Does precipitated copper carbonate contain impurities I recently performed a double replacement reaction between copper sulfate and sodium carbonate to yield copper carbonate as a precipitate. I then filtered the precipitate, but I noticed that the precipitate still contained a large amount of water. 

Would there be a significant amount of sodium sulfate dissolved in this water, making the copper carbonate impure? If so, how would I separate the remaining sodium sulfate from the copper carbonate?
Yes, the water contained in the freshly filtered precipitate will contain dissolved $\ce{Na2SO4}$, as the latter is the soluble by-product of your double displacement reaction. To get rid of it, you need to wash your precipitate thoroughly with distilled water (pH 7). If you really want to make sure that all $\ce{Na2SO4}$ has been removed, you can test samples of the wash water filtrate for $\ce{SO4^2-}$ by adding diluted hydrochloric acid and aqueous $\ce{BaCl2}$. When a white precipitate of $\ce{BaSO4}$ no longer forms, the aqueous sodium sulfate can be considered separated from the $\ce{CuCO3}$ precipitate.