The answer to this, I recon, *is that they don't*.

They use molecular oxygen (O<sub>2</sub>) dissolved in the water for respiration, where is acts as a terminal electron acceptor, just as we use molecular oxygen in the air for respiration. We can speak of the water as being *oxygenated*. 

What *is* split in photosynthesis, where **reducing equivalents from water** are used to reduce NADP<sup>+</sup> (giving NADPH).

One of the great discoveries of biology, IMO, **is that the oxygen formed in green-plant photosynthesis comes from water, not CO<sub>2</sub>**.

**Tricarboxylic Acid Cycle (Krebs Cycle) Rant**

Despite claims to the contrary, most infamously by Racker (1976, pp 28 - 29) and Wieser (1980), but also by Madeira (1988) and Mego (1986) for example, water is *not* split in the tricarboxylic acid cycle (Krebs Cycle). Banfalvi (1991) also sails pretty close to the wind on this one.

That is, reducing equivalents from water are *not* passed down the respiratory chain, or in any way used to make ATP, or are in any way a 'source' of free energy.  Such claims, IMO, are nonsense.

The definitive answers to the Wieser (1980) paper are given by Atkinson (1981) and Herreros & Garcia-Sancho (1981). Both of these articles are models of clarity, and categorically refute the claims of Wieser (1980).  Nevertheless, as shown by the references above, the controversy surfaces periodically.

The only source of reducing equivalents in the TCA cycle are carbon compounds, and the only electrons passed down the respiratory chain are those 'held' in C-H and C-C bonds (Herreros & Garcia-Sancho, 1981).  An ionization is neither an oxidation nor a reduction (see Atkinson, 1981) and neither is a hydration. Adding water to (say) a double bond *does not* make the compound any more oxidized or reduced.  As far as oxygen and electrons are concerned, and to generalize from a biological point of view, what is has it holds - except in photosynthesis. 

As you may have guessed, the splitting of the water in the TCA cycle is a pet rant of mine.  Thanks for the opportunity of airing my views! 

(end rant)


**Edit 2**

As [rwst](http://biology.stackexchange.com/users/1122/rwst) and [Alan Boyd](http://biology.stackexchange.com/users/1320/alan-boyd) have drawn attention to, the concentration of dissolved oxygen in water is all important, and varies with (for example) temperature.  

In air-saturated buffer at 25<sup>o</sup>C the concentration of oxygen (O<sub>2</sub> molecules) is about 0.24 mM (0.24 umoles/ml, or about 0.474 ug-atoms of oxygen per ml). [[Chappell](http://www.biochemj.org/bj/090/0225/0900225.pdf)] (1964)]. This figure decreases with increasing temperature. 


Great question, BTW.


**References**

(Apologies for the **incomplete Atkinson and Herreros & Garcia-Sancho references**. I have a photocopy of these papers but have been unable to trace the full source. They are both in the 'Letters to the Editor' section of the February 1981 edition of *Trends in Biochemical Sciences*. I'll update)

 - Atkinson, D.E. (1981) TCA Cycle Confusion.  *Trends in Biochemical Sciences* (full ref to follow)

 - Banfalvi,G. (1991)  Conversion of Oxidative Energy to Reductive Power in the Citrate Cycle. *Biochemical Education*, **19**, 24 - 26  [see [here](http://onlinelibrary.wiley.com/doi/10.1016/0307-4412%2891%2990138-X/abstract)] (pdf apparently free to all)

 - Chappell (1964) The oxidation of citrate, isocitrate and cis-aconitate by isolated mitochondria. *Biochem J.*, **90**, 225-237.[[pubmed](http://www.ncbi.nlm.nih.gov/pubmed/4378636)]  [[pdf](http://www.biochemj.org/bj/090/0225/0900225.pdf)]

 - Herreros, B. & Garcia-Sancho, J. (1981) TCA Cycle Confusion.  *Trends in Biochemical Sciences* (full ref to follow)

 - Madeira, V.M.C. (1988) Stoichiometry of Reducing Equivalents and Splitting
of Water in the Citric Acid Cycle.  *Biochemical Education* **16**, 94 - 96 [[pdf](http://onlinelibrary.wiley.com/doi/10.1016/0307-4412%2888%2990069-6/pdf)] (apparently free to all.)

 - Mego, J.L. (1986)  The Role of Water in Glycolysis *Biochemical Education*,  **14**, 130 - 131. (see [here](http://onlinelibrary.wiley.com/doi/10.1016/0307-4412%2886%2990175-5/abstract))

 - Racker, E. (1976) A New Look at Mechanisms in Bioenergetics.  Academic Press, New York.

 - Weiser (1980) Textbook Errrors: The splitting of water by the tricarboxylic acid cycle.  Textbook error or textbook omission? *TIBS* (1980) **5** (Issue 11), 284. [see [here](http://www.sciencedirect.com/science/journal/09680004/5/11)].  [[pdf](http://download.cell.com/trends/biochemical-sciences/pdf/PII0968000480901590.pdf?intermediate=true)], apparently free to all.