Barry M. answered • 01/19/20
Professor, CalTech Grad; Many Years Tutoring Math, SAT/ACT Prep, Chem
I recommend the factor-label method, in which units are treated algebraically just like variables and numbers. They multiply and divide, and can be cancelled top and bottom when in numerator and denominator. You use conversion factors, and multiply by 1 to get the answer. You obtain 1 by relating one unit being equal to another through a number, and then putting one on top of the other to make numerator over denominator = 1. You will need to select which is on top, and which on bottom. Do it in a way that the unwanted units cancel.
2M means 2 moles per liter, so your equality will be 2 mol = 1 L, and therefore 2 mol/1 L = 1 or as needed, 1L/2 mol = 1. Note that I use / for convenience of writing here; I suggest you write with the division line horizontal, so it's clear what's the numerator and what's the denominator.
You are given 24 mol, so start with that and multiply:
24 mol X 1 L/12 mol . The mol units cancel top and bottom, and 24/12 gives 2. So that leaves 12 L.
Now one possible complication. The question, as worded, requires the amount of water needed to make the solution. The definition of M, molarity, is mol per liter of solution. So really, you need enough water to make 12L total solution. If you use 12 L water, and add the HCl solid, most likely the final volume will be greater than 12L. Sometimes mixtures are additive in their volume, but sometimes not--5 L of X and 5 L of Y can result in considerably less than 10 L. But, given only the information above, 12 L should give a fairly close result.
