2.7 Concentration Units
Concentration is a measure of solute to solvent ratios and can be expressed in many ways. The units chosen generally depend on the state of matter of the solute and/or solvent.
g/100g
- The common form of solubility
- Units: g solute / 100 g solvent
- Temperature independent
\[r = \dfrac{\mathrm{g~solute}}{100~\mathrm{g~solvent}}\]
Mass Concentration
- Given as \(\rho\)
- Units: g L–1
- Temperature dependent
- Used when molecular weights are unknown but masses are known
\[\rho = \dfrac{\mathrm{g~solute}}{\mathrm{L~solution}}\] Mass concentration is the density of a component in a mixture (mass over volume), hence the use of the Greek letter \(\rho\) to represent mass concentration as it is used to represent density,
Molarity
- Given as M
- Units: mol L–1
- Temperature dependent
- Used for quantitative solution reactions and titrations
\[M = \dfrac{\mathrm{mol~solute}}{\mathrm{L~solution}}\]
Molarity is derived from mass concentration by converting grams of solute into moles of solute via molar mass.
Molality
- Given as m
- Units: mol kg–1
- Temperature independent
- Used in colligative property calculations
\[m = \dfrac{\mathrm{mol~solute}}{\mathrm{kg~solvent}}\]
Mole Fraction
- Given as \(\chi\)
- Unitless
- Used for characterizing the partial pressures of gases and vapor pressures of solutions
- Temperature independent
\[\chi_{\mathrm{solute}} = \dfrac{n_{\mathrm{solute}}}{n_{\mathrm{solution}}}\] \[\chi_{\mathrm{solvent}} = \dfrac{n_{\mathrm{solvent}}}{n_{\mathrm{solution}}}\]
Mole Percent
- Given as mol %
- Units: %
- Used for characterizing the partial pressures of gases and vapor pressures of solutions
- Temperature independent
\[\mathrm{mol~\%~solute} = \chi_{\mathrm{solute}} \times 100\%\] \[\mathrm{mol~\%~solvent} = \chi_{\mathrm{solvent}} \times 100\%\]
Mass Fraction
- Given as \(\omega\)
- Unitless
- Generally used for solid- and liquid-phase solutions
- Temperature independent
\[\omega_{\mathrm{solute}} = \dfrac{m_{\mathrm{solute}}}{m_{\mathrm{solution}}}\] \[\omega_{\mathrm{solvent}} = \dfrac{m_{\mathrm{solvent}}}{m_{\mathrm{solution}}}\]
Mass Percent
- Given as mass %, wt %, % wt, percent by mass, weight-weight percentage, wt/wt %, w/w %
- Units: %
- Generally used for solid- and liquid-phase solutions
- Note: Assume a volume of solution (100g) if starting with this.
- Temperature independent
\[\mathrm{mass~\%~solute} = \omega_{\mathrm{solute}} \times 100\%\] \[\mathrm{mass~\%~solvent} = \omega_{\mathrm{solvent}} \times 100\%\]
Mass-Volume Percent
- Given as m/v %, (m/v%)
- Also called weight volume % – w/v %, (w/v%)
- Ratio of solute mass (in g) to volume (in mL) of solution multiplied by 100%
- Generally used for liquid- and gas-phase solutions
\[m/v~\% = \dfrac{m_{\mathrm{solute~(g)}}}{V_{\mathrm{solution~(mL)}}} \times 100\%\]
Parts by Mass
- Generally used for dilute to very dilute solutions
- Temperature independent
\[\dfrac{m_\mathrm{{solute}}}{m_\mathrm{{solution}}} \times \mathrm{~multiplication~factor}\]
Unit and multiplication factor
- Parts per hundred (percent by mass; %) – 100
- Parts per million (ppm) – 106
- Parts per billion (ppb) – 109
Parts by Volume
- Generally used for dilute to very dilute solutions of gases
\[\dfrac{V_\mathrm{{solute}}}{V_\mathrm{{solution}}} \times \mathrm{~multiplication~factor}\]
Unit and multiplication factor
- Parts per hundred (percent by volume; %) – 100
- Parts per million (ppm) – 106
- Parts per billion (ppb) – 109