  We calculate the minimum mass of heavy elements required in the envelopes of
Jupiter and Saturn to match the observed oversolar abundances of volatiles.
Because the clathration efficiency remains unknown in the solar nebula, we have
considered a set of sequences of ice formation in which the fraction of water
available for clathration is varied between 0 and 100 %. In all the cases
considered, we assume that the water abundance remains homogeneous whatever the
heliocentric distance in the nebula and directly derives from a gas phase of
solar composition. Planetesimals then form in the feeding zones of Jupiter and
Saturn from the agglomeration of clathrates and pure condensates in proportions
fixed by the clathration efficiency. A fraction of Kr and Xe may have been
sequestrated by the H3+ ion in the form of stable XeH3+ and KrH3+ complexes in
the solar nebula gas phase, thus implying the formation of at least partly Xe-
and Kr-impoverished planetesimals in the feeding zones of Jupiter and Saturn.
These planetesimals were subsequently accreted and vaporized into the hydrogen
envelopes of Jupiter and Saturn, thus engendering volatiles enrichments in
their atmospheres, with respect to hydrogen. Taking into account both
refractory and volatile components, and assuming plausible molecular mixing
ratios in the gas phase of the outer solar nebula, we show that it is possible
to match the observed enrichments in Jupiter and Saturn, whatever the
clathration efficiency. Our calculations predict that the O/H enrichment
decreases from 6.7 to 5.6 times solar (O/H) in the envelope of Jupiter and from
18.1 to 15.4 times solar (O/H) in the envelope of Saturn with the growing
clathration efficiency in the solar nebula.
