Ways of expressing a solution

There are several ways of expressing the concentration of a solution.

Explanation:

Concentration is the proportion of a substance in a mixture. There are several ways of expressing them, each with their own usefulness. What's incredibly useful is with a little math and conversion factors, these can all be interconverted.

Molarity (M) - amount (mol) of solute / volume (L) of solutionPros: Very common in labs, makes conversions easy. Cons: Effected by temperature (liquid expands with heat so unit volume of hot solution has less solute than cold solution) and mixing (volumes are not always additive (for instance, 50 mL of water and 50 mL of ethanol is not exactly 100 mL of mixture due to solvent-solvent interactions).Molality (m) - amount (mol) of solute / mass (kg) of solventPros: Preferred when temperature and density could change; molal is based on masses, not volume so molality does not change with temperature. Masses, unlike volumes sometimes, are always additive.Cons: When dealing with moles in reactions conversions are harder.Parts by mass a.k.a mass % (% w/w) - mass of solute / mass of solutionPros: Good indication of how pure a substance is; and good for very small concentrations such as toxin or pollutant levels in a biological or environmental setting, respectively.Cons: Not the most useful for reaction stoichiometry.Parts by volume a.k.a volume % (%v/v) - volume of solute / volume of solutionPros: Very good and common for measuring main ingredients in things, such as alcohol in hand sanitizer, hydrogen peroxide in those brown bottles you see, and how much alcohol in wine bottles.Cons: Again, not the easiest to use for reaction stoichiometry.Mole fraction (X) - amount (mol) of solute/ amount (mol) of solute + amount (mol) of solvent Pros: N/ACons: N/AMass per volume percentage - mass of solute / volume of solutionPros: Common for measuring main ingredients in medicine, such as how much of it is in an aqueous solution (example: benzocaine)Cons: Difficult to use with stoichiometry.Parts per million and parts per billion (ppm or ppb) - mass of substance  / mass of sample * 10^6 or 10^9Pros: Excellent for expressing concentrations of very trace components such as a toxin or pollutant in blood, for example. Cons: Not very useful for large quantities of things.

Note: to find the percent of some of these, such as for mass percent or volume percent, multiply the result by 100.

Additionally, with some practice you can answer a question such as, "The label on a 0.750-L bottle of Italian chianti says "11.5% alcohol by volume." How many liters of alcohol does the wine contain?". etc...

I really hope this helps! Take care.