Indicate whether a protonated amine (RN⁺H₃) with a pKa value of 9 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
4. pH = 7
5. pH = 10
6. pH = 13

Verified step by step guidance

1. Determine the relationship between pKa and pH using the Henderson-Hasselbalch equation: \( \text{pH} = \text{pKa} + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) \). Here, the base is the neutral amine (RNH2), and the acid is the protonated amine (RN+H3).
2. Rearrange the equation to solve for the ratio of base to acid: \( \frac{[\text{Base}]}{[\text{Acid}]} = 10^{(\text{pH} - \text{pKa})} \).
3. Substitute the given pKa value (9) and the pH values from Problem 41 into the equation to calculate the ratio of neutral (base) to charged (acid) molecules for each pH value.
4. Interpret the ratio: If the ratio \( \frac{[\text{Base}]}{[\text{Acid}]} \) is greater than 1, there are more neutral molecules (RNH2). If the ratio is less than 1, there are more charged molecules (RN+H3).
5. For each pH value, compare the pH to the pKa: If \( \text{pH} > \text{pKa} \), the solution favors the base (neutral form). If \( \text{pH} < \text{pKa} \), the solution favors the acid (charged form).

Key Concepts

pKa and pH Relationship

The pKa value of a compound indicates the pH at which half of the species are protonated and half are deprotonated. A lower pKa means a stronger acid, while a higher pKa indicates a weaker acid. In this case, the pKa of 9 suggests that at pH values below 9, the amine will predominantly exist in its protonated form (charged), while at pH values above 9, it will be more neutral.

Protonation of Amines

Amines can exist in both protonated (charged) and deprotonated (neutral) forms. The protonated form (RN+H3) occurs when the amine accepts a proton (H+), making it positively charged. The equilibrium between these forms is influenced by the solution's pH relative to the amine's pKa, determining the predominant species in solution.

Acid-Base Equilibrium

Acid-base equilibrium describes the balance between protonated and deprotonated species in a solution. The Henderson-Hasselbalch equation can be used to predict the ratio of these species based on pH and pKa. Understanding this equilibrium is crucial for determining whether more charged or neutral molecules of the amine will be present at specific pH levels.