Calculate the pH of a solution prepared by mixing 20.00 mL of aniline, C6 H5 NH2(d=1.022 g / m

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Calculate the pH of a solution prepared by mixing 20.00 mL...

Calculate the pH of a solution prepared by mixing $20.00 \mathrm{~mL}$ of aniline, $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}(d=1.022 \mathrm{~g} / \mathrm{mL})$, with $35.0 \mathrm{~mL}$ of $1.67 M$ HCl. $K_{\mathrm{b}}$ for aniline is $4.3 \times 10^{-10} .$ (Assume volumes are additive.)

Calculate the pH of a solution prepared by mixing $20.00 \mathrm{~mL}$ of aniline, $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}(d=1.022 \mathrm{~g} / \mathrm{mL})$, with $35.0 \mathrm{~mL}$ of $1.67 M$ HCl. $K_{\mathrm{b}}$ for aniline is
$4.3 \times 10^{-10} .$ (Assume volumes are additive.)

Key Concepts

Acid?Base Neutralization and Buffer Formation

When a weak base is mixed with a strong acid, the acid will protonate part of the base, converting some of it into its conjugate acid. If both the weak base and its conjugate acid are present in significant amounts after the reaction, a buffer solution is formed. Buffer solutions resist changes in pH upon addition of small amounts of acid or base, making them important for maintaining pH stability in chemical and biological systems.

Stoichiometry in Acid–Base Reactions

Stoichiometry involves calculating the moles of reactants and products in a chemical reaction. In acid–base reactions, knowing the volumes and concentrations of the acid and base allows one to determine which reagent is limiting and to calculate the amounts of the weak base and its conjugate acid after the reaction. This step is crucial for setting up the appropriate equilibrium and buffer calculations.

Equilibrium Constants and pKa Conversion

The reaction of a weak base with a proton results in the formation of its conjugate acid, whose dissociation constant (Ka) is related to the base’s equilibrium constant (Kb) by the ionization constant of water (Kw). Converting Kb to Ka allows one to determine the acidity of the conjugate acid and calculate its pKa value. This conversion is essential when applying the Henderson–Hasselbalch equation to buffer solutions.

Henderson–Hasselbalch Equation

The Henderson–Hasselbalch equation relates the pH of a buffer solution to the pKa and the ratio of the concentrations of the conjugate base to the conjugate acid. It is given by pH = pKa + log([base]/[acid]). This equation provides a straightforward method to estimate the pH of solutions that contain both a weak acid (or weak base’s conjugate acid) and its conjugate base (or weak base), which is particularly useful in buffer calculations.