When elements combine to form compounds, do their properties change?

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Yes, when elements combine to form compounds, their individual properties are lost. In comparison, elements retain some (or many) of their property when they are mixed to form a mixture. For example, a common compound such as water is made up of 2 elements hydrogen and oxygen, both of which are gases, yet water is liquid. Similarly, hydrogen is an extremely combustible gas. Oxygen is required for combustion. Yet, their compound, water is used for extinguishing fire. Similarly, most of the food that we eat contains some organic hydrocarbons (compounds of carbon, oxygen and hydrogen). Two of the main constituents are gases, yet we get solid or liquid food and it certainly tastes different from individual elements. On the other hand, if we mixed powdered iron and copper, we can still separate them by density difference of difference in magnetic properties (iron is magnetic and copper is not) and iron can still rust.

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