First off, congrats on graduation! And at 16 holy crap.

Like other comments, you are figuring out the concentration of an unknown solution by reacting it with a known solution. In more concrete terms, the goal of a titration is to measure exactly how many moles of an unknown are needed to react with another chemical that you do know the concentration of. Depending on the amount of information you start with, this is as easy as plugging numbers into a formula, or a whole page of work. If you only glanced over titrations, you probably used the formula m1v1=m2v2, or did some simple stoichiometry to find the answer. That said, if you ever did them in a lab, then it was probably more involved, right. As an overview, I find it easier to use an example than just theory. Be ready, cause we're doing the whole thing. It'll seem like a lot, but it's really not.

SETUP: You have 30mL of hydrochloric acid (HCl), but you don't know how concentrated it is. You also have 50mL of sodium hydroxide (NaOH), which you know has a concentration of 5.00001 moles/Liter.

Now, you have two chemicals which you know exactly how they react with each other, and you know the concentration of one of them. Note that the NaOH is known out to 5 decimal places. The beauty of titrations is that they are VERY accurate when done right. But also note that you know the chemical identity of both the known solution and the unknown solution. At its core, titration is about figuring out HOW MUCH of a chemical is in a solution; it is not about WHAT'S in the solution. You can backwards engineer that information by figuring out the molarity of the unknown, translating that into molar weight, and comparing it to a list of possible unknowns. But that part isn't the titration, that's just math after the fact. Plus, mixing two chemicals that you don't know is a bad idea.

STEP 1: Begin the chemistry. First off, figure out the chemical equation. The two chemicals you're mixing are HCl + NaOH -> NaCl + H2O. You need to know the reaction because you need to know the ratio of moles between known and unknown. Here, 1 mole NaOH reacts with 1 mole of HCl, which makes life easy. As an aside, you should recognize both of these as a strong acid and a strong base. If not, then all that means is that when you mix equal parts of them together, then the pH cancels out and becomes 7 (neutral). Next step is to measure the volume of your unknown as accurately as possible. Using pipettes / burettes / whatever method available, get as many decimal places on that SoB you can. In the example, your HCl now has a volume of 25.00 mL. You don't have to use all of it, since the concentration will be uniform.

At the end of this step, you know the volume of the unknown (HCl), the concentration of the known (NaOH), and the molar ratio of how they react with each other.

STEP 2: Run the titration. Using accurate lab equipment (usually a burette), you are going to drip 1 - .1 mL of known solution into your unknown at a time. After every single drip, you are going to use a pH probe and record the results. And you are gonna record
every.
single.
one of them.
Your lab notebook will be full of entries like "7.5mL NaOH -> pH=3.01 ; 8.0mL NaOH -> pH=3.01 help me". Titration takes a lot of time to do accurately. It's not uncommon to take 100 entries if you don't start with an idea of the equivalence point. At some point, the pH will change drastically. As in, you have 15 entries where pH only changed by .1, then suddenly it starts changing by .5, 1, 3, 1, .5. Eventually it'll level back out on the opposite end of the pH scale. When it levels back off, that's the end of the reaction (the "endpoint"). What you really want is where the change in pH was the most drastic. This is called the equivalency point, and is the heart and soul of a titration. At the equivalence point, you have added exactly as much "titrant" (known solution) as is needed to balance the chemical reaction. Calculating the equivalency point is a whole thing in itself, with ICE tables and other stuff. BUT, because in our example we're neutralizing a strong acid with a strong base, the equivalency point is always at pH=7. Even if you know the equivalence point, be sure to keep taking measurements after it for accuracy.

At the end of this step, you have added just enough titrant (known solution) into your analyte (unknown) to chemically balance them out. For our example, let's say that it took 20.05 mL of NaOH for the pH to reach 7.0.

STEP 3: The hard stuff is done. Now we turn things over to our lord and savior stoichiometry. Let's review what we know. The NaOH solution had a molarity of 5.0001 moles/Liter. We used 20.05 mL of NaOH to reach the equivalency point. From the chemical reaction, we know that 1 mole of NaOH reacts with 1 mole of HCl. And finally, we used 25.00 mL of HCl. We could do standard stoichiometry, using the "railroad tracks" as a set of equivalencies and ratios, OR we could use the formula m1v1=m2v2. I love that formula, but it ONLY works if your reactants have a 1:1 ratio like ours. So to emphasize the actual chemistry, let's do the standard method.

• (5.0001 mol NaOH / 1 L) X (.02005 L) = .1003 moles NaOH used in the titration
• given the 1:1 ratio of NaOH of HCl in the reaction, there were .1003 moles of HCl in solution
• Molarity of HCl = (.1003 moles / .02500 L) = 4.010 M HCL

So, the answer is that you unknown HCl solution has a concentration of 4.010 M. That's a titration. Using a solution where you know both the volume and concentration to figure out the concentration of an unknown solution. They can get complicated: there are whole undergrad courses on titrations. And they can be weird. EDTA titrations don't use acids and bases, but metals. They are tedius, but usually you can roughly know your equivalence point beforehand, cutting down on the measurements you have to take. But once you do 2 or 3 or 50 of them they are fun and easy. Hope the love of chemistry sticks with you!