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I have an assigment question that I need help with.

The Q states that sodium hydroxide absorbs water from the atmosphere. Then the saturated NaOH absorbs carbon dioxide from the air to form a thin coating of sodium carbonate.
A piece of sodium hydroxide has been left on a watch glass. It is then dried, dissolved in water and excess barium nitrate solution is added. Is the precipitate that forms barium carbonate?

yes, barium carbonate is insoluble.

Yes I know that barium carbonate is soluble. What I wanted to know is: is barium carbonate the likely precipitate in this equation.

The solubilities are quite different.

BaCO3 0.002 g per 100 ml
Ba(OH)2 5.6 g per 100 ml

(both in cold water)

so yes, barium carbonate is the most likely ppt.

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