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*Determine the concentration of species in solution when two (or more) solutions are mixed.

Concentration describes the amount of a solute in a solution versus the total amount of solvent and/or solution present. Concentration can be expressed in a variety of ways, which are outlined below.

The mass fraction describes the mass of solute in a solution divided by the total mass of the solution. The mass fraction will always have a value between zero and one, representing the two extreme cases in which there is no solute (mass fraction = 0) or no solvent (mass fraction = 1). The mass fraction can be converted into a mass percentage by multiplying it by 100%. The mass percentage would range in value from 0% to 100%. We can express mass fractions in units of parts per million (ppm) if we multiply them by one million ( 10^6 ). By extension, we can express mass fractions in units of parts per billion (ppb) or parts per trillion (ppt) by multiplying the mass fraction by one billion ( 10^9 ) or one trillion ( 10^{12} ), respectively.

The concentration of a solute in a solution could also be expressed as a mole fraction ( X_i ) that equals the moles of solute in the solution divided by the total number of moles present in the solution (moles of solute + moles of solvent). Mole fractions can also be expressed in units of ppm, ppb, or ppt. For example, to express a mole fraction in units of ppm, you would multiply the mole fraction by 10^6 . We will not use mole fraction until we cover gases.

We can also express concentration in terms of molarity (M). The molarity of a solute in a solution is equal to the number of moles of the solute in the solution divided by the total number of liters of solution. The unit molar (M) is used to express concentration in terms of molarity. If the concentration of a solute in a solution is 1 M, that means that one liter of that solution would contain one mole of that solute.