At $20$ degree C$,$ the density of a $20\mathrm{.}0\%$ by mass ethanol$-$water solution is $968\mathrm{.}7$ kg$/$m$^3.$ Given that the partial molar volume of ethanol in the solution is $52\mathrm{.}2$ cm$^3/$mol$,$ calculate the partial molar volume of water.

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