  The initial mass distribution in the solar nebula is a critical input to
planet formation models that seek to reproduce today's Solar System.
Traditionally, constraints on the gas mass distribution are derived from
observations of the dust emission from disks, but this approach suffers from
large uncertainties in grain growth and gas-to-dust ratio. On the other hand,
previous observations of gas tracers only probe surface layers above the bulk
mass reservoir. Here we present the first partially spatially resolved
observations of the $^{13}$C$^{18}$O J=3-2 line emission in the closest
protoplanetary disk, TW Hya, a gas tracer that probes the bulk mass
distribution. Combining it with the C$^{18}$O J=3-2 emission and the previously
detected HD J=1-0 flux, we directly constrain the mid-plane temperature and
optical depths of gas and dust emission. We report a gas mass distribution of
13$^{+8}_{-5}\times$(R/20.5AU)$^{-0.9^{+0.4}_{-0.3}}$ g cm$^{-2}$ in the
expected formation zone of gas and ice giants (5-21AU). We find the total
gas/millimeter-sized dust mass ratio is 140 in this region, suggesting that at
least 2.4M_earth of dust aggregates have grown to >centimeter sizes (and
perhaps much larger). The radial distribution of gas mass is consistent with a
self-similar viscous disk profile but much flatter than the posterior
extrapolation of mass distribution in our own and extrasolar planetary systems.
