Can two things be separated based on their densities?

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Yes, two different chemical entities can be separated based on their densities, assuming that the densities of the two items are different enough from one another.  Solids and liquids can easily be separated from each other by simple filtration.  The mixture is passed through some type of filter, either filter paper or a type of sieve.  The solid is collected on the filter surface and the liquid simply passes through.  A denser, thicker liquid can be aided through the use of vacuum pressure to pass it through the filter.

Two different solids and two different liquids can be separated from each other based on their densities, though the process is more complex.  Two different liquids can be separated from each other as long as the two liquids are not miscible, meaning that they do not mix together.  Ethanol cannot be separated from methanol based strictly on density because the two liquids are completely miscible (another technique like distillation must be used).  But oil can be separated from water because the two liquids have different densities and are not miscible.  Since the water is more dense than the oil, the water will fall to the bottom of a container and the oil will float on top of the water.  A centrifuge can be utilized to separate two liquids that do not separate from each other as easily.  The spinning action causes the denser liquid to collect on the bottom of the tube, thus displacing the less dense liquid to sit on top of it.

Two different solids can also be separated from each other based on density (as long as the solids are dry and able to freely move without sticking to each other).  If you mix the two solids together in a container, agitating the container (either shaking or rolling type action) will allow the solid particles to move around in relation to one another.  The denser particles will find their way to the bottom of the container while the less dense particles are sitting on top.

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