How Scientists Measure The Concentration of Solutions

This is analytical chemistry!

Titrations
This is by far the most old school method for measuring the concentration of something in a liquid. The scientist prepares a solution of something that reacts with the other compound and then adds it drop by drop until there is a color change or other easy to recognize event that means the reaction is over. When the reaction is over, we call that the equivalence point. It is the time when amount of the known compound is equal to the amount of the unknown compound. Since the scientist knows how much of the unknown compound was added, some easy math can be used to calculate the concentration of the unknown. A classic example of this is done with acids and bases.
A scientist wants to know the concentration of acetic acid in a bottle of vinegar so she adds a drop of indicator to the vinegar then titrates 100mL of the vinegar with 0.1M sodium hydroxide until the equivalence point is reached. Once the equivalence point has been reached, she knows how much NaOH was used to neutralize the acetic acid, so she can easily calculate the concentration of acetic acid in the vinegar.
Doctors sometimes say that they are titrating a patient onto a medication. That is a fancy way of saying that they give the patient a little bit more medicine each day until they have found the right dose.

Spectrophotometry and UV-Vis Spectrometry
If you are making fruit punch, and you add water to it, the color of your beverage will not be as dark.
Beer’s law says that the amount of light a liquid absorbs is directly related to it’s concentration. So if you can use a machine to measure how much light does not make it through a sample of the liquid, you can easily calculate the concentration. Not all chemicals absorb light at every wavelength.
Biochemists use a spectrophotometer to check the concentration and purity of DNA and Protein solutions every day. Proteins absorb UV radiation at 280nm and DNA absorbs at 260nm. By calculating the ratio of absorbance at 260nm and 280nm, the purity of DNA or protein can be determined. Biochemists do this all the time.

High Performance Liquid Chromatography HPLC
Just about every drug company in the country hires a ton of people to do HPLC for them. This method of measuring concentrations uses a high pressure pump to squirt liquid through a little column. In that column, each compound travels at a different speed. Every compound comes out of the column at a different time. A detector, usually a spectrophotometer or a mass spectrometer, can then tell you how much stuff came out of the column. This method of analysis requires a calibration curve.


Gas Chromatography GC
This works the same way as liquid chromatography, but only for volatile compounds. That usually means compounds with a molecular weight below 500 and a low boiling point.