\\ & =& 10\text{H's}\end{array}$

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 ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}$.

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 $10\text{C's}$ 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.

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

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 after hydrogenation is three.

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.

$\begin{array}{rll}\text{Number}\text{of}\pi \text{bonds}& =& 5-3\\ & =& 2\end{array}$

Hence, the number of pi bonds is two.

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.

$\begin{array}{rll}5& =& 2+\text{Number}\text{of}\text{rings}\\ \text{Number}\text{of}\text{rings}& =& 5-2\\ & =& 3\end{array}$

Hence, the number of rings is three.

For compound B:

After hydrogenation, the molecular formula is ${\text{C}}_{\text{4}}{\text{H}}_{\text{10}}$.

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 $4\text{C's}$ is $2\left(4\right)+2=10$.

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

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

Since both maximum number of $\text{H's}$ possible and actual $\text{H's}$ are same. The number of $\text{H's}$ fewer than the maximum is zero.

Hence, the degree of unsaturation after hydrogenation is zero.

The number of pi bonds in B 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 number of pi bonds and degree of unsaturation after hydrogenation in the above formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}\text{before hydrogenation}& =& 0+1\\ & =& 1\end{array}$

Hence, degree of unsaturation before hydrogenation is one.

Before hydrogenation,

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 $4\text{C's}$ is $2\left(4\right)+2=10$.

The degree of unsaturation is calculated by the formula,

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

Hence, the number of $\text{H's}$ fewer than the maximum is two.

The number $\text{H's}$ 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 $\text{H's}$ fewer than the maximum in the above formula.

$\begin{array}{rll}\text{Actual}\text{H's}& =& 10\text{H's}-2\text{H's}\\ & =& \text{8H's}\end{array}$

Hence, the molecular formula before hydrogenation is ${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}$.

For compound C:

Before hydrogenation, the molecular formula is ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}$

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 $10\text{C's}$ is $2\left(6\right)+2=14$.

The number $\text{H's}$ 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.

$\begin{array}{rll}\text{Fewer}\text{than}\text{maximum}\text{H's}& =& 14\text{H's}-8\text{H's}\\ & =& 6\text{H's}\end{array}$

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.

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 rings in the above formula.

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

Hence, the number of pi bonds is two.

The degree of unsaturation after hydrogenation is equal to the number of rings present in the compound. Hence, degree of unsaturation after hydrogenation is one.

After hydrogenation,

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 $2\left(6\right)+2=14$.

The degree of unsaturation is calculated by the formula,

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

Hence, the number of $\text{H's}$ fewer than the maximum is two.

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 $\text{H's}$ fewer than the maximum in the above formula.

$\begin{array}{rll}\text{Actual}\text{H's}& =& 14\text{H's}-2\text{H's}\\ & =& \text{12H's}\end{array}$

Hence, the molecular formula before hydrogenation is ${\text{C}}_6{\text{H}}_{12}$.

The missing information about compounds A, B and C is completed in the table given below.

Compound	Molecular formula before hydrogenation	Molecular formula after hydrogenation	Number of rings	Number of pi bonds
A	${\text{C}}_{\text{10}}{\text{H}}_{\text{12}}$	${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}$	2	3
B	${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}$	${\text{C}}_4{\text{H}}_{\text{10}}$	0	1
C	${\text{C}}_6{\text{H}}_8$	${\text{C}}_6{\text{H}}_{12}$	1	2

Table 1

Conclusion

The missing information about compounds A, B and C is completed in the table 1.

Interpretation Introduction

Interpretation: The missing information in the given table is to be completed.

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 12.7P

The missing information about compounds A, B and C is completed in the table given below.

Compound	Molecular formula before hydrogenation	Molecular formula after hydrogenation	Number of rings	Number of pi bonds
A	${\text{C}}_{\text{10}}{\text{H}}_{\text{12}}$	${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}$	2	3
B	${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}$	${\text{C}}_4{\text{H}}_{\text{10}}$	0	1
C	${\text{C}}_6{\text{H}}_8$	${\text{C}}_6{\text{H}}_{12}$	1	2

Explanation of Solution

For compound A:

Before hydrogenation, the molecular formula is ${\text{C}}_{\text{10}}{\text{H}}_{\text{12}}$.

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.

$\begin{array}{rll}\text{Fewer}\text{than}\text{maximum}\text{H's}& =& 22\text{H's}-12\text{H's}\\ & =& 10\text{H's}\end{array}$

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 ${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}$.

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 $10\text{C's}$ 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.

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

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 after hydrogenation is three.

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.

$\begin{array}{rll}\text{Number}\text{of}\pi \text{bonds}& =& 5-3\\ & =& 2\end{array}$

Hence, the number of pi bonds is two.

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.

$\begin{array}{rll}5& =& 2+\text{Number}\text{of}\text{rings}\\ \text{Number}\text{of}\text{rings}& =& 5-2\\ & =& 3\end{array}$

Hence, the number of rings is three.

For compound B:

After hydrogenation, the molecular formula is ${\text{C}}_{\text{4}}{\text{H}}_{\text{10}}$.

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 $4\text{C's}$ is $2\left(4\right)+2=10$.

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

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

Since both maximum number of $\text{H's}$ possible and actual $\text{H's}$ are same. The number of $\text{H's}$ fewer than the maximum is zero.

Hence, the degree of unsaturation after hydrogenation is zero.

The number of pi bonds in B 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 number of pi bonds and degree of unsaturation after hydrogenation in the above formula.

$\begin{array}{rll}\text{Degree}\text{of}\text{unsaturation}\text{before hydrogenation}& =& 0+1\\ & =& 1\end{array}$

Hence, degree of unsaturation before hydrogenation is one.

Before hydrogenation,

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 $4\text{C's}$ is $2\left(4\right)+2=10$.

The degree of unsaturation is calculated by the formula,

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

Hence, the number of $\text{H's}$ fewer than the maximum is two.

The number $\text{H's}$ 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 $\text{H's}$ fewer than the maximum in the above formula.

$\begin{array}{rll}\text{Actual}\text{H's}& =& 10\text{H's}-2\text{H's}\\ & =& \text{8H's}\end{array}$

Hence, the molecular formula before hydrogenation is ${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}$.

For compound C:

Before hydrogenation, the molecular formula is ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}$

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 $10\text{C's}$ is $2\left(6\right)+2=14$.

The number $\text{H's}$ 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.

$\begin{array}{rll}\text{Fewer}\text{than}\text{maximum}\text{H's}& =& 14\text{H's}-8\text{H's}\\ & =& 6\text{H's}\end{array}$

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.

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 rings in the above formula.

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

Hence, the number of pi bonds is two.

The degree of unsaturation after hydrogenation is equal to the number of rings present in the compound. Hence, degree of unsaturation after hydrogenation is one.

After hydrogenation,

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 $2\left(6\right)+2=14$.

The degree of unsaturation is calculated by the formula,

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

Hence, the number of $\text{H's}$ fewer than the maximum is two.

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 $\text{H's}$ fewer than the maximum in the above formula.

$\begin{array}{rll}\text{Actual}\text{H's}& =& 14\text{H's}-2\text{H's}\\ & =& \text{12H's}\end{array}$

Hence, the molecular formula before hydrogenation is ${\text{C}}_6{\text{H}}_{12}$.

The missing information about compounds A, B and C is completed in the table given below.

Compound	Molecular formula before hydrogenation	Molecular formula after hydrogenation	Number of rings	Number of pi bonds
A	${\text{C}}_{\text{10}}{\text{H}}_{\text{12}}$	${\text{C}}_{\text{10}}{\text{H}}_{\text{16}}$	2	3
B	${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}$	${\text{C}}_4{\text{H}}_{\text{10}}$	0	1
C	${\text{C}}_6{\text{H}}_8$	${\text{C}}_6{\text{H}}_{12}$	1	2

Table 1

Conclusion

The missing information about compounds A, B and C is completed in the table 1.