Answer
$m(H_2O)=109.53g$
Work Step by Step
Considering stoichiometric coefficients, we can conclude that 2 moles of water produce 2 moles of hydrogen, and 1 mole of hydrogen produces 2 moles of hydrogen chloride. Hence, 2 moles of water produce 4 moles of $HCl$. In other words, 1 mole of water produces 2 moles of $HCl$.
$n(H_2O) = 0.5n(HCl) =0.5\frac{m(HCl)}{M(HCl)}=0.5\frac{444.2g}{36.5\frac{g}{mol}}=6.085mol\implies m(H_2O) = M(H_2O)\times n(H_2O) = 18\frac{g}{mol}\times 6.085mol=109.53g$
