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Ch. 2 - Acids and Bases: Central to Understanding Organic Chemistry
Bruice - Organic Chemistry 8th Edition
Bruice8th EditionOrganic ChemistryISBN: 9780135213711Not the one you use?Change textbook
Chapter 3, Problem 40

As long as the pH is not less than ___________, at least 50% of a protonated amine with a pKa value of 10.4 will be in its neutral, nonprotonated form.

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1
Understand the relationship between pH, pKa, and the protonation state of an amine. The Henderson-Hasselbalch equation is key here: pH = pKa + log([A^-][HA]), where [A^-] is the concentration of the deprotonated (neutral) form and [HA] is the concentration of the protonated form.
Recognize that the problem asks for the pH at which at least 50% of the amine is in its neutral, nonprotonated form. This means the ratio of [A^-] to [HA] is 1:1.
Substitute the ratio [A^-]/[HA] = 1 into the Henderson-Hasselbalch equation. The logarithm of 1 is 0, so the equation simplifies to pH = pKa.
Identify the pKa value given in the problem, which is 10.4. This means that when the pH equals 10.4, 50% of the amine will be in its neutral form.
Conclude that the pH must not be less than 10.4 for at least 50% of the protonated amine to be in its neutral, nonprotonated form.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

pKa and pH Relationship

The pKa of a compound is the pH at which half of the species are protonated and half are deprotonated. For a weak acid or base, if the pH is below the pKa, the protonated form predominates; if above, the deprotonated form is favored. Understanding this relationship is crucial for predicting the ionization state of amines in solution.
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Protonated vs. Nonprotonated Forms

A protonated amine carries a positive charge due to the addition of a proton (H+), while its nonprotonated form is neutral. The balance between these forms is influenced by the pH of the solution relative to the pKa of the amine. Recognizing this distinction helps in determining the predominant form of the amine at a given pH.
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Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates pH, pKa, and the ratio of protonated to nonprotonated species in a solution. It is expressed as pH = pKa + log([A-]/[HA]). This equation is essential for calculating the pH at which a specific percentage of an amine is in its neutral form, aiding in the answer to the question posed.
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