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The LHCb experiment will be installed in the proton-proton Large Hadron Collider (LHC) at CERN, Geneva. The detector is a single arm spectrometer currently under construction: LHC running and LHCb data taking will start in 2007. LHCb will then benefit from the prolific source of B-mesons provided by the LHC. The main goals of the LHCb experiment are to measure the CP asymmetries in the B-meson sector and to study rare decays of b-hadrons. These will extend the measurements presently made with B0d mesons by the Belle (Japan) and BABAR (USA) experiments. The expected accuracy on the comprehensive measurements with both B0d and B0s mesons will allow to open new windows on physics beyond the Standard Model. The Standard Model of particle physics (SM) provides the framework for the description of a possible violation of the CP symmetry in the neutral B-meson sector. In particular, it predicts an asymmetry due to CP violation in the time dependent rates for B0d,s and B0d,s to a common CP eigenstate when this transition is dominated by the subprocess b → ccs: this is due to the interference between the decay and the mixing of these neutral mesons. In this case, the CP violation is directly related to sin (Φd,s) where Φd,s is the B0d,s weak mixing phase. The B0s meson system can be used for the measurement of such an asymmetry. However it requires hadron machines and high luminosities to compensate the low branching ratio to CP eigenstates. In contrary to the "golden channel" B0s → J/Ψ Φ which demands an angular analysis to distinguish the different CP eigenstates contributions, the J/Ψ η final state is a pure CP-even eigenstate. This channel can therefore provide an excellent probe to the Φs phase. The reconstruction and performances of this decay mode will be detailed in this dissertation. They are performed with a full Monte Carlo simulation. An annual yield of about 9'000 events for the B0s → J/Ψ(μ+ μ–) η(γ γ) channel and 3000 for the B0s → J/Ψ(μ+ μ–) η(π+ π– π0) decay will be collected with a background-to-signal ratio smaller than 3. The mass and proper time resolutions are quite limited due to the electromagnetic calorimeter photon reconstruction low quality. Hopefully they can be improved by the application of a Kalman Filter fit. The sensitivity of the LHCb experiment to the weak mixing phase Φs has been determined with a toy Monte Carlo. This simulation uses the B0s → J/Ψ η decay channels enriched by the B0s → ηc Φ pure CP eigenstate channel. It takes into account the event-by-event proper time error, the time-dependent selection efficiency, the B/S ratio, the tagging efficiencies and the reconstruction performances of each decay channel. The combined sensitivity to Φs is found to be 0.068 rad when the SM prediction for this phase is Φs ≃ –0.04 rad. These results have been finally compared to the B0s → J/Ψ Φ channel, whose sensitivity to Φs reaches 0.031 rad with a annual yield of 125'000 events. The combined sensitivity of all these channels then increases to 0.028 rad. The contribution of the pure CP eigenstates is estimated to ~ 17%. Even with much smaller statistics, the pure CP eigenstate decay channels provide a non-negligible contribution to the determination of the B0s weak mixing phase Φs.