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Can a chemical be introduced to a volume of water which can actually reduce the volume of water in that container?

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Yes, at least if only the total volume should decrease:

Density of water: $\pu{1000 kg/m^3}$
Density of ethanol: $\pu{789 kg/m^3}$
Expected density of 52 Vol.% ethanol solution: $\pu{890 kg/m^3}$
True density of 52 Vol.% ethanol solution: $\pu{909 kg/m^3}$
All values are for the same conditions.

The volume of every ethanol-water solution is smaller than the sum of the original volumes of water and ethanol. For example if you add $\pu{52 mL}$ of ethanol to $\pu{48 mL}$ water you will get a solution with an volume of approximately $\pu{97.9 mL}$.
This effect is known as volume contraction and depends on the mixing ratio of both components in a nonlinear way. Its reason is the formation of additional bonding forces (e.g., hydrogen bridges) between the molecules, which results in a higher density.

Note: I don´t think that there is something that can increase density of water in such a way that the resulting total volume is actually smaller than the volume of water used.

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