Tris(hydroxymethyl)aminomethane, known as TRIS or THAM, is a...

Tris(hydroxymethyl)aminomethane, known as TRIS or THAM, is a water-soluble base used in synthesizing surfactants and pharmaceuticals, as an emulsifying agent in cosmetics, and in cleaning mixtures for textiles and leather. In biomedical research, solutions of TRIS are used to maintain nearly constant pH for the study of enzymes and other cellular components. Given that the $\mathrm{p} K_{\mathrm{b}}$ is $5.91,$ calculate the $\mathrm{pH}$ of 0.075 $\mathrm{M}$ TRIS.

Key Concepts

Weak Base Equilibrium

This concept refers to the reversible reaction in which a weak base reacts with water to form its conjugate acid and hydroxide ions. Unlike strong bases, a weak base does not completely ionize in water, and only a fraction of its molecules accept a proton from water, establishing an equilibrium condition that is governed by the base’s dissociation constant (Kb).

Relationship between pKb and pKa

In aqueous solution at 25°C, there is a fundamental relationship between the base dissociation constant (pKb) of a weak base and the acid dissociation constant (pKa) of its conjugate acid, given by the equation pKa + pKb = 14. This relation is essential for converting between the two constants and understanding the acid-base behavior of a substance in solution.

pH and pOH Relationship

The pH of a solution is a measure of its acidity or basicity, defined as the negative logarithm of the hydronium ion concentration. pOH, defined similarly with respect to hydroxide ion concentration, is related to pH by the equation pH + pOH = 14 at 25°C. This relationship allows for the calculation of pH once the concentration of hydroxide ions is known in a basic solution.

Approximations in Equilibrium Calculations

When dealing with weak bases, the extent of ionization is typically small, which allows for useful approximations in equilibrium calculations. Assuming that the change in concentration due to ionization is negligible compared to the initial concentration simplifies the mathematical treatment, making it easier to estimate the concentration of produced ions and thereby calculate pH.

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