Sketch a titration curve (pH versus mL of titrant) for each...

Sketch a titration curve (pH versus mL of titrant) for each of the following three hypothetical weak acids when titrated with $0.100 \mathrm{M} \mathrm{NaOH} .$ Select suitable indicators for the titrations from Figure $17-7$. [Hint: Select a few key points at which to estimate the pH of the solution.] (a) $10.00 \mathrm{mL}$ of $0.100 \mathrm{M} \mathrm{HX} ; K_{\mathrm{a}}=7.0 \times 10^{-3}$ (b) $10.00 \mathrm{mL}$ of $0.100 \mathrm{M} \mathrm{HY} ; K_{\mathrm{a}}=3.0 \times 10^{-4}$ (c) $10.00 \mathrm{mL}$ of $0.100 \mathrm{M} \mathrm{HZ} ; K_{\mathrm{a}}=2.0 \times 10^{-8}$

Sketch a titration curve (pH versus mL of titrant) for each of the following three hypothetical weak acids when titrated with $0.100 \mathrm{M} \mathrm{NaOH} .$ Select suitable indicators for the titrations from Figure $17-7$. [Hint:
Select a few key points at which to estimate the pH of the solution.]
(a) $10.00 \mathrm{mL}$ of $0.100 \mathrm{M} \mathrm{HX} ; K_{\mathrm{a}}=7.0 \times 10^{-3}$
(b) $10.00 \mathrm{mL}$ of $0.100 \mathrm{M} \mathrm{HY} ; K_{\mathrm{a}}=3.0 \times 10^{-4}$
(c) $10.00 \mathrm{mL}$ of $0.100 \mathrm{M} \mathrm{HZ} ; K_{\mathrm{a}}=2.0 \times 10^{-8}$

Key Concepts

Titration Curve

A titration curve is a graphical representation of the pH of a solution as a function of the volume of titrant added. In acid-base titrations, the curve reflects the changes in pH from the initial acidic (or basic) solution, through the buffering region, to the equivalence point and past it, clearly showing how the addition of a titrant alters the hydrogen ion concentration. This curve is fundamental for analyzing the titration process, determining the pKa, and identifying the suitable regions for indicator transitions.

Equivalence Point

The equivalence point in a titration is where the amount of titrant added is stoichiometrically equivalent to the amount of analyte present. In the context of a weak acid titrated with a strong base, the pH at the equivalence point will be greater than 7 due to the hydrolysis of the conjugate base formed. Identifying this point is critical as it is used to calculate the concentration of unknown species and to choose the proper indicator.

Buffer Region and Half-Equivalence Point

The buffer region during a titration occurs when both the weak acid and its conjugate base are present, resisting large changes in pH. At the half-equivalence point, the concentrations of the acid and its conjugate base are equal, and the pH is equal to the pKa of the acid. This region is important for understanding the acid’s dissociation behavior and helps in accurately sketching the titration curve.

Acid Strength (Ka and pKa)

The acid dissociation constant, Ka, and its logarithmic form, pKa, quantify the strength of an acid. In titration curves, acids with higher Ka (or lower pKa) values will show less pronounced buffering and higher initial pH increases, whereas very weak acids display a more gradual change in pH. Understanding Ka and pKa is essential for predicting the titration curve’s shape and for determining the appropriate points for curve sketching.

Indicator Selection

Selecting an appropriate indicator for titration involves matching its color change range with the pH change around the equivalence point of the titration. For weak acid-strong base titrations, the pH at the equivalence point exceeds 7, and an indicator with a transition range in the alkaline region is preferred. This ensures that the observed color change closely corresponds to the true equivalence point, facilitating accurate titration results.

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