pH and Alkalinity: 18-Env-A4 Water and Wastewater Engineering, December 2014, Q3

Question 3: pH and Alkalinity (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(i) pH — Definition and Significance

pH is defined as the negative base-10 logarithm of the hydrogen-ion activity, $\text{pH}=-\log_{10}[\text{H}^+]$, giving a dimensionless 0–14 scale (7 neutral at 25°C) that describes how acidic or basic water is at the instant of measurement. Its significance to disinfection is direct and large: chlorine's active disinfecting species, hypochlorous acid (HOCl), is in a pH-dependent equilibrium with the far weaker hypochlorite ion, $\text{HOCl}\rightleftharpoons\text{H}^++\text{OCl}^-$ (pKℎ ≈ 7.5); HOCl is roughly 80–100 times more effective a disinfectant than OCl⁻, so as pH rises from 6.5 toward 8.5 the fraction present as HOCl falls sharply and required CT (or chlorine dose) for the same log-inactivation rises correspondingly — plants therefore typically chlorinate in the pH 6.5–7.5 range for efficiency. pH is equally critical to coagulation-flocculation: metal coagulants (alum, ferric chloride/sulfate) only hydrolyze to insoluble, positively-charged metal-hydroxide flocs within a defined optimum pH band (roughly 5.5–7.5 for aluminum, 5–8.5 for ferric); outside that band the coagulant remains soluble or redissolves, colloidal charge neutralization fails, and turbidity/NOM removal collapses. Because both processes have narrow, different, and downstream-linked pH optima, treatment plants routinely dose lime, soda ash, CO₂ or acid to bring the water into the coagulation window first and re-adjust before final chlorination.

(ii) Alkalinity from the Double Titration

The phenolphthalein end point (pH 8.3) marks the point where all hydroxide has been neutralized and carbonate has been converted only halfway, to bicarbonate ($\text{CO}_3^{2-}+\text{H}^+\rightarrow\text{HCO}_3^-$); the acid volume to this point defines the phenolphthalein alkalinity, P. Continuing the same titration to the Bromocresol Green end point (pH 4.5) neutralizes all remaining bicarbonate (both the original bicarbonate and that just formed from carbonate); the total acid volume to this point defines the total alkalinity, T. Comparing P against T/2 (the standard Sawyer & McCarty classification) then reveals which of hydroxide, carbonate and bicarbonate alkalinity are actually present — this is the "other type of alkalinity" the question is asking for beyond the two directly-titrated numbers.

Given.

Given data
Quantity	Symbol	Value
Sample volume	$V_s$	50 mL
Acid normality	$N$	0.02 eq/L (0.02N H₂SO₄)
Acid volume to phenolphthalein end point (pH 8.3)	$V_P$	5 mL
Acid volume to Bromocresol Green end point (pH 4.5), cumulative from start	$V_T$	8 mL

Find. The type and value of alkalinity indicated by each end point, and any additional alkalinity component(s) that can be derived from the two titration volumes.

Approach. Convert each titration volume to an alkalinity in mg/L as CaCO₃ using the standard normality relation, then apply the Sawyer & McCarty P-vs-T/2 classification to split the total alkalinity into its hydroxide, carbonate and bicarbonate components.

Phenolphthalein alkalinity, P. $$P=\frac{V_P\,N\,(50{,}000)}{V_s}=\frac{5\times0.02\times50{,}000}{50}=\boxed{100\ \text{mg/L as CaCO}_3}.$$
Total alkalinity, T. $$T=\frac{V_T\,N\,(50{,}000)}{V_s}=\frac{8\times0.02\times50{,}000}{50}=\boxed{160\ \text{mg/L as CaCO}_3}.$$
Classify against T/2. $T/2=80$ mg/L, and $P=100>T/2$, so by the standard table both hydroxide and carbonate alkalinity are present, and bicarbonate alkalinity is zero: $$\text{OH}^-=2P-T=2(100)-160=\boxed{40\ \text{mg/L as CaCO}_3},\qquad \text{CO}_3^{2-}=2(T-P)=2(160-100)=\boxed{120\ \text{mg/L as CaCO}_3},\qquad \text{HCO}_3^-=0.$$
Check. The three components must reconstitute the total: $40+120+0=160\ \text{mg/L}=T$. ✓

Check: P > T/2 is the signature of a water whose alkalinity is dominated by hydroxide and carbonate with essentially no bicarbonate left — typical of a lime-softened or otherwise strongly-basic water rather than a natural groundwater (which is normally P = 0, pure bicarbonate). The BCG titration volume is read as cumulative acid delivered from the start of the same titration (the standard Standard Methods 2320B procedure continues the same burette past the phenolphthalein end point), not as a second, independent 8 mL addition — that convention is what makes $T\ge P$ and the component check above self-consistent.

Quantity	Value
Phenolphthalein alkalinity, P (indicates OH⁻ + ½ CO₃²⁻)	100 mg/L as CaCO₃
Total alkalinity, T (indicates OH⁻ + CO₃²⁻ + HCO₃⁻)	160 mg/L as CaCO₃
Hydroxide alkalinity, OH⁻ (derived from P and T)	40 mg/L as CaCO₃
Carbonate alkalinity, CO₃²⁻ (derived from P and T)	120 mg/L as CaCO₃
Bicarbonate alkalinity, HCO₃⁻	0 mg/L as CaCO₃

Concept & Theory

Topic. pH's role in disinfection and coagulation chemistry; the phenolphthalein/total double-titration method for alkalinity speciation.

Key relations. $\text{pH}=-\log_{10}[\text{H}^+]$; $\text{Alkalinity (mg/L as CaCO}_3)=\dfrac{V\,N\,(50{,}000)}{V_s}$; Sawyer & McCarty table: for $P>T/2$, $\text{OH}^-=2P-T$, $\text{CO}_3^{2-}=2(T-P)$, $\text{HCO}_3^-=0$.

Why this works. The phenolphthalein end point sits exactly halfway through the carbonate-to-bicarbonate conversion, so P alone conflates "all the hydroxide" with "half the carbonate" — a single titration cannot separate them. Adding the second end point (total acid to pH 4.5, where every alkaline species is fully neutralized to carbonic acid) gives a second independent equation, and because there are at most two of {OH⁻, CO₃²⁻, HCO₃⁻} present at once (they cannot coexist as OH⁻+HCO₃⁻ in solution — they would react), two titration numbers are always enough to solve for all three components.

Common pitfall. Treating the 8 mL BCG figure as an additional volume added after the phenolphthalein end point rather than the cumulative total from the start (this would roughly double T and give a wrong classification); applying the wrong branch of the P-vs-T/2 table; forgetting that pH's effect on chlorine speciation and coagulant hydrolysis are two separate, independently-optimized windows that a plant must reconcile in sequence.

Source. Davis & Cornwell, Introduction to Environmental Engineering, alkalinity & coagulation chapters; Standard Methods for the Examination of Water and Wastewater, 2320B (Alkalinity) and 2310B (Acidity/pH).

Question 3 of 5: pH and Alkalinity

Question 3: pH and Alkalinity (25 marks)

(i) pH — Definition and Significance

(ii) Alkalinity from the Double Titration