# Two ways to calculate dissolved oxygen

To calculate the dissolved oxygen in water at saturation pressure at 25 °C, we do:

$$D_\ce{O2} = K_\mathrm{H} \times M \times p_\mathrm{g}$$

$$D_\ce{O2}~[\pu{g/L}]= 1.26\times10^{-3}~[\pu{mol/L/atm}] \times 32~[\pu{g/mol}] \times 0.21~[\pu{atm}]$$

I used $\pu{1.26E-3 mol/L/atm}$ for the Henry's constant for $\ce{O2}$ in water at 25C which is from Warneck and Williams (2012), which was in turn taken from Battino (1981). This returns a dissolved oxygen of $\pu{8.47 mg/L}$.

Benson (1980) reports dissolved oxygen for "a body of pure water is in thermodynamic equilibrium with an atmosphere of standard composition saturated with water vapor at a total pressure $P$" as 8.26 mg/L which is a difference of 2.5 %. The Benson paper suggests an error of around 0.02 %. Why is there a difference in these two methods? Is it due to different assumptions being made? Or perhaps rounding errors in how data is presented?

• To me, 8.26 vs 8.47 is no difference at all, and bold claims about 0.02% should be taken cum grano salis. – Ivan Neretin Jun 27 '18 at 6:18
• The 21% figure is for dry air. Benson assumes air is saturated with water vapor. – MaxW Jun 27 '18 at 6:56
• In either case it is a case of the grain of salt when the numbers used have a 1e-3 resolution and the precision is reported as "around" 2e-4. I'd call BS right then and there (unless OP has truncated) – Stian Yttervik Jun 27 '18 at 13:50

The 21.0% of oxygen by volume in air is from dry air. Data for dry air from webpage of Columbia University's Department of Earth and Environmental Sciences.

Note that the "% by volume"/100 for dry air also corresponds to the partial pressure in atmospheres. For air saturated with water at 25 C, the vapor pressure of water, according to Wikipedia, is 0.0313 atm. The second column is calculated by multiplying all dry air values by (1-0.0313)=0.9687.

$$\newcommand{\d}{#1.&\hspace{-1em}#2} \begin{array}{lrl} \hline \text{Gas} &\hspace{-5em}\text{dry air}&\ce{H2O}\text{ sat. air} \\ & \text{% by volume} & \text{% by volume} \\ \hline \ce{N2} & 78.084 & 75.640 \\ \ce{O2} & 20.947 & 20.291 \\ \ce{H2O} & 0.0 & 3.13 \\ \ce{Ar} & 0.934 & 0.905 \\ \ce{CO2} & 0.035 & 0.034 \\ \ce{Ne} & 0.001818 & 0.001761 \\ \ce{He} & 0.000524 & 0.000508 \\ \ce{CH4} & 0.00017 & 0.00016 \\ \ce{Kr} & 0.000114 & 0.000110 \\ \ce{H2} & 0.000053 & 0.000053 \\ \ce{N2O} & 0.000031 & 0.000030 \\ \ce{Xe} & 0.0000087& 0.0000084 \\ \hline \text{TOTAL}& 100.0027187 & 100.0026304 \\ \hline \end{array}$$

Now correcting the data from Warneck and Williams (evidently Warneck, P. and Williams, J.: The Atmospheric Chemist’s Companion: Numerical Data for Use in the Atmospheric Sciences, Springer Verlag, 2012) for the value of water saturated air

$\ce{O2} = \dfrac{20.291}{21}\times 8.47 = 8.18$ mg/L

This is much better agreement with the Benson (1980) data.

The OP's value of 1.26e-3 Mol/L/atm for the Henry's constant for O2 in water at 25C was evidently take from Table 8.23 of Warneck and Williams. The value also has a list error bracket of +/- 0.02.

$$\dfrac{0.02}{1.26}\times 100\text{%} = 1.6 \text{ %}$$

For the two dissolved oxygen values:

$$\dfrac{8.26-8.18}{8.26}\times100\text{ %} = -0.97 \text{ %}$$

so the values are within the error limits for Henry's constant.