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how would you make 500.0mL of a 0.200M NaOH solution from a 15.0 M stock NaOH solution??

I assume that you want the volumes rather than the mechanics of carrying it out?

a) How many moles do you need in the 500 ml to have 0.200 M?

b) What volume of 15.0 M would contain the number of moles from a)?

In principle you would transfer this volume to a 500 ml volumetric flask and make the volume upto the line with water. Not so easy to achieve the 3 significant figures implied in the question in practice because of the small volume needed.

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