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How would one prepare a one molar sodium hydroxide solution?

I see a few issues with this:

  • $\ce{NaOH}$ absorbs carbon dioxide. So old NaOH samples might have a significant portion of $\ce{NaHCO3}$ or sodium bicarbonate. How would get get rid of the sodium bicarbonate?
  • I am told that $\ce{NaOH}$ is hygroscopic. So it absorbs water, apparently. What is the mechanism for this? I can see the hydroxide attacking carbon dioxide in the above bullet point, that's easy, but I can't really see $\ce{NaOH}$ attacking water. Also couldn't we circumvent the water absorption problem by cooking the $\ce{NaOH}$?
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There is a difference in preparing a solution and determining its concentration. As you said, NaOH solutions absorb carbon dioxide over time. It is possible to remove the absorbed carbon dioxide by boiling, but it is just as easy to use the solution as is and re-determine its concentration when you use it.

The concentration of sodium hydroxide solutions can be determined by titrating a known amount of dried potassium hydrogen phthalate.

If you really need an exact concentration of the solution, make it slightly more concentrated, standardize it and then dilute it to get the concentration desired. It would only be accurate for a few hours.

I am told that NaOH is hygroscopic.

The powder and pellets of sodium hydroxide are hygroscopic, but the solutions of sodium hydroxide already have water, so it is unlikely more will be absorbed.

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1)In short, you can't prepare exactly $1M$ solution of $\ce{NaOH}$. It is common to prepare roughly $1M$ solution and then titrate it to get an exact value of its molarity. For preparation of standards people usually avoid usage of $\ce{NaOH}$ and similar compounds that adsorb something from air. For exapmple, $\ce{NaHCO3}$ is a nice option.

2)$\ce{NaOH}$ granules adsorb water from air, forming a solution of the hydroxide in water. The driving force behind it is energy of solvation of $\ce{Na^+}$ and $\ce{OH^-}$ ions (as far as these words are applicable to concentrated solutions)

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