## Determination of dissolved oxygen with a Clark cell

### How it works

Applying a potential difference pd (between 700 and 1200 mV), leads to electrolysis: the platinum (or gold) electrode acts as the cathode (reduction) and the silver electrode as an anode (oxidation). The reactions are:

With a microampere meter, the cathodic current I_{C} is measured. It gives the diffusion limit for the reduction reaction of O_{2} to HO^{-} or H_{2}O I_{c}^{lim}. The intensity of this current is directly proportional to the diffusion rate of O_{2} towards the cathode and the dissolved oxygen concentration [O_{2}]:

where F is the Faraday constant, D_{m} is the diffusion coefficient of O_{2} through the membrane, K_{m} is the solubility product constant for O_{2} in the membrane, P_{m} is the membrane permeability which is D_{m}K_{m}, S is surface area of the electrode and e is the thickness of the membrane.

Dioxygen concentrations in the electrolyte solution and outside the cell are in equilibrium: if the dioxygen concentration in the solution increases, then that of the electrolyte solution increases as well. This makes it possible to determine O2 concentration by measuring the diffusion-limited current of the reduction reaction.