You find the mass of a piece of iron metal, let it rust outside, and measure the mass gain. the mass has increased. does this violate the principle of conservation of mass? explain.

No, when the iron rusted, it went through a chemical reaction and in doing so added oxygen to the iron. So the rust is really the mass of the iron it was before it combined with oxygen from the air. The increase in mass is the added oxygen to the original iron.

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c. heat could easily travel through the molecules in the air and escape/enter the flask. removing the air slows down the heat transfer.  

every chemical equation adheres to the law of conservation of mass, which states that matter cannot be created or destroyed. therefore, there must be the same number of atoms of each element on each side of a chemical equation.