# Hydrogen storage using activated carbons

On Wikipedia, a possibility of using activated carbons to store hydrogen is reported. According to the Wikipedia page, this solution can be used to store around 5 wt% by cooling down the hydrogen to -196$$\;^\circ$$C at 1 bar. I am wondering if the storage system has to be kept always at this temperature?

Long answer: I'll skip some intermediate physicochemical derivations for brevity. The phenomenon we are dealing with is called adsorption. Perhaps, the simplest theoretical explanation of adsorption was given by Langmuir. Langmuir adsorption isotherm can be written as $$\theta = \frac{Kp}{1 + Kp},$$ where $$\theta$$ is a fraction of the surface of adsorbent (solid) covered by the adsorbate (gas) and $$K$$ is an equilibrium constant. It is seen that at a constant temperature the more pressure you apply to the system, the more surface is covered (i.e. the more gas is adsorbed).
But what about the temperature dependence? Since $$K$$ is an equilibrium constant, its temperature dependence is defined by the van't Hoff equation. Also, $$K$$ is directly proportional to the pressure required for a certain amount of gas to be adsorbed. In other words, when $$\theta$$ is constant, $$\ln{K}+\ln{p}=\mathrm{const}$$, transforming our van't Hoff into something like $$\left(\frac{\partial\ln{p}}{\partial(1/T)}\right)_\theta=\frac{\Delta_{ad}H^○}{R}.$$ Here, $$R$$ is the gas constant, and the sign of $$\Delta_{ad}H^○$$ - adsorption enthalpy - is negative, for adsorption is exothermic. Consequently, the slope of $$\ln{p}$$ vs $$1/T$$ line is negative. In plain English, the equation above reads like this: in order to obtain the same amount of adsorbate $$\theta$$ you should either decrease the temperature or increase the pressure.