Using far-infrared spectroscopy, we have studied the magnetic field and temperature dependence of the spin gap modes in the chains of Sr14Cu24O41. Two triplet modes T-1 and T-2 were found in the center of the Brillouin zone at Delta(1)=9.65 meV and Delta(2)=10.86 meV in zero magnetic field. The T-1 mode was excited when the electric field vector E of the light was polarized along the b axis (perpendicular to the planes of chains and ladders) and T-2 was excited for E parallel to a (perpendicular to the chains and along the rungs). Up to the maximum magnetic field of 18 T, applied along the chains, the electron g factors of these two modes were similar, g(1c)=2.049 and g(2c)=2.044. Full linewidth at half maximum for both modes was 1 cm(-1) (0.12 meV) at 4 K and increased with T. The temperature dependence of mode energies and line intensities was in agreement with the inelastic neutron scattering results from two groups [M. Matsuda , Phys. Rev. B 59, 1060 (1999); L. P. Regnault , ibid 59, 1055 (1999)]. The T-1 mode has not been observed by inelastic neutron scattering in the points of the k space equivalent to the center of the Brillouin zone. Our study indicates that the zone structure model of magnetic excitations of Sr14Cu24O41 must be modified to include a triplet mode at 9.65 meV in the center of the magnetic Brillouin zone.