A $0\mathrm{.}538$g sample of steam at $105\mathrm{.}3^$C is condensed into a container with $5\mathrm{.}77$g of water at $16\mathrm{.}1^$C$.$ What is the final temperature of the water mixture if no heat is lost? The specific heat of water is $4\mathrm{.}18$ J$/$gC$,$ the specific heat of steam is $2\mathrm{.}01$ J$/$g$^$C$,$ and $$Delta H$\_$vap $=40\mathrm{.}7$kJ $/$ mol.