Consider an unknown base, RNH. One experiment titrates a 50.0-mL aqueous solution containing 2.5

Consider an unknown base, RNH. One experiment titrates a...

Consider an unknown base, RNH. One experiment titrates a $50.0-\mathrm{mL}$ aqueous solution containing $2.500 \mathrm{~g}$ of the base. This titration requires $59.90 \mathrm{~mL}$ of $0.925 \mathrm{M} \mathrm{HCl}$ to reach the equivalence point. A second experiment uses a $50.0-\mathrm{mL}$ solution of the unknown base identical to what was used in the first experiment. To this solution is added $29.95 \mathrm{~mL}$ of $0.925 \mathrm{M}$ HCl. The pH after the HCl addition is 10.77 . (a) What is the molar mass of the unknown base? (b) What is $K_{\mathrm{b}}$ for the unknown base? (c) What is $K_{\mathrm{a}}$ for $\mathrm{RNH}_{2}^{+} ?$

Consider an unknown base, RNH. One experiment titrates a $50.0-\mathrm{mL}$ aqueous solution containing $2.500 \mathrm{~g}$ of the base. This titration requires $59.90 \mathrm{~mL}$ of $0.925 \mathrm{M} \mathrm{HCl}$ to reach the equivalence point. A second experiment uses a $50.0-\mathrm{mL}$ solution of the unknown base identical to what was used in the first experiment. To this solution is added $29.95 \mathrm{~mL}$ of $0.925 \mathrm{M}$ HCl. The pH after the HCl addition is 10.77 .
(a) What is the molar mass of the unknown base?
(b) What is $K_{\mathrm{b}}$ for the unknown base?
(c) What is $K_{\mathrm{a}}$ for $\mathrm{RNH}_{2}^{+} ?$

Key Concepts

Base and Acid Dissociation Constants (Kb and Ka)

The base dissociation constant (Kb) measures the strength of a weak base in solution by its ability to accept a proton, whereas the acid dissociation constant (Ka) measures the strength of its conjugate acid. These constants are interrelated through the water dissociation constant (Ka × Kb = Kw), and calculating them is essential for understanding the acid–base behavior of the substances involved.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the pKa (or pKb) and the ratio of the concentrations of conjugate base to weak acid. In titration problems where a weak base and its conjugate acid coexist, this equation provides a way to calculate either the pH or the dissociation constant, given the concentration ratio.

Weak Base Equilibrium

Weak base equilibrium refers to the reversible reaction of a weak base with water, where only a fraction of the base accepts a proton to form its conjugate acid. Understanding this equilibrium is critical for calculating the base dissociation constant (Kb), which quantifies the strength of the weak base.

Titration

Titration is an analytical technique used to determine the concentration of a solute in a solution by reacting it with a titrant of known concentration. In the context of acid–base titrations, it involves the gradual addition of an acid to a base or vice versa until the reaction reaches completion at the equivalence point, where the amount of titrant added is stoichiometrically equivalent to the analyte present.

Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. By using the known concentrations and volumes of the titrant and the measured equivalence point, one can relate the moles of reactants involved. This is fundamental for deducing the molar mass of an unknown substance and understanding the reaction's balanced equation.

Equivalence Point

The equivalence point in a titration is the stage where the moles of titrant added equal the moles of the analyte originally present in the solution. This concept is crucial for accurately determining the stoichiometry of the reaction and subsequently calculating properties such as the molar mass of an unknown compound.

Molar Mass Determination

Molar mass determination is the process of calculating the mass of one mole of a substance. In titration experiments, after finding the number of moles of the substance reacting through stoichiometry, dividing the known mass of the substance by its mole value gives its molar mass, which is an essential physical property in characterizing compounds.