The thermalization of a pulse of fast neutrons in a large, homogeneous water assembly is investigated numerically. The effect of chemical binding is studied by comparing the results obtained with the free-hydrogen gas and the Nelkin kernels. It is found that chemical binding has an observable effect on some of the quantities of interest in a pulsed-neutron experiment. Two definitions of mean slowing-down time are considered and their relationship examined. Comparisons are made to several experimental measurements and earlier calculations.