Chapter 13, Problem 13.104QP

Interpretation Introduction

Interpretation: The graph of carbon-to-hydrogen in carboxylic acid for the increasing number of carbon is to be plotted and compared with that of alkane and alkene.

Concept introduction: The general formula for the carboxylic acid is ${\text{C}}_{\text{2}}{\text{H}}_{\text{2n}}\text{O}$.

The general formula for the alkene is ${\text{C}}_{\text{2}}{\text{H}}_{\text{2n}}$

The general formula for the alkane is ${\text{C}}_{\text{2}}{\text{H}}_{\text{2n+2}}$

To determine: The plot of carbon-to hydrogen ratio and its comparison with that of alkane and alkene.

Answer to Problem 13.104QP

The plot of carbon to hydrogen ratio in carboxylic acid correlates better with the plot of carbon to hydrogen in alkenes.

Explanation of Solution

The molecular formula of carboxylic acid containing one to six carbons, the number of carbon and hydrogen atoms and its ratio is,

$\begin{array}{cccc}\begin{array}{l}\text{Molecular}\\ \text{formula}\end{array}& \begin{array}{l}\text{Number}\text{of}\\ \text{carbon}\text{atom}\end{array}& \begin{array}{l}\text{Number}\text{of}\\ \text{hydrogen}\text{atoms}\end{array}& \begin{array}{l}\text{Carbon}\text{to}\\ \text{hydrogen}\text{ratio}\end{array}\\ {\text{C}}_{\text{1}}{\text{H}}_{\text{2}}{\text{O}}_2& 1& 2& 1:2\\ {\text{C}}_{\text{2}}{\text{H}}_{\text{4}}{\text{O}}_2& 2& 4& 1:2\\ {\text{C}}_{\text{3}}{\text{H}}_{\text{6}}{\text{O}}_2& 3& 6& 1:2\\ {\text{C}}_{\text{4}}{\text{H}}_{\text{8}}{\text{O}}_2& 4& 8& 1:2\\ {\text{C}}_{\text{5}}{\text{H}}_{\text{10}}{\text{O}}_2& 5& 10& 1:2\\ {\text{C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_2& 6& 12& 1:2\end{array}$

Table 1

From the above data it is concluded that the general formula for the carboxylic acid is ${\text{C}}_{\text{2}}{\text{H}}_{\text{2n}}{\text{O}}_2$ and the carbon to hydrogen ratio in carboxylic acid is $1:2$.

The plot of carbon-to-hydrogen ratio in carboxylic acid as a function of number of carbon atoms is,

Figure 1

The general formula for the alkene is ${\text{C}}_{\text{2}}{\text{H}}_{\text{2n}}$

The molecular formula of alkene containing one to six carbons, the number of carbon and hydrogen atoms and its ratio is,

$\begin{array}{cccc}\begin{array}{l}\text{Molecular}\\ \text{formula}\end{array}& \begin{array}{l}\text{Number}\text{of}\\ \text{carbon}\text{atom}\end{array}& \begin{array}{l}\text{Number}\text{of}\\ \text{hydrogen}\text{atoms}\end{array}& \begin{array}{l}\text{Carbon}\text{to}\\ \text{hydrogen}\text{ratio}\end{array}\\ {\text{C}}_{\text{1}}{\text{H}}_{\text{2}}& 1& 2& 1:2\\ {\text{C}}_{\text{2}}{\text{H}}_{\text{4}}& 2& 4& 1:2\\ {\text{C}}_{\text{3}}{\text{H}}_{\text{6}}& 3& 6& 1:2\\ {\text{C}}_{\text{4}}{\text{H}}_{\text{8}}& 4& 8& 1:2\\ {\text{C}}_{\text{5}}{\text{H}}_{\text{10}}& 5& 10& 1:2\\ {\text{C}}_{\text{6}}{\text{H}}_{\text{12}}& 6& 12& 1:2\end{array}$

Table 2

From the above data it is concluded that the carbon to hydrogen ratio in alkene is $1:2$.

The general formula for the alkane is ${\text{C}}_{\text{2}}{\text{H}}_{\text{2n+2}}$

The molecular formula of alkane containing one to six carbons, the number of carbon and hydrogen atoms and its ratio is,

$\begin{array}{cccc}\begin{array}{l}\text{Molecular}\\ \text{formula}\end{array}& \begin{array}{l}\text{Number}\text{of}\\ \text{carbon}\text{atom}\end{array}& \begin{array}{l}\text{Number}\text{of}\\ \text{hydrogen}\text{atoms}\end{array}& \begin{array}{l}\text{Carbon}\text{to}\\ \text{hydrogen}\text{ratio}\end{array}\\ {\text{C}}_{\text{1}}{\text{H}}_4& 1& 4& 1:4\\ {\text{C}}_{\text{2}}{\text{H}}_6& 2& 6& 1:3\\ {\text{C}}_{\text{3}}{\text{H}}_8& 3& 8& 3:8\\ {\text{C}}_{\text{4}}{\text{H}}_{10}& 4& 10& 2:5\\ {\text{C}}_{\text{5}}{\text{H}}_{\text{12}}& 5& 12& 5:12\\ {\text{C}}_{\text{6}}{\text{H}}_{\text{14}}& 6& 14& 3:7\end{array}$

Table 3

From the above data it is concluded that the carbon to hydrogen ratio in alkane changes as the numbers of carbon and hydrogen atom increases.

Therefore, the plot of carbon to hydrogen ratio in carboxylic acid correlates better with the plot of carbon to hydrogen in alkenes.

Conclusion

The plot of carbon to hydrogen ratio in carboxylic acid correlates better with the plot of carbon to hydrogen in alkenes.