How do I get the molarity of solution 1 given volume 1, molarity 2, and volume 2? For example:


  What is the molarity of a $\ce{NaOH}$ solution if $25\rm~mL$ of the solution is exactly neutralized by $44\rm~mL$ of $0.32\rm~M~HCl$?


I know that the abstract function is 

$$\text{Given Volume of Known Molarity} \times \text{Molarity Factor} \times \text{Mole Ratio} \times \text{Per Volume Factor} \times \text{Conversion Factor Per Liter}$$
The reaction that occurs: H+ + OH- --> H2O

When you multiply the volume of HCl by the molarity of HCl you get the total amount of moles of H+ that reacted (mol/L x L = mol).
This means that the same amount of OH- was needed for the reaction (1:1). 
Volume of NaOH is known and thus yields the answer.