Rationalize the trend in water solubility for the following simple alcohols: $$\begin{array}{lc} \text { Alcohol } & \begin{array}{c} \text { Solubility } \\ \left(\mathrm{g} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O} \text { at } 20^{\circ} \mathrm{C}\right) \end{array} \\ \hline \text { Methanol, } \mathrm{CH}_{3} \mathrm{OH} & \text { Soluble in all proportions } \\ \text { Ethanol, } \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} & \text { Soluble in all proportions } \\ \text { Propanol, } \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} & \text { Soluble in all proportions } \\ \text { Butanol, } \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{2} \mathrm{CH}_{2} \mathrm{OH} & 8.14 \\ \text { Pentanol, } \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{3} \mathrm{CH}_{2} \mathrm{OH} & 2.64 \\ \text { Hexanol, } \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{4} \mathrm{CH}_{2} \mathrm{OH} & 0.59 \\ \text { Heptanol, } \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{5} \mathrm{CH}_{2} \mathrm{OH} & 0.09 \\ \hline \end{array}$$

Step by step solution

01

Understanding molecular structure and solubility

In order to rationalize the trend in water solubility for the given simple alcohols, it's necessary to first understand how molecular structure can influence solubility. In general, solubility depends on the ability of a substance to form favorable interactions with the solvent. In this case, the solvent is water, which is a highly polar molecule due to the presence of polar O-H bonds. Thus, substances that are also polar and can participate in hydrogen bonding will generally be more soluble in water.

02

Analyze the structures of the given alcohols

The alcohols given in the exercise have the following general structure: $$\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)^{n}\mathrm{CH}_{2}\mathrm{OH}$$ where n is the number of methylene (-CH2-) groups in the molecule. As the number n increases, the size of the hydrocarbon chain increases as well. Notice that each alcohol has a polar hydroxyl (O-H) group at the end of the molecule, which can participate in hydrogen bonding with water molecules.

03

Relate molecular structure to solubility

As n increases in the general structure of the alcohols, the hydrocarbon chain (the non-polar part of the molecule) becomes larger, while the polar hydroxyl group remains the same. This means that as the alcohols become larger, the proportion of the molecule that can effectively interact with the polar water molecules decreases. Consequently, the balance between the polar and non-polar portions of the molecule shifts towards the non-polar portion, causing the overall solubility in water to decrease.

04

Consider the solubility values

The given solubilities are as follows: - Methanol, Ethanol, and Propanol: Soluble in all proportions - Butanol: 8.14 g/100g H2O - Pentanol: 2.64 g/100g H2O - Hexanol: 0.59 g/100g H2O - Heptanol: 0.09 g/100g H2O It is evident that as the size of the alcohol molecules increases (from methanol to heptanol), the solubility in water decreases. This trend supports our reasoning that as the hydrocarbon chain becomes larger, the molecule becomes less polar, resulting in a decrease in solubility in water. In summary, the trend in water solubility for the simple alcohols can be rationalized by considering the balance between the polar hydroxyl groups and the non-polar hydrocarbon chains in the molecules. As the size of the hydrocarbon chain increases, so does the non-polar character of the alcohol, causing a decrease in solubility in the polar solvent (water).

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