  (Abridged*) Models of the young solar nebula assume a hot initial disk with
most volatiles are in the gas phase. The question remains whether an actively
accreting disk is warm enough to have gas-phase water up to 50 AU radius. No
detailed studies have yet been performed on the extent of snowlines in an
embedded accreting disk (Stage 0). Quantify the location of gas-phase volatiles
in embedded actively accreting disk system. Two-dimensional physical and
radiative transfer models have been used to calculate the temperature structure
of embedded protostellar systems. Gas and ice abundances of H$_2$O, CO$_2$, and
CO are calculated using the density-dependent thermal desorption formulation.
The midplane water snowline increases from 3 to 55 AU for accretion rates
through the disk onto the star between $10^{-9}$-$10^{-4} \ M_{\odot} \ {\rm
yr^{-1}}$. CO$_2$ can remain in the solid phase within the disk for $\dot{M}
\leq 10^{-5} \ M_{\odot} \ {\rm yr^{-1}}$ down to $\sim 20$ AU. Most of the CO
is in the gas phase within an actively accreting disk independent of disk
properties and accretion rate. The predicted optically thin water isotopolog
emission is consistent with the detected H$_2^{18}$O emission toward the Stage
0 embedded young stellar objects, originating from both the disk and the warm
inner envelope (hot core). An accreting embedded disk can only account for
water emission arising from $R < 50$ AU, however, and the extent rapidly
decreases for low accretion rates. Thus, the radial extent of the emission can
be measured with ALMA observations and compared to this limit. Volatiles
sublimate out to 50 AU in young disks and can reset the chemical content
inherited from the envelope in periods of high accretion rates. A hot young
solar nebula out to 30 AU can only have occurred during the deeply embedded
Stage 0, not during the T-Tauri phase of our early solar system.
