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We present an observer design to estimate the partial pressure of hydrogen in the anode channel of a fuel cell. A precise knowledge of this pressure is of importance to ensure reliable and efficient operation of the fuel cell power system. Our design makes use of a monotonic nonlinear growth property of the voltage output on hydrogen partial pressures at the inlet and at the exit of the channel. By treating the slowly varying inlet partial pressure as an unknown parameter, an adaptive observer is developed that employs a nonlinear voltage injection term. We then study the robustness of this observer against variations in the inlet partial pressure, and analyze its sensitivity to other modeling errors. We also prove a robustness property of the observer against the parameter estimation error, which means that it can be implemented with alternative parameter estimator designs.