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I just found a random example so I could highlight my inquiry:

A chemist wants to make .5L of a 20M solutionusing $\ce{NaOH}$. The solution will be made from solid $\ce{NaOH}$ and water. How many grams of $\ce{NaOH}$ are needed to make this solution?"

In this case, I am finding the moles of $\ce{NaOH}$ that would equate to the number of moles in 0.5L of a 20M solution. But, is it saying that (x grams of $\ce{NaOH}$ + x volume of $\ce{H2O}$) make up the total 0.5L ? or am I adding x grams of $\ce{NaOH}$ to .5L of $\ce{H2O}$ and not considering the changes in volume?

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If the final volume of the solution is .5L then what is important here is how many moles/grams of the substance would be used to make the solution. In general when making a solution, the solution is raised to the final volume after the mixture. So whether .5L of $\ce{H2O}$ is used, or .4998L of $\ce{H2O}$ is used doesn't matter.

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is it saying that (x grams of $\ce{NaOH}$ + x volume of $\ce{H2O}$) make up the total 0.5L

That would be the exact way!

Molarity is defined as $\mathrm{\frac{moles_{solute}}{\mathbf{total}\ volume_{solution}}}$

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