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A compound is similar to a homogeneous mixture in that the proportions of the atoms throughout the compound/mixture are always fixed and do not vary. For example, a sample of pure C02 gas is a compound and will always have two parts oxygen to every carbon atom. Likewise, a homogeneous mixture of salt water will always have a fixed proportion of salt ions to water. (However, a heterogeneous mixture, such as muddy water would not always have a fixed proportion of mud to water since the mud might settle towards the bottom. The solution strength of a heterogeneous mixture can vary while a homogeneous mixture remains constant).
A homogeneous mixture can be separated into its constituent components by physical means. For example, you can evaporate off the water off a sugar-water mixture, or you can filter a mixture of water and sand.

A compound, however, requires some kind of chemical reaction to separate it into its constituent elements.

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