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This paper presents the third in a series of single-dish studies of molecularabundances in the envelopes around a large sample of 18 low-mass pre- andprotostellar objects. It focuses on typical grain mantle products and organicmolecules, including H2CO, CH3OH and CH3CN. With a few exceptions, all H2COlines can be fit by constant abundances of 7e(-11)-8e(-9) throughout theenvelopes if ortho- and para lines are considered independently. The currentobservational dataset does not require a large H2CO abundance enhancement inthe inner warm regions, but this can also not be ruled out. Through comparisonof the H2CO abundances of the entire sample, the H2CO ortho-para ratio isconstrained to be 1.6+/-0.3 consistent with thermalization on grains attemperatures of 10-15 K. The H2CO abundances can be related to the empiricalchemical network established on the basis of our previously reported survey ofother species and is found to be closely correlated with that of thenitrogen-bearing molecules. These correlations reflect the freeze-out ofmolecules at low temperatures and high densities. An improved fit to the datais obtained with a `drop' abundance structure in which the abundance decreasewhen the temperature is lower than the evaporation temperature and the densityhigh enough so that the timescale for depletion is less than the lifetime ofthe core. The derived abundance structures for CH3OH are consistent with ascenario where CH3OH probes the action of compact outflows on the envelopes,which is further supported by comparison to high frequency, high excitation CSJ=10-9 and HDO line profiles. The extent to which the outflow dominates theabundance enhancements compared with the passively heated inner envelopedepends on the filling factors of the two components in the observing beam.Comment: Accepted for publication in A&A. Abstract abridge

H2CO and CH3OH abundances in the envelopes around low-mass protostars

H₂CO and CH₃OH abundances in the envelopes around low-mass protostars