The MuCap experiment measures the mu^- disappearance rate, l_-, in a gaseous hydrogen time projection chamber (TPC) and compares it to the free mu^+ decay rate, l_+, to obtain the mu p singlet capture rate L_S. The motivation is a determination of the pseudoscalar form factor, g_P, of the proton, which relates quadratically to L_S. A mu p atom, created after a muon stops in the TPC, can form molecular hydrogen at the rate l_ppmu. Muon capture from the molecular state is slower than from the singlet state and l_ppmu must be known to correctly extract L_S. New data from the MuCap experiment reduces the uncertainty in l_- by a factor of 2.4, making the improved measurement of l_ppmu critical.This work presents results for l_ppmu based on data obtained using an argon-doped hydrogen gas, but under otherwise identical TPC conditions as the main MuCap data set taken with ultra pure hydrogen. Argon introduces additional atomic processes involving the muon, which affect the time spectra of muon decay electrons and capture neutrons. Fits to these data determine l_ppmu to a precision that is a significant improvement to the current world average. The main results are extracted from the decay electron time spectrum, which determines l_ppmu to a relative precision of ~3%, a threefold improvement compared to previous efforts. The measurement of l_ppmu presented in this thesis contributes to a clear interpretation of the final result of the MuCap experiment.
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A determination of the formation rate of muonic hydrogen molecules in the MuCap experiment