In the table in Figure 13.20, we list all of the alkanes...

In the table in Figure 13.20, we list all of the alkanes containing eight carbon atoms, along with their boiling points and associated Wiener indices. Add tnis data to the data for alkanes containing between two and seven carbon atoms, and use data-analysis software to derive a power equation $B=\alpha W^\beta$ approximating the boiling point versus Wiener index relationship for alkanes having between two and eight carbon atoms. $$ \begin{array}{|l|c|c|} \hline \text { Name } & \text { WI } & \text { BP }(\mathbf{K}) \\ \hline \text { n-octane } & 84 & 399 \\ \hline \text { 2-methylheptane } & 79 . & 391 \\ \hline \text { 3-methylheptane } & 76 & 392 \\ \hline \text { 4-methylheptane } & 75 & 391 \\ \hline \text { 2,2-dimethylhexane } & 71 & 380 \\ \hline \text { 2,3-dimethylhexane } & 70 & 389 \\ \hline \text { 2,4-dimethylhexane } & 71 & 382 \\ \hline \text { 2,5-dimethylhexane } & 74 & 382 \\ \hline \end{array} $$ $$ \begin{array}{|l|l|l|} \hline \text { 3,4-dimethylhexane } & 68 & 391 \\ \hline \text { 3,3-dimethylhexane } & 67 & 385 \\ \hline \text { 3-ethylhexane } & 72 & 392 \\ \hline \text { 2,2,3-trimethylpentane } & 63 & 383 \\ \hline \text { 2,3,4-trimethylpentane } & 65 & 386 \\ \hline \text { 3-ethyl-2-methylpentane } & 67 & 389 \\ \hline \text { 2,2,4-trimethylpentane } & 66 & 372 \\ \hline \text { 2,3,3-trimethylpentane } & 62 & 388 \\ \hline \text { 3-ethyl-3-methylpentane } & 64 & 391 \\ \hline \end{array} $$

In the table in Figure 13.20, we list all of the alkanes containing eight carbon atoms, along with their boiling points and associated Wiener indices. Add tnis data to the data for alkanes containing between two and seven carbon atoms, and use data-analysis software to derive a power equation $B=\alpha W^\beta$ approximating the boiling point versus Wiener index relationship for alkanes having between two and eight carbon atoms.
$$
\begin{array}{|l|c|c|}
\hline \text { Name } & \text { WI } & \text { BP }(\mathbf{K}) \\
\hline \text { n-octane } & 84 & 399 \\
\hline \text { 2-methylheptane } & 79 . & 391 \\
\hline \text { 3-methylheptane } & 76 & 392 \\
\hline \text { 4-methylheptane } & 75 & 391 \\
\hline \text { 2,2-dimethylhexane } & 71 & 380 \\
\hline \text { 2,3-dimethylhexane } & 70 & 389 \\
\hline \text { 2,4-dimethylhexane } & 71 & 382 \\
\hline \text { 2,5-dimethylhexane } & 74 & 382 \\
\hline
\end{array}
$$
$$
\begin{array}{|l|l|l|}
\hline \text { 3,4-dimethylhexane } & 68 & 391 \\
\hline \text { 3,3-dimethylhexane } & 67 & 385 \\
\hline \text { 3-ethylhexane } & 72 & 392 \\
\hline \text { 2,2,3-trimethylpentane } & 63 & 383 \\
\hline \text { 2,3,4-trimethylpentane } & 65 & 386 \\
\hline \text { 3-ethyl-2-methylpentane } & 67 & 389 \\
\hline \text { 2,2,4-trimethylpentane } & 66 & 372 \\
\hline \text { 2,3,3-trimethylpentane } & 62 & 388 \\
\hline \text { 3-ethyl-3-methylpentane } & 64 & 391 \\
\hline
\end{array}
$$

Key Concepts

Structure-Property Relationships

Structure-property relationships explore how variations in molecular structure, such as chain length, branching, and connectivity, affect the physical and chemical properties of substances. This approach is central in physical chemistry and materials science, as it allows prediction and tuning of properties like boiling points based on quantifiable structural parameters.

Wiener Index

The Wiener index is a topological descriptor derived from graph theory, used in chemistry to quantify the structure of a molecule by summing the shortest path distances between all pairs of atoms. It provides a numerical value that can be correlated with various physical and chemical properties of molecules, and is particularly useful in studying structure-property relationships in organic compounds.

Alkanes

Alkanes are saturated hydrocarbons consisting solely of carbon and hydrogen atoms arranged in single bonds. Their structural simplicity, combined with variations in chain length and branching, makes them ideal models for investigating how molecular structure influences physical properties such as boiling points and melting points.

Boiling Point

Boiling point is a key physical property that indicates the temperature at which a substance transitions from a liquid to a gaseous state. In the context of organic chemistry, boiling points can be influenced by molecular size, shape, and branching, and are often correlated with structural descriptors to understand trends among different homologous series.

Power Law Equation

A power law equation, represented as B = ?W^?, describes a mathematical relationship where one variable (in this case, boiling point) varies as a power of another variable (the Wiener index). This type of relationship is useful for modeling scaling behavior in physical systems, where changes in molecular descriptors result in non-linear changes in physical properties.

Nonlinear Regression Analysis

Nonlinear regression analysis is a statistical method used to fit models where the relationship between independent and dependent variables is nonlinear. It is essential in deriving equations such as power laws from empirical data, helping to estimate the parameters (? and ?) that best describe the observed relationship between molecular descriptors and properties like boiling points.

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