Quick questions on Titration curves (strong vs weak combinations) and indicator choice explained: HSC Chemistry Module 6

A good indicator has an end point that coincides (within experimental tolerance) with the equivalence point. Indicator selection is the art of matching colour-change range to equivalence pH.

For a 0.100 mol/L analyte titrated with 0.100 mol/L titrant from a burette, with 25.0 mL of analyte:

Example: 0.100 mol/L $HCl$ titrated with 0.100 mol/L $NaOH$.

Example: 0.100 mol/L $CH_3COOH$ titrated with 0.100 mol/L $NaOH$.

Example: 0.100 mol/L $HCl$ titrated with 0.100 mol/L $NH_3$.

The steep section is short or absent because both sides resist pH change. The equivalence pH depends on the relative $K_a$ of the cation and $K_b$ of the anion: if $K_a > K_b$, slightly acidic; if $K_b > K_a$, slightly basic; if equal, exactly 7.

An indicator is itself a weak acid: $HIn \rightleftharpoons H^+ + In^-$, with the two forms different colours. Its colour change ($HIn$ to $In^-$) is half-complete at $pH = pK_{a,HIn}$ and effectively complete over $\pm 1$ unit. For a sharp end point, this range must lie within the steep vertical portion of the titration curve. Outside that portion, the colour change is gradual and the end point is imprecise.

Weak acid alone. $[H^+] \approx \sqrt{K_a c} = \sqrt{1.8 \times 10^{-5}} = 4.24 \times 10^{-3}$ mol/L, $pH = 2.37$.

$[HCOOH] = [HCOO^-]$, so $pH = pK_a = -\log_{10}(1.8 \times 10^{-4}) = 3.74$.

All acid converted to $HCOO^-$, total volume 50.0 mL, so $c(HCOO^-) = 0.0500$ mol/L. $K_b = K_w/K_a = 5.56 \times 10^{-11}$. $[OH^-] \approx \sqrt{K_b c} = 1.67 \times 10^{-6}$, $pOH = 5.78$, $pH = 8.22$.

Equivalence pH 8.22 lies just inside the phenolphthalein range (8.3 to 10.0). Phenolphthalein is acceptable; thymol blue (8.0 to 9.6) would also work and might give a slightly sharper transition.

True only for strong-strong. Weak acid plus strong base equivalence is basic; weak base plus strong acid equivalence is acidic.

They should coincide, but they are conceptually distinct. Equivalence is set by stoichiometry; end point is set by the indicator.

The equivalence pH is around 5; phenolphthalein would change at pH 8 to 10, far past equivalence. Use methyl orange or methyl red.

When 25.0 mL of acid is neutralised by 25.0 mL of base, the total volume is 50.0 mL. The conjugate ion concentration is half the original acid concentration.