Question about Fundamentals G.25?

[Connie Liang 3L]

I'm confused by this quote from the solutions manual.

"In order to find the number of times the volume must be doubled to get to one molecule, we can solve for the number of times this amount of molecules must be cut in half until it equals 1."

I understand the basic concept that when you double the volume of a solution, you're cutting the molarity in half. And when you cut the molarity in half, you also halve the number of moles by definition of molarity. But I'm confused because I thought no matter how many times you dilute a solution, the number of moles stays the same.

[Kaylee Messick 3J]

The moles of solute do stay the same when diluting a solution. For example, the equation c=n/V is the equation for molarity. When we increase the volume of the solution (V), the molarity (c) should go down because we are dividing by the volume, therefore making c smaller. However, the number of moles (n) stayed the same because the only thing we changed was adding more volume. Hope this helps!

[Connie Liang 3L]

@Kaylee

Thanks for the reply! But if the number of moles stays the same then how is it possible to cut the number of molecules in half? Isn't the number of molecules dependent on the number of moles?

[Kaylee Messick 3J]

Sorry I didn't see this post until now! If you look in section G.4 of the textbook, Figure G.9 in the dilution section explains how the number of molecules goes down while moles stays the same. Basically, they are only looking at a specific area, and when diluted, the specific area will have less molecules, even though there might be the same number of molecules overall. Hope this makes sense!

[Connie Liang 3L]

Thank you so much! I didn't examine the figure, so it was super helpful that you pointed that out!