A student pulls a bottle of TRIS off a shelf and notes that...

A student pulls a bottle of TRIS off a shelf and notes that the bottle says, "TRIS (basic form), $\mathrm{p} K_{\mathrm{a}}=8.3 . "$ The student tells you that if you add 0.1 mol of this compound to $100 \mathrm{mL}$ of water, the pH will be $8.3 .$ Is the student correct? Explain.

Key Concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a solution to the pKa of the acidic component and the ratio of the concentrations of the conjugate base to its acid form. This equation is central to buffer chemistry because it predicts the pH of a buffer solution when the proportions of the two species are known, particularly showing that a pH equal to the pKa corresponds to a 1:1 ratio.

pKa and Acid-Base Equilibrium

The pKa of a compound indicates the pH at which its weak acid and conjugate base are present in equal concentrations, according to its dissociation constant. It is a measure of the intrinsic strength of an acid (or the conjugate base in this case) and tells us that at the pKa, the chemical species exist in a 1:1 ratio, which is essential for understanding how the compound behaves in solution.

Buffer Solutions

Buffer solutions are mixtures of weak acids and their conjugate bases (or weak bases and their conjugate acids) that resist changes in pH upon addition of small amounts of strong acids or bases. The effectiveness of a buffer depends on both its pKa (relative to the target pH) and the appropriate ratio between the acid and base, ensuring that the pH remains stable.

Impact of Adding a Base Alone to Water

Simply dissolving a weak base in water does not automatically set the pH equal to its pKa because the pH of the solution depends on the established equilibrium between the base and its protonated form. Without the presence of the corresponding conjugate acid to form a buffer system, the final pH will be determined by other factors, including the concentration of the base and water's own ionization.

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