Answer
$1.526\times10^{-6}\ g/mL$
Work Step by Step
Vapor pressure of water: $23.8\ torr\times 1.0\ bar/750.06\ torr=0.032\ bar$
The partial pressure of Hydrogen: $1.00-0.032=0.968\ bar$
Henry's Law:
$S=k_HP$
$S=7.8\times10^{-4}\ mol/kg.bar\times0.968\ bar$
$S=7.55\times10^{-4}\ mol/kg$
Assuming that the mass of the mixture is approximately the mass of water and that it has a density of 0.001 kg/mL
$7.55\times10^{-4}\ mol/kg\times 2.02\ g/mol\times0.001\ kg/mL=1.526\times10^{-6}\ g/mL$
