Lesson 8 · 30 min

Dissolved oxygen: the Winkler titration and the Clark electrode

Warm water holds less oxygen, seawater and mountain lakes less still: compute the saturation values with the Benson–Krause equations. The Winkler method fixes oxygen as MnO(OH)₂ and counts it by iodometry; a Clark electrode’s current follows the oxygen partial pressure, and the meter needs the salinity to give mg/L.

In this lesson

Estimate the saturation oxygen content of water with Henry’s law and the Benson–Krause equations, and explain the effects of temperature, salinity and altitude
Write the three reactions of the Winkler method, explain why one O₂ uses four S₂O₃²⁻, and calculate dissolved oxygen from a titre
Explain why a Clark electrode measures oxygen partial pressure, how the meter converts it to mg/L, and what a wrong salinity setting does

On the morning after a hot summer night, the fish in a pond often come up to gulp at the surface: warm water holds less oxygen to begin with, and at night the plants and microbes in it only consume oxygen without making any. Dissolved oxygen is one of the most basic measures of water quality, measured daily by sewage works, fish farms and ocean research ships.

There are two ways to measure it. In 1888 the Hungarian chemist L. W. Winkler published a titration: first “fix” the oxygen in the sample as a brown precipitate, then count it by iodometry — still the reference against which other methods are calibrated. In 1956 the American physiologist L. C. Clark hid a platinum electrode behind a gas-permeable membrane, making an oxygen electrode that can be dipped straight into blood or water.

Predict first

Fresh water in equilibrium with air holds 14.6 mg/L of dissolved oxygen at 0 °C. About how much does it hold at 30 °C?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

Still about 14.6 mg/L About 12 mg/L About 7.6 mg/L — roughly half About 2 mg/L

How much oxygen water holds

By Henry’s law the dissolved gas at equilibrium is proportional to its partial pressure: c = K_H p(O₂). Oxygen is 20.946 % of dry air, but the air over water is saturated with water vapour, so p(O₂) = 0.20946 (p − p_vapour). K_H falls as the temperature rises, and the salt in seawater pushes oxygen out (salting out).

For accurate work one uses the equations Benson and Krause (1980, 1984) fitted to thermodynamic data, adopted by the US Geological Survey since 2011: the saturation concentration of fresh water at 1 atm from the temperature, multiplied by a salinity factor and a pressure factor. Between 0 and 40 °C and salinities of 0 to 40 ‰ the fit is good to about 0.001 mg/L.

c_{\mathrm{O_2}} = K_\mathrm{H}(T, S)\,p_{\mathrm{O_2}},\qquad p_{\mathrm{O_2}} = 0.20946\,(p - p_{\mathrm{w}})

The Benson–Krause equations express the temperature and salinity dependence of K_H as fits; the pressure factor also accounts for the vapour pressure of water and the non-ideality of oxygen.

$c_{\mathrm{O_2}}$: saturation dissolved oxygen
$K_\mathrm{H}$: Henry’s-law constant
$p$: barometric pressure
$p_{\mathrm{w}}$: vapour pressure of water

Benson–Krause equations (as adopted by the USGS) · in equilibrium with moist air

How much oxygen water can hold

Water temperature 20.0 °C Salinity 0 ‰ Altitude 0 m (pressure 1.000 atm)

Water in equilibrium with air

Saturation oxygen against temperature

fresh water (0 ‰)
seawater (35 ‰)

Saturation 9.09 mg/L, or 0.284 mmol/L. Oxygen partial pressure in the air 0.2046 atm; a litre of water holds only 3.3 % of the O₂ in a litre of that air.

Try the four typical cases: a lake in winter holds over 13 mg/L; a tropical sea surface only about 6.3 mg/L; a lake at 3600 m, where the pressure is only 0.64 atm, holds just 7.2 mg/L even at 10 °C.

Worked example

Saturation oxygen in a mountain lake

A lake lies at 3600 m and its water is at 10 °C. What is the pressure at that altitude in the US Standard Atmosphere, and what is the saturation oxygen content? Compare with sea level.

The Winkler method: fix the oxygen, then count it

Oxygen escapes from a sample and also dissolves into it from the air, so the first step is to fix it on the spot: fill a 300 mL oxygen bottle with the sample (no bubbles), add MnSO₄ and a concentrated alkali containing iodide, giving white Mn(OH)₂, which the dissolved O₂ at once oxidises to a brown precipitate of MnO(OH)₂. With the stopper in, the oxygen is locked up in the precipitate.

Back in the laboratory, concentrated sulfuric acid dissolves the precipitate, the Mn(IV) oxidises the excess I⁻ to I₂ (present as I₃⁻), and the iodine is titrated with sodium thiosulfate using starch as the indicator:

\ce{2Mn(OH)2 + O2 -> 2MnO(OH)2}

\ce{MnO(OH)2 + 3I- + 4H+ -> Mn^2+ + I3- + 3H2O}

\ce{I3- + 2S2O3^2- -> 3I- + S4O6^2-}

One O₂ → two MnO(OH)₂ → two I₃⁻ → four S₂O₃²⁻. Sodium azide is added to destroy any nitrite in the sample, which would otherwise also oxidise I⁻ to I₂.

\mathrm{DO} = \frac{c(\mathrm{S_2O_3^{2-}})\,V_\mathrm{t}\,M(\mathrm{O_2})}{4\,V_\mathrm{s}}

Titrating the equivalent of 200 mL of original sample with 0.02500 M thiosulfate, each millilitre is exactly 1.00 mg/L. The two 1 mL reagent additions push 2 mL of sample out of the bottle, so 200 × 300/298 = 201.3 mL is taken.

$V_\mathrm{t}$: titre
$V_\mathrm{s}$: equivalent volume of original sample
$M(\mathrm{O_2})$: molar mass of O₂

300 mL oxygen bottle · 0.02500 M Na₂S₂O₃ · starch indicator

The Winkler titration for dissolved oxygen

Sample temperature 20 °C 100 % of air saturation

\ce{2Mn(OH)2 + O2 -> 2MnO(OH)2}

\ce{MnO(OH)2 + 3I- + 4H+ -> Mn^2+ + I3- + 3H2O}

\ce{I3- + 2S2O3^2- -> 3I- + S4O6^2-}

③ Measure 201.3 mL (equal to 200 mL of the original water) into the flask and titrate

Burette reading 0.00mL

I₃⁻ left0.00 µM

Flow rate · 0.25 mL/s

Fix, then acidify, then titrate: yellow-brown → pale yellow, add starch → deep blue → colourless.

Fix, acidify, then titrate in order: when the yellow-brown has faded to pale yellow, add starch — deep blue — and continue drop by drop until the blue just disappears. Set the saturation to 0 % and the fixed precipitate stays white.

Worked example

Dissolved oxygen in a river sample

A river sample at 15 °C is fixed and acidified by the Winkler method, and 201.3 mL (equal to 200 mL of original water) needs 7.85 mL of 0.02500 M Na₂S₂O₃. Find the dissolved oxygen and the percentage saturation.

The Clark electrode: it measures pressure

In a Clark electrode a platinum cathode and a silver anode sit in KCl electrolyte, separated from the sample by a thin gas-permeable plastic membrane. The cathode is held at about −0.7 V, so every O₂ that crosses the membrane is reduced at once and the oxygen pressure at the cathode surface falls to zero. A steady pressure gradient forms across the membrane, and the current is set by how fast oxygen diffuses through it — the limiting current of the previous lesson:

i = \frac{nFA\,P_\mathrm{m}}{L}\,p_{\mathrm{O_2}}

with n = 4, A the cathode area, and P_m and L the permeability and thickness of the membrane. The current is proportional to the oxygen partial pressure in the sample, not to its concentration. So the meter is first calibrated to 100 % in water-saturated air and actually measures percentage saturation; to display mg/L it must be told the temperature, salinity and pressure, and converts with the Benson–Krause equations. The electrode consumes oxygen, so the sample must be stirred or flowing; and the membrane’s permeability changes strongly with temperature, which a thermistor in the meter compensates.

Current proportional to oxygen partial pressure · the meter converts to mg/L with the Benson–Krause equation

The Clark oxygen electrode

Sample Temperature 25 °C Actual salinity 35 ‰ Oxygen saturation 100 %

Meter setting Salinity entered in the meter 0 ‰

100% 8.26mg/L

Cross-section of the probe

Pt cathode: O₂ + 2H₂O + 4e⁻ → 4OH⁻

Ag anode: Ag + Cl⁻ → AgCl + e⁻

Oxygen partial pressure across the membrane

One signal, different mg/L

true value for the sample
meter’s conversion

Signal 100 % (p(O₂) = 20.56 kPa). The meter shows 8.26 mg/L; the true value is 6.77 mg/L — off by +22.0 %.

The sample is air-saturated seawater at 25 °C, but the meter’s salinity is still set to 0: the probe signal is right (100 %), yet the meter converts as if for fresh water and shows 8.26 mg/L when the true value is only 6.77 mg/L. Set the meter’s salinity to 35 ‰ and the two agree.

Concept check

The same calibrated Clark electrode is dipped first into fresh water and then into seawater, both at 25 °C and in equilibrium with air. What does the electrode current do?

It is the same both times: the oxygen partial pressures are equal, even though seawater holds about 18 % less dissolved oxygen It is about 18 % smaller in seawater, because less oxygen is dissolved It is larger in seawater, because seawater conducts better It is zero in seawater, because salt blocks the membrane

Try the calculation

A biochemical oxygen demand (BOD₅) test: 30 mL of wastewater is diluted to 300 mL; the dissolved oxygen is 8.45 mg/L straight after dilution and 3.10 mg/L after 5 days in the dark at 20 °C. With BOD₅ = (D₁ − D₂)/P, where P is the volume fraction of wastewater, what is the BOD₅ in mg/L?

Key takeaways

Dissolved oxygen follows Henry’s law: fresh water in equilibrium with air holds 14.6 mg/L at 0 °C but only 7.6 mg/L at 30 °C; seawater holds about a fifth less, and less still at altitude as the pressure falls. Accurate values come from the Benson–Krause equations.
The Winkler method: O₂ is fixed as MnO(OH)₂, which releases I₂ in acid for a thiosulfate titration; one O₂ is worth four S₂O₃²⁻, and with 0.02500 M titrant and 200 mL of original sample, 1 mL = 1 mg/L.
The limiting current of a Clark electrode is proportional to the oxygen partial pressure: calibrated in air, the meter measures percentage saturation and has to convert it to mg/L using temperature, salinity and pressure.

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Data and references

L. W. Winkler, “Die Bestimmung des im Wasser gelösten Sauerstoffes”, Ber. Dtsch. Chem. Ges. 21, 2843–2854 (1888).
B. B. Benson, D. Krause Jr., “The concentration and isotopic fractionation of oxygen dissolved in freshwater and seawater in equilibrium with the atmosphere”, Limnol. Oceanogr. 29, 620–632 (1984).
US Geological Survey, Office of Water Quality Technical Memorandum 2011.03, “Change to solubility equations for oxygen in water” (2011), equations 7–11.
L. C. Clark, “Monitor and control of blood and tissue oxygen tensions”, Trans. Am. Soc. Artif. Intern. Organs 2, 41–48 (1956).
U.S. Standard Atmosphere, 1976 (NOAA, NASA and US Air Force, 1976).