Chemistry molarity problem 1L vs 0.5L with same # of mols

[Stephen2009]

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So I just did a problem where we have 0.005 moles of substance in 1L of solution. Now what is the concentration in a 0.5 L sample of this "beverage"?

Now the answer is 0.005M. How do we do the math behind this?

Now we can't use M1V1 = M2V2 b/c that is a dilution formula and we're not diluting anything... I understand the intuitive way to approach this, but what about the math behind this?

Thanks!

 

[Rabolisk]

The real math is...

M = M

You initially have a solution with a volume of 1L, and solute of 0.005 moles. Hence its molarity is 0.005. Now, take a sample of this "beverage". No matter how much you take, the concentration cannot change because solutions are homogeneous. By taking half of the solution, you also take half of the solutes, and thus, you end up with the same concentration.

You can always dilute by adding water, but you cannot make a dilute solution more concentrated without distillation or some sort of chemical reaction (or adding more solutes, of course).

 

[Stephen2009]

Thanks! Your explanation helped a ton!