Spatially-resolved and unresolved magnetic resonance measurements are used in combination with a partial least squares regression (PLSR) method to measure chemical composition within catalyst pellets during the 1-octene hydrogenation reaction occurring in a fixed bed of 0.3wt% Pd/Al$2$O$3$ catalyst pellets. The PLSR method is used to discriminate between chemical species within and external to the void space of the catalyst pellets. The spatially-resolved data show that the hydrogenation and isomerisation reactions are dominant in the upper and lower region of the reactor, respectively. The local intra-pellet compositions also show product accumulation inside catalyst pellets consistent with reaction occurring under conditions of mass transfer limitation. An average measure of the intra-pellet composition within the whole bed was then used to estimate the liquid-solid mass transfer coefficient during the course of the reaction. The values of k$\mathrm{LS}$ obtained from the NMR measurements were in the range 0.15×10$\mathrm{<mrow\; data-mjx-texclass="ORD">-5</mrow>}$ ms$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ < k$\mathrm{LS}$ < 0.25×10$\mathrm{<mrow\; data-mjx-texclass="ORD">-5</mrow>}$ ms$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, for reactor operating conditions characterised by gas and liquid Reynolds numbers 0.2 < $ReL$ < 0.6 and 0.1 < $ReG$ < 0.3; these values are shown to be consistent with those predicted by existing literature correlations. Closest agreement was found with values predicted from dissolution experiments performed under similar hydrodynamic conditions in trickle flow. In addition to introducing a method for the direct measurement of k$\mathrm{LS}$, the data presented also confirm that estimates of k$\mathrm{LS}$ are more accurate when performed in an environment in which the hydrodynamics and fluid-solid contacting conditions are representative of the system of interest.