Chemical Oxygen Demand Calculator
Calculate the chemical oxygen demand (COD) of a water sample from a dichromate back-titration. Enter the blank and sample FAS titration volumes, the titrant normality, and the sample volume to get the result in mg/L as O₂.
Find COD from a Blank and Sample Titration
Chemical Oxygen Demand Formula
Where:
- \(V_b\) — blank titration volume, mL of FAS used for the distilled-water blank
- \(V_s\) — sample titration volume, mL of FAS used for the digested sample
- \(N\) — normality of the ferrous ammonium sulfate (FAS) titrant (eq/L)
- \(S\) — volume of the original water sample added to the reflux flask (mL)
- \(8000\) — conversion factor: 8 mg/meq (the milliequivalent weight of O₂) × 1000 mL/L
The formula converts the difference between the blank and sample titrations into the oxygen equivalent of the organic matter that consumed dichromate during digestion.
Chemical Oxygen Demand – Calculation Example
Example: a wastewater sample is refluxed with dichromate. The blank requires 25.0 mL of 0.1 N FAS, the digested sample requires 20.5 mL, and the sample volume was 20 mL.
\[ \text{COD} = \frac{(25 - 20.5) \times 0.1 \times 8000}{20} \]
\[ \text{COD} = \frac{4.5 \times 0.1 \times 8000}{20} = 180 \ \text{mg/L as O}_2 \]
Result: 180 mg/L as O₂ — a value typical of a moderately loaded wastewater stream.
How to Use the COD Calculator
- Enter the Blank Titration Volume (Vb) in mL — the FAS needed to titrate the distilled-water blank after refluxing.
- Enter the Sample Titration Volume (Vs) in mL — the FAS needed to titrate the digested sample. This must be smaller than or equal to the blank volume.
- Enter the Titrant Normality (N) — the normality of the FAS solution, standardized on the day of use (typically about 0.1 N).
- Enter the Sample Volume (S) in mL — the volume of original water sample placed in the reflux flask (commonly 20 mL).
- Read the Chemical Oxygen Demand (COD) in mg/L as O₂, along with a step-by-step breakdown of the calculation.
What Is Chemical Oxygen Demand?
Chemical oxygen demand (COD) is a measure of the total amount of oxygen required to chemically oxidize the organic — and some inorganic — matter dissolved or suspended in a water sample. It is one of the most widely used indicators of water quality in wastewater treatment, industrial discharge monitoring, and river pollution studies: the higher the COD, the more oxidizable pollution the water contains.
In the standard dichromate method (APHA Standard Methods 5220B, ISO 6060), the sample is refluxed for about two hours with a known excess of potassium dichromate (K₂Cr₂O₇) in strongly acidic solution, with silver sulfate as a catalyst. Oxidizable matter reduces Cr₂O₇²⁻ to Cr³⁺. After digestion, the remaining dichromate is back-titrated with ferrous ammonium sulfate (FAS) using ferroin indicator.
The key to the calculation is the difference between the two titration volumes. The blank contains no oxygen demand, so all of its dichromate survives and the full amount of FAS is needed to titrate it. The sample consumes part of its dichromate, so less FAS is required. The difference \(V_b - V_s\), multiplied by the titrant normality, equals the milliequivalents of dichromate consumed — which is exactly the oxygen equivalent of the oxidized matter.
The factor 8000 deserves a brief explanation. Oxygen (M = 32 g/mol) accepts 4 electrons per molecule, so its equivalent weight is 32/4 = 8 g/eq, or 8 mg per milliequivalent. Multiplying by 1000 converts the per-mL basis of the titration to per liter. The result is therefore reported as mg/L of O₂, even though no oxygen is actually consumed in the test.
Interpreting the Result
Some benchmark values help put a COD number in context: clean river water typically shows 5–30 mg/L; well-treated municipal effluent 30–100 mg/L; raw domestic sewage 300–600 mg/L; and certain industrial wastes can exceed several thousand mg/L. Discharge permits usually specify a maximum COD, so the result is often compared directly against a regulatory limit.
COD differs from biochemical oxygen demand (BOD): COD measures everything chemically oxidizable — including compounds that bacteria cannot degrade — and takes hours rather than the 5 days required for BOD₅. For most wastewaters, the COD/BOD ratio falls between 1.5 and 3, and COD is often used as a rapid estimate of BOD once the ratio for a given effluent has been established.
Assumptions, Limitations and Practical Tips
- Titrant standardization: the FAS normality must be verified against the blank or a primary standard on the day of use; FAS slowly oxidizes in storage. The standardization must use the same setup as the sample titration.
- Sample must consume less titrant than the blank: if \(V_s > V_b\), something is wrong — the sample was not digested, the volumes were swapped, or the titration endpoint was missed.
- Chloride interference: chloride ions are oxidized by dichromate and inflate the result. Mercuric sulfate is added to complex chloride, but above roughly 2000 mg/L Cl⁻ the sample should be diluted. Note that mercury-containing waste must be handled and disposed of as hazardous.
- Incomplete oxidation: pyridine and related nitrogen heterocycles, and some straight-chain aliphatics, are not fully oxidized even with the silver catalyst. Volatile compounds may also be lost if the reflux apparatus leaks.
- High-COD samples: if the calculated COD exceeds about 1000 mg/L, most of the dichromate has been consumed and the excess is no longer guaranteed. Dilute the sample and repeat the determination.
- Zero result: equal blank and sample volumes mean no measurable dichromate was consumed. This can be genuine for very clean water, but it is worth confirming the digestion was complete.
If you are working through the stoichiometry of other analytical or electrochemical techniques, you may also find our Standard Cell Potential Calculator, Solubility Product Calculator, or Chromatography Theoretical Plates Calculator useful.
Frequently Asked Questions
Why is COD reported as mg/L of O₂ when the test actually uses dichromate?
COD is an oxygen equivalent: it answers the question "how much oxygen would be needed to oxidize this matter?" Dichromate accepts 6 electrons per formula unit, just as \(\text{O}_2\) accepts 4 electrons when it acts as an oxidant. The 8000 factor (8 mg/meq × 1000) converts the measured electron transfer into the mass of oxygen that would have accepted those same electrons, giving a result comparable across methods.
What is the difference between the normality and molarity of the FAS titrant?
Normality (eq/L) counts the reactive capacity, while molarity (mol/L) counts molecules. For ferrous ammonium sulfate this matters: each \(\text{Fe}^{2+}\) ion donates exactly one electron, so for FAS alone the normality equals the molarity — a 0.1 M FAS solution is 0.1 N. Note that for the dichromate reagent the two differ: \(\text{K}_2\text{Cr}_2\text{O}_7\) accepts 6 electrons per mole, so 0.25 N corresponds to about 0.0417 M.
How do I convert COD between mg/L, ppm, and other units?
In dilute aqueous solutions, mg/L as O₂ is essentially identical to ppm by mass: 1 mg/L ≈ 1 ppm. To convert, divide by 1000 for g/L, or multiply by 1000 for µg/L (ppb). For reporting in kg of O₂ per day (common in treatment-plant load calculations), multiply the COD in mg/L by the flow in m³/day and divide by 1000. Always keep the "as O₂" qualifier when reporting, since other bases (e.g., as C) are occasionally used.
Can I calculate BOD from a COD result?
Not directly — COD and BOD measure different things. COD captures everything chemically oxidizable, while BOD only counts what microorganisms can degrade over the test period. However, for a given wastewater stream the COD/BOD ratio is fairly stable (commonly 1.5–3 for municipal sewage), so once you have established that ratio from paired measurements, COD can serve as a quick same-day estimate of \(\text{BOD}_5\). The ratio must be verified for each specific effluent and rechecked periodically.
How do I account for diluting the sample before the COD determination?
If you diluted the sample before pipetting it into the reflux flask — for example 10 mL of sample made up to 20 mL — the calculator computes the COD of the diluted mixture, which underestimates the original. Multiply the result by the dilution factor \(\frac{V_{final}}{V_{sample}}\). Note this differs from pipetting a smaller original sample volume directly (e.g., 10 mL instead of 20 mL): in that case simply enter the smaller volume as S and no correction is needed.
What are the most common mistakes that skew COD titration results?
Frequent errors include using unstandardized FAS (it weakens during storage, inflating results), misreading the ferroin endpoint (overshooting the blue-to-reddish-brown transition), swapping the blank and sample volumes, and letting the reflux condenser leak so volatile organics escape. Also watch for chloride-rich samples: above roughly 2000 mg/L Cl⁻ even mercuric sulfate cannot fully mask the interference, so dilute the sample. Finally, ensure the full 2-hour digestion — an incomplete reflux gives falsely low values.