Various Concentration Terms

Concentration is defined as amount of solute per amount of solution or solvent. The "amounts" you chose is what gives each concentration term it's own uniqueness.

• percent conc = (mass of solute)/(mass of solution) x 10²
• ppm = (mass of solute)/(mass of solution) x 10⁶
• ppb = (mass of solute)/(mass of solution) x 10⁹
• molarity = (mol of solute)/(liters of solution)

For the rest of this page, concentration is assumed to be in MOLARITY.

Molarity

• Concentration is often depicted with square brackets around the solute of interest.
  concentration of hydrogen ion is depicted as [H⁺]. The concentration is assumed to be molarity (mol/L or mmol/mL).
• Concentration is also sometimes shown as molarity with an italicized capital "M" and a subscript for the solute.
  The concentration of hydroxide would be M_OH^-. Unfortunately, italics are not always used - sometimes, like here,
  the non-italized version just looks better (M_OH^-).

Dilutions - adding more solvent (ie. water) to an already existing solution

M₁·V₁ = M₂·V₂

ANY concentration and volume unit will work here as long as the same units are on BOTH sides of the equation.

Titrations (1:1 ratios)

M_acid·V_acid = M_base·V_base

NOTE: This equation only works for MONOprotic acids (one proton in the formula) and monobases (one hydroxide in the formula). Why? Because then the moles of acid will equal the moles of base, a nice 1:1 ratio. If you have ANY other ratio (not 1:1) you must use the following formula:

Titrations (any ratio)

(Macid · Vacid)		(Mbase · Vbase)
	=
nacid		nbase

Where the "n" is the number of moles of acid and base in the BALANCED chemical equation.

More Volumetric Stuff - getting moles or millimoles

For a given volume of any solution, you can always calculate the number of moles of solute...

(M_solute V_solution) = moles of solute = n_solute

To get moles you MUST use molarity for the concentration and liters as the volume. If you use milliliters (mL) for volume you will get millimoles (mmol) for the amount. Be careful and note which type unit you are using. Like in class, I often prefer to use mL and get mmol. Just make sure you know what you are using.

If you pour together multiple solutions of the same solute, you must calculate the number of moles in each separate solution first, then add all the moles together, and divide by the total combined volume. As long as you quantify all the mole sources (whether solutions, solids, or whatever) and the total accumulated volume, you can easily calculate the concentration.

Mix solutions A, B, and C (all different concentrations and volumes, but all the same solutes)

new molarity = (M_A V_A + M_B V_B + M_C V_C) / (V_A + V_B + V_C)

Note that the numerator here is just a total of all the moles of solute and the denominator is a total of all the volumes.

Acid/Base Formulas

Be sure and know how to get any one of these values from any one of the others...

pH = -log[H+]		pOH = -log[OH-]
[H+] = 10-pH		[OH-] = 10-pOH
Kw = [H+][OH-]		pH + pOH = 14
Kw = 1.0 x 10-14

the value for K_w is only valid at 25 C