Estimation of Alkalinity of Water by Acid–Base Titration
Comprehensive notes for IITs/NITs and other colleges students: principle, reagents, apparatus, procedure, derivations, solved example, diagrams, exam tips and revision box. By Mohan Dangi( Gold medalist) NIT-Warangal-2024
1. Objective
Determine the alkalinity of a water sample and express it as mg/L (ppm) as CaCO3 by titration with a standard strong acid using phenolphthalein and methyl orange endpoints.
2. Definitions & Units
- Alkalinity: the acid‑neutralizing capacity of water — the amount of strong acid required to lower the pH to a specified endpoint (commonly pH 8.3 and pH 4.5).
- Reported units: mg/L as CaCO3 (same convention as hardness).
- Equivalent weight of CaCO3 = $M_{CaCO_3}/2 \approx 50.0435\ \mathrm{g\ per\ eq}$.
3. Principle & Key Reactions
Alkalinity derives from species that react with H+: hydroxide (OH−), carbonate (CO32−), and bicarbonate (HCO3−). The titration with a strong acid neutralizes these species in sequence depending on pH.
Key equilibrium reactions:
- $\mathrm{CO_3^{2-} + H^+ \rightleftharpoons HCO_3^- }$
- $\mathrm{HCO_3^- + H^+ \rightleftharpoons H_2CO_3 }$
- $\mathrm{OH^- + H^+ \rightarrow H_2O }$
4. Types of Alkalinity (P, M/T)
Phenolphthalein alkalinity (P): measured by titration to pH ≈ 8.3 (phenolphthalein endpoint). It corresponds to the acid equivalents attributable to hydroxide (OH−) and half the carbonate (CO32−) species, commonly expressed in meq/L.
Total (methyl orange) alkalinity (M or T): measured by titration to pH ≈ 4.5 (methyl orange endpoint). Total alkalinity includes OH−, CO32−, and HCO3−.
Relationships:
- MO (total) alkalinity (meq/L) = [OH−] + [HCO3−] + 2[CO32−]
- P (phenolphthalein) alkalinity (meq/L) = [OH−] + [CO32−]
5. Reagents & Standard Solutions
| Reagent | Notes |
|---|---|
| Standard acid (e.g., 0.0200 N H$_2$SO$_4$ or 0.0200 N HCl) | Standardize against primary standard (e.g., Na$_2$CO$_3$ or potassium hydrogen phthalate as appropriate) |
| Phenolphthalein indicator | Endpoint ~ pH 8.3 (pink → colourless) |
| Methyl orange indicator | Endpoint ~ pH 4.5 (yellow → red/orange depending on conc.) |
6. Procedure (Short)
- Pipette a known volume of sample (commonly 50.00 mL) into a conical flask.
- Add 2–3 drops phenolphthalein indicator. If pink, titrate with standard acid until the pink just disappears. Record volume $V_P$ (mL) — this gives phenolphthalein alkalinity.
- Add methyl orange indicator to the same flask (or use a fresh aliquot) and continue titration (or titrate fresh aliquot) until methyl orange changes colour (to the methyl orange endpoint, ~pH 4.5). Record total titrant volume $V_T$ (mL) required from initial (unacidified) sample to methyl orange endpoint.
- Optionally perform titration directly to the methyl orange endpoint and record volume; then $V_P$ is volume to phenolphthalein, $V_T$ to methyl orange.
- Repeat for concordant readings.
7. Calculations — Formulae & Worked Example
Fundamental relation
Using Normality (N, eq·L−1) of acid and bicarbonate chemistry: 1 equivalent of acid neutralizes 1 equivalent of alkalinity. Equivalent weight of CaCO3 = 50.0435 g·eq−1.
Formula (with volumes in mL):
$\displaystyle \text{Alkalinity (mg/L as CaCO}_3) = \frac{N\times V_t(\mathrm{mL})\times 50.0435\times 1000}{V_s(\mathrm{mL})}$
Or equivalently (common lab approximation):
$\displaystyle \text{Alk (mg/L as CaCO}_3) \approx \frac{N\times V_t\times 50000}{V_s}$
Worked numerical example (digit‑by‑digit)
Given: Standard acid normality $N=0.02000$ N, sample volume $V_s=50.00$ mL, titrant volume to methyl orange endpoint $V_t=12.35$ mL.
Step 1 — Calculate equivalents of acid used (in eq):
V_t (L) = 12.35 mL = 0.01235 L
Equivalents = N * V_t(L) = 0.02000 * 0.01235 = 0.0002470 eq
Step 2 — Mass of CaCO3 equivalent (g) = equivalents * 50.0435 g/eq
= 0.0002470 * 50.0435 = 0.01236074 g
Convert to mg = 12.36074 mg
Step 3 — Alkalinity (mg/L as CaCO3) = mass (mg) / sample volume (L)
Sample volume = 50.00 mL = 0.05000 L
Alkalinity = 12.36074 / 0.05000 = 247.2148 mg/L ≈ 247.21 mg/L as CaCO3
Interpreting P and M values
If you measure phenolphthalein alkalinity (P, using $V_P$ mL) and total alkalinity (M, using $V_T$ mL), convert both to mg/L or meq/L and then deduce carbonate/bicarbonate/hydroxide fractions using:
$P\; (\text{meq/L}) = [OH^-] + [CO_3^{2-}]$
$M\; (\text{meq/L}) = [OH^-] + [HCO_3^-] + 2[CO_3^{2-}]$
Solve these linear equations to find species concentrations. Typical cases: if $P=0$, only bicarbonate alkalinity present; if $P=M$, carbonate alkalinity dominates; if $P>M/2$ hydroxide may be present.
8. Interferences & Precautions
- Strong acids/bases in wastewater or high ionic strength samples may distort endpoints; use a pH meter for precise endpoints if necessary.
- Perform titration promptly — CO2 exchange with atmosphere can change alkalinity.
- Use freshly standardized acid; perform blanks when using indicators prepared in solvents.
- Indicators: phenolphthalein endpoint can be subtle—practice to detect endpoint reliably.
9. Exam / Interview Tips
- Always convert volumes to litres when computing equivalents (or use the formula with mL consistently).
- Remember equivalent weight of CaCO3 ≈ 50.04 g·eq−1 (use exact value 50.0435 g/eq for precision).
- Know relationships between P and M alkalinities and how to compute CO32− and HCO3− fractions from two titration results.
- Practice the digit-by-digit arithmetic — small mistakes in unit conversion are common in exams.
10. Concise Revision Box
- Alkalinity = acid neutralizing capacity; reported as mg/L as CaCO3.
- Phenolphthalein endpoint ~ pH 8.3 (P alkalinity); methyl orange ~ pH 4.5 (total alkalinity).
- Calculation: use equivalents & equivalent weight of CaCO3 (50.0435 g/eq).
- Common lab formula: Alk (mg/L as CaCO3) = (N × V × 50.0435 × 1000)/Vs (V, Vs in mL).
Prepared for IITs/NITs and other College students. By Mohan Dangi( Gold medalist) NIT-Warangal-2024 .
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