⟵ 05 Carbonated Water (Narrative) · Contents · 05 Carbonated Water (Problem Set) ⟶
Carbonated Water: Engineering Notes
“If you are reading this straight through, you can skip this section and lose nothing essential to the story. These notes are for the operators, engineers, and technicians who need to do the math.”
Why This Matters in the Field
Carbonate chemistry is not a mystery - it just takes time to internalize. These calculations let you:
- Predict pH drift in open systems: CO₂ stripping drives pH upward even if nothing is added.
- Estimate scale risk: carbonate speciation controls CaCO₃ precipitation potential.
- Quantify boiler CO₂ generation: alkalinity in makeup becomes carbonic acid in condensate.
- Budget chemical demand: neutralizing amines and acid feed are often proportional to alkalinity-derived CO₂.
Core Tools & Constants
| Constant / Conversion | Value |
|---|---|
| CaCO₃ molecular weight | 100 g/mol |
| CaCO₃ equivalent weight | 50 g/eq |
| CO₂ molecular weight | 44 g/mol |
| 1 meq/L alkalinity | = 50 mg/L as CaCO₃ |
| CO₂ from alkalinity (boiler rule) | 0.79 ppm CO₂ per 1 ppm alk as CaCO₃ |
| Total (M) alkalinity titration endpoint | pH ≈ 4.3 |
| CO₂/HCO₃– crossover | pH ≈ 6.3 |
| Phenolphthalein (P) alkalinity titration endpoint | pH ≈ 8.3 |
| HCO₃–/CO₃²– crossover | pH ≈ 10.3 |
Carbonate System Recap
The carbonate equilibria:
CO₂(g) ⇌ CO₂(aq) ⇌ H₂CO₃ ⇌ HCO₃⁻ + H⁺ ⇌ CO₃²⁻ + 2H⁺
Although carbonic acid is often shown explicitly, in practice it is convenient to treat dissolved CO₂ and H₂CO₃ as a combined species. This is done because they exist in rapid equilibrium with one another, and analyses generally measure their combined concentration.
Practical translation:
- Low pH: CO₂/H₂CO₃ dominate (corrosion zone)
- Neutral range: HCO₃⁻ dominates (buffering zone)
- High pH: CO₃²⁻ grows rapidly (scale zone)
Concentrations Expressed “mg/L as Calcium Carbonate”
In water treatment, alkalinity is rarely reported as the actual mass of bicarbonate, carbonate, or hydroxide present. Instead, it is usually expressed as mg/L as CaCO₃. That convention exists because these species vary in molecular weight and, more importantly, they vary in the amount of acid they can neutralize.
A milligram of bicarbonate does not neutralize the same amount of acid as a milligram of carbonate. A milligram of hydroxide is different again. If we compare them only by mass, we are comparing apples to oranges. What matters in alkalinity chemistry is not just how much material is present, but how much neutralizing capacity it carries.
That is why water treatment uses equivalent weight.
Molecular weight tells you how much a mole weighs, which determines how much of a substance is present. Equivalent weight tells you how much of a substance is needed to do a fixed amount of chemistry. In terms of alkalinity, that usually means: how much of this substance is needed to neutralize one mole of hydrogen ion (H+)?
For example:
- OH⁻ neutralizes 1 H⁺
- HCO₃⁻ neutralizes 1 H⁺
- CO₃²⁻ neutralizes 2 H⁺
So even though these species have different masses, we can convert them to a common basis by asking how much acid each one can neutralize.
Calcium carbonate became the standard reference because its numbers are convenient. One mole of CaCO₃ weighs 100 g, and one mole can neutralize 2 moles of H⁺. That means its equivalent weight is:
100 ÷ 2 = 50 g/eq
This makes the conversion useful:
50 mg/L as CaCO₃ = 1 meq/L
Once concentrations are expressed as mg/L as CaCO₃, different chemicals can be placed on the same footing. It converts them into a common chemical currency based on neutralizing capacity.
Converting Alkalinity to milliequivalents
With alkalinity expressed as mg/L as CaCO3 – regardless of which species are present – it can be converted directly to milliequivalents per liter:
(mg/L as CaCO₃) ÷ 50 = meq/L
This works because all of those concentrations have already been converted to the same neutralizing basis per unit volume.
If alkalinity is 100 mg/L as CaCO₃:
meq/L = 100 ÷ 50 = 2 meq/L
Which can be expressed in equivalents per liter:
eq/L = 2 ÷ 1,000 = 0.002 eq/L
This idea extends beyond alkalinity. A milliequivalent per liter expresses concentration in terms of reactive charge. One meq/L of positive charge will always balance one meq/L of negative charge.
That is why hardness ions - like calcium and magnesium - are often reported as mg/L as CaCO3. This places both hardness and alkalinity on the same equivalent basis, where they can be compared directly in softening calculations, scaling indices, and charge-balance relationships. Without that common basis, every comparison would require a separate molecular-weight conversion.
A mole counts molecules. An equivalent counts reactive charge. In water treatment, meq/L is often the more useful unit because it tells you how much chemistry the water can do.
P- and M-alkalinity Speciation
M-alkalinity is measured to about pH 4.3 and represents the total acid-neutralizing capacity contributed by hydroxide, carbonate, and bicarbonate.
P-alkalinity is measured to about pH 8.3 and represents the alkalinity neutralized before the phenolphthalein endpoint. It includes all hydroxide alkalinity and half of the carbonate alkalinity, but it does not include bicarbonate alkalinity.
That half-carbonate behavior is the key.
During the P-alkalinity titration, hydroxide is neutralized and carbonate is converted to bicarbonate:
OH⁻ + H⁺ → H₂O
CO₃²⁻ + H⁺ → HCO₃⁻
But the titration stops at pH 8.3, before bicarbonate is neutralized to carbonic acid. The M-alkalinity titration continues to about pH 4.3, where bicarbonate is converted to carbonic acid/CO₂:
HCO₃⁻ + H⁺ → H₂CO₃ ⇌ CO₂ + H₂O
This is why comparing P to M allows us to infer which alkalinity species are present.1
Relationships (as CaCO₃):
- If P = 0 → all alkalinity is bicarbonate
- If P < ½M → mix of bicarbonate + carbonate
- If P = ½M → all alkalinity is carbonate
- If P > ½M → mix of carbonate + hydroxide
- If P = M → all alkalinity is hydroxide
| Condition | Hydroxide (OH−) | Carbonate (CO32−) | Bicarbonate (HCO3−) |
|---|---|---|---|
| P = 0 | 0 | 0 | M (All Bicarbonate) |
| P < ½ M | 0 | 2P | M−2P |
| P = ½ M | 0 | 2P (All Carbonate) | 0 |
| P > ½ M | 2P−M | 2(M−P) | 0 |
| P = M | M (All OH) | 0 | 0 |
Doing multiple titrations in the field can feel like busywork. But when you understand the role of carbonate equilibrium, it becomes chemical reconnaissance.
Estimating pH from OH-Alkalinity
If you know the Hydroxide Alkalinity (calculated from the table above), you can estimate high-range pH without a meter.
Example: OH-Alkalinity: 300 ppm as CaCO3.
Step 1: Convert to Molarity
Alkalinity is reported as Calcium Carbonate Equivalents:
Equivalent Weight of CaCO3 = 50,000 mg/eq
Therefore:
300 mg/L ÷ 50,000 mg/eq = 0.006 eq/L
Because hydroxide is monovalent, it carries one equivalent per mole. This means that eq/L and mol/L are numerically identical here:
[OH⁻] = 0.006 mol/L
Step 2: Calculate pOH
pOH = -log10(0.006) = 2.22
Step 3: Calculate pH
pH = 14 - 2.22 = 11.78
Note: Some handbooks calculate this by dividing by 100 (Molecular weight) instead of 50 (Equivalent weight). That is incorrect for alkalinity conversions and leads to a pH error of ~0.3 units.
CO₂ Generation in Boilers (Rule-of-Thumb)
When bicarbonate decomposes inside a boiler, it produces CO₂ that travels with steam and re-dissolves in condensate.
Thermal Decomposition (driven by heat):
2HCO₃⁻ ⇌ CO₃²⁻ + H₂O + CO₂↑
Further Breakdown (at high pressure):
CO₃²⁻ + H₂O ⇌ 2OH⁻ + CO₂↑
Field Estimation:
For many low- to medium-pressure boilers, a useful rule of thumb is:
1 ppm M-Alkalinity as CaCO₃ (feedwater) → 0.79 ppm CO₂ (in steam/cond.)
Note: This is a field estimate, not a universal stoichiometric law. Actual CO₂ generation depends on boiler pressure, alkalinity form, cycles, steam purity, and operating conditions.
Interpretation:
100 ppm alkalinity as CaCO3 in feedwater → ~79 ppm CO₂ in steam/cond.
This can be managed in two places: upstream by removing alkalinity before the boiler, or downstream by neutralizing the carbonic acid formed in the condensate.
For downstream management, amine demand is estimated:
- Target: pH 8.3 - 8.8
- Dosage: Typically 2-3 ppm active amine per 1 ppm CO₂ (product-dependent)
⟵ 05 Carbonated Water (Narrative) · Contents · 05 Carbonated Water (Problem Set) ⟶
Footnotes
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Standard Methods for the Examination of Water and Wastewater, Method 2320, “Alkalinity.” APHA, AWWA, WEF. Confirm the current edition at time of publication. ↩