Problem 47 - Chemistry The Science in Context

Question

Which of these substances is the least soluble in water? a. \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{2} \mathrm{CH}_{2} \mathrm{OH}\) b. \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{4} \mathrm{CH}_{2} \mathrm{OH}\) c. \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{6} \mathrm{CH}_{2} \mathrm{OH}\) d. \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{8} \mathrm{CH}_{2} \mathrm{OH}\)

Step-by-Step Solution

Answer

a) \(\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{3}\mathrm{CH}_2\mathrm{OH}\) b) \(\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{5}\mathrm{CH}_2\mathrm{OH}\) c) \(\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{7}\mathrm{CH}_2\mathrm{OH}\) d) \(\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{8}\mathrm{CH}_2\mathrm{OH}\) Answer: d) \(\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{8}\mathrm{CH}_2\mathrm{OH}\)

Step 1: Identify the functional groups in each substance

The substances given are all alcohol compounds, as evident by the presence of the \(\mathrm{OH}\) group in each molecule. The differentiating factor is the length of the carbon chain attached to the hydroxyl group. Longer carbon chains typically decrease solubility in water.

Step 2: Examine the hydrocarbon portion of each molecule

The hydrocarbon portion of each molecule is the \(\mathrm{CH}_3\left(\mathrm{CH}_2\right)_n\mathrm{CH}_2\) part, where n varies between 2 and 8. Longer hydrocarbon chains in an alcohol molecule make the molecule more hydrophobic (water repelling). This is because the hydrocarbon part has only weak London dispersion forces with water molecules, while the polar \(\mathrm{OH}\) group can form strong hydrogen bonds with water. As the size of the hydrocarbon chain increases, the hydrophobic part of the molecule becomes more dominant.

Step 3: Determine the substance with the longest hydrocarbon chain

Comparing the substances based on their hydrocarbon chains, the substance (d) \(\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{8}\mathrm{CH}_2\mathrm{OH}\) has the longest chain.

Step 4: Identify the least soluble substance

Since the substance with the longest hydrocarbon chain is more hydrophobic and has the least ability to form hydrogen bonds with water molecules, it will be the least soluble in water. Thus, the answer is (d) \(\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{8}\mathrm{CH}_2\mathrm{OH}\).

Key Concepts

Hydrocarbon Chains

Hydrocarbon chains are composed of carbon (C) and hydrogen (H) atoms linked together. These chains can vary in length and are a fundamental component of many organic compounds.

In the substances discussed in the exercise, the hydrocarbon chains are expressed as \( \mathrm{CH}_3\left(\mathrm{CH}_2\right)_n\mathrm{CH}_2 \), where \( n \) can be 2, 4, 6, or 8.

• The longer the hydrocarbon chain, the more hydrophobic (water-repelling) the molecule becomes.
• Hydrocarbons interact with water molecules through weak London dispersion forces, which are much weaker than the forces water molecules exert on each other.

So, a molecule with a longer hydrocarbon chain will tend to be less soluble in water compared to one with a shorter chain. The large chain resists mixing with polar substances like water, leading it to exclude or "push away" water molecules.

Alcohol Functional Group

The alcohol functional group is characterized by the presence of an -OH group, also known as a hydroxyl group. This group is bonded to one of the carbon atoms in a molecule.

• The -OH group is polar because of the electronegativity difference between oxygen and hydrogen, allowing it to engage in hydrogen bonding with water molecules.
• This helps increase solubility by creating attractions between the alcohol molecules and water molecules.

In our exercise, each substance regardless of its chain length has an alcohol functional group. This constant feature contributes to each molecule's basic ability to dissolve in water. However, the effectiveness of the -OH group in promoting solubility diminishes as the hydrocarbon chain lengthens, due to the overall increased hydrophobic character of the molecule.

Hydrogen Bonding

Hydrogen bonding is a special type of attraction between a hydrogen atom, which is covalently linked to an electronegative atom like oxygen, and another electronegative atom.

• The polar nature of the alcohol's -OH group means that it can form hydrogen bonds with water, enhancing solubility.
• Hydrogen bonds are stronger than London dispersion forces, which increases their role in determining water solubility.

Despite the potent influence of hydrogen bonding, its effectiveness is compromised as the hydrocarbon chain grows longer. This is because the increased hydrophobic portion of the molecule reduces overall solubility, overshadowing the hydrogen bonding ability. The balance between the hydrophobic carbon chain and hydrogen bonding dictates the solubility of alcohols in water.