Theory — Strong Base Titrated by Strong Acid
H⁺(aq) + OH⁻(aq) → H₂O(l)
In this titration the titrand is a strong base solution (fully dissociated, usually NaOH or KOH),
and the titrant is a strong monoprotic acid (fully dissociated, usually HCl or HNO₃). At 25 °C,
activities are taken ≈ concentrations and water autoionization is negligible except exactly at equivalence.
Symbols
- \( C_b \) — base concentration \((\mathrm{mol\cdot L^{-1}})\)
- \( V_b \) — initial base volume \((\mathrm{mL})\ \text{or}\ (\mathrm{L});\ \text{be consistent}\)
- \( C_a \) — acid concentration \((\mathrm{mol\cdot L^{-1}})\)
- \( V_a \) — acid volume added \((\mathrm{mL})\ \text{or}\ (\mathrm{L})\)
- \( V_{\text{tot}} = V_b + V_a \) — total volume \((\text{same unit})\)
Equivalence & key volumes
- Equivalence point: moles H⁺ = moles OH⁻
\[
C_a V_a^{(\text{eq})} \;=\; C_b V_b
\quad\Rightarrow\quad
V_a^{(\text{eq})} \;=\; \frac{C_b V_b}{C_a}
\]
For strong/strong at 25 °C, pH ≈ 7.00.
- Halfway point: \(V_a = \tfrac{1}{2}V_a^{(\text{eq})}\). For strong/strong this is not a buffer and
does not satisfy pH = pKₐ; pH is found by the “before equivalence” formula below.
- ±1 mL around equivalence are often reported to show the steep jump and to aid indicator selection.
pH formulas used by the calculator
Let \(n_{\mathrm{OH^-}} = C_b\,V_b\) and \(n_{\mathrm{H^+}} = C_a\,V_a\) (with volumes in liters):
- Before equivalence \((n_{\mathrm{H^+}} < n_{\mathrm{OH^-}})\): excess base
\[
[\mathrm{OH^-}] \;=\; \frac{n_{\mathrm{OH^-}} - n_{\mathrm{H^+}}}{V_{\text{tot}}},\qquad
\mathrm{pOH} = -\log_{10}[\mathrm{OH^-}],\qquad
\mathrm{pH} = 14 - \mathrm{pOH}.
\]
- At equivalence \((n_{\mathrm{H^+}} = n_{\mathrm{OH^-}})\): neutral solution at 25 °C
\[
\mathrm{pH} \approx 7.00.
\]
- After equivalence \((n_{\mathrm{H^+}} > n_{\mathrm{OH^-}})\): excess acid
\[
[\mathrm{H^+}] \;=\; \frac{n_{\mathrm{H^+}} - n_{\mathrm{OH^-}}}{V_{\text{tot}}},\qquad
\mathrm{pH} = -\log_{10}[\mathrm{H^+}].
\]
How the curve is built
- The app evaluates pH at \(V_a=0\), \(V_a=\tfrac{1}{2}V_a^{(\text{eq})}\), \(V_a=V_a^{(\text{eq})}\),
and at
±1 mL around equivalence for a crisp jump.
- Any custom \(V_a\) values you add are also computed.
- The smooth curve is drawn from many intermediate volumes (denser sampling near the jump) and overlaid with
markers at key points.
Indicator choice (practical)
- Because the jump spans roughly pH ≈ 4 → 10 within a tiny volume interval, any indicator with a transition close to 7 is suitable.
- Good choices: bromothymol blue (≈ 6.0–7.6). Phenolphthalein (≈ 8.2–10) also works due to the steep jump but turns slightly after the true equivalence.
- Avoid methyl orange (≈ 3.1–4.4) for this system; it changes too early.
Unit consistency & assumptions
- Use consistent units for volumes (all mL or all L). The calculator accepts mL and internally converts to liters for mole balances.
- Model assumes 25 °C, strong electrolytes (complete dissociation), low ionic strength, and
concentrations typically ≥ 10⁻⁵ M. At very low concentrations, water autoionization may slightly shift the equivalence pH from 7.
Quick workflow (what the calculator does)
- Compute \(V_a^{(\text{eq})} = (C_b V_b)/C_a\) and \(V_a^{(\text{half})} = \tfrac{1}{2}V_a^{(\text{eq})}\).
- For each requested \(V_a\), evaluate the proper regime (before/at/after equivalence) and apply the formulas above.
- Report pH at
0 mL, halfway, equivalence, ±1 mL, and all custom points, then plot the curve with those highlights.
