Indicate whether an alcohol (ROH) with a pK_a value of 15 has more charged or more neutral molecules in a solution with the pH values given in Problem 41.
1. pH = 1
2. pH = 3
3. pH = 5

Verified step by step guidance

1. Step 1: Recall the relationship between pKa, pH, and the ratio of charged to neutral species. The Henderson-Hasselbalch equation is used to determine the ratio of the conjugate base (charged form, RO⁻) to the neutral form (ROH): \( \text{pH} = \text{pKa} + \log \left( \frac{[\text{RO}^-]}{[\text{ROH}]} \right) \).
2. Step 2: Rearrange the Henderson-Hasselbalch equation to solve for the ratio \( \frac{[\text{RO}^-]}{[\text{ROH}]} \): \( \frac{[\text{RO}^-]}{[\text{ROH}]} = 10^{\text{pH} - \text{pKa}} \).
3. Step 3: For each pH value (12, 33, and 5), calculate \( \text{pH} - \text{pKa} \) to determine whether the solution favors the charged form (RO⁻) or the neutral form (ROH). If \( \text{pH} > \text{pKa} \), the charged form (RO⁻) predominates. If \( \text{pH} < \text{pKa} \), the neutral form (ROH) predominates.
4. Step 4: For pH = 12, calculate \( \text{pH} - \text{pKa} = 12 - 15 = -3 \). Since \( \text{pH} < \text{pKa} \), the neutral form (ROH) predominates in this case.
5. Step 5: Repeat the process for pH = 33 and pH = 5. For pH = 33, \( \text{pH} - \text{pKa} = 33 - 15 = 18 \), so the charged form (RO⁻) predominates. For pH = 5, \( \text{pH} - \text{pKa} = 5 - 15 = -10 \), so the neutral form (ROH) predominates.

Key Concepts

pKa and pH Relationship

The pKa value of a compound indicates the acidity of that compound, with lower pKa values corresponding to stronger acids. In a solution, the pH reflects the concentration of hydrogen ions (H+). When the pH is lower than the pKa, the compound is more likely to be protonated (charged), while at a higher pH, it tends to be deprotonated (neutral). Understanding this relationship is crucial for predicting the charge state of alcohols in different pH environments.

Protonation and Deprotonation

Protonation refers to the addition of a proton (H+) to a molecule, which can change its charge state. For alcohols, the hydroxyl group (–OH) can be protonated to form an oxonium ion (–OH2+), making it positively charged. Conversely, deprotonation occurs when a proton is removed, resulting in a neutral molecule. The balance between these processes is influenced by the solution's pH relative to the compound's pKa.

Charge Distribution in Solutions

In a solution, the distribution of charged versus neutral molecules depends on the pH relative to the pKa of the solute. For an alcohol with a pKa of 15, at very low pH (like 1 or 3), the majority of molecules will be protonated and thus charged. As the pH increases towards 5, more molecules will be deprotonated, leading to a higher proportion of neutral molecules. This concept is essential for predicting the behavior of alcohols in various pH conditions.