QUANTITATIVE EXPRESSION OF COMPOSITION OF MIXTURES AND SOLUTIONS
The relative atomic mass (Ar) of an element is the ratio between the average mass of its atoms and 1/12 of the mass of an atom of of nuclide 12C. The relative molecular mass (Mr) is equal to the sum of the relative atomic mass of all the atoms that comprise the empirical formula. For example, the relative molecular mass of sulphuric acid, Mr(H2SO4) is equal to:
Mr(H2SO4)
= 2*Ar(H) + Ar(S) + 4*Ar(O)
= 2*1.00794 + 32.066 + 4*15.9994
= 2.01 + 32.07 + 64.00
= 98.08
The relative molecular mass is a dimensionless quantity, it has no units.
The amount of a substance (n) is equal to the ratio between the number of elementary entities: atoms, ions, molecules, electrons... (N) and the Avogadro constant (L = 6.022045·1023 mol-1)
The molar mass of a substance (M) is the weight of one mole of the substance, or rather the mass of 6.022045·1023 elementary entities of the substance. The SI unit for molar mass is kg mol-1, though the decimal unit g mol-1 is more commonly used. The molar mass is numerically equal to the relative molecular mass, so the molar mass of sulphuric acid, M(H2SO4), is equal to 98.08 g mol-1.
The density of a substance is defined as a ratio between the mass (m) and volume (V) at a specified temperature. The unit for density is kg m-3, though the decimal SI unit kg dm-3 is used more commonly. It's important to specify the temperature at which the density was measured since a change of temperature usually results in a change of volume, and with it a change of density as well.
Solutions are homogeneous mixtures of pure substances. Solutions contain two or more substances (components) mixed together in a state of molecular dispersion. The component that forms the majority of a solution is known as the solvent, while the other components are called the solutes. Its worth noting that the solvent itself can be a mixture.
The quantitative composition of a solution can be expressed with:
- concentration (molar, mass and volume)
- fraction (molar, mass and volume)
- ratio (molar, mass and volume)
- molality
Unless specified otherwise, the ratio referes to the mass ratio.
Molar, weight, and volume fractions are numbered, dimensionless units most commonly expressed as a:
- percentage, (% = 1/100)
- per mil or parts-per-thousand, (‰ = 1/1 000)
- parts-per-million, (ppm = 1/1 000 000)
Remember: a percentage is not a unit - it's instead the ratio of a certain number divided with 100, so 7 % is the same as 0.07.
| Physical quantity | Symbol | Definition | Unit | Description |
|---|---|---|---|---|
| Concentration | c |
cA =
nA
V
|
mol m-3 | Molar concentration, or just the concentration of component A, is the ratio between the amount of solute A and the solution volume. |
| Mass concentration | γ |
γA =
mA
V
|
kg m-3 | Mass concentration of component A is equal to the ratio between the mass of solute A and the solution volume. |
| Volume concentration | σ |
σA =
VA
V
|
m3 m-3 | Volume concentration of component A is equal to the ratio between the volume of solute A and the solution volume. |
| Mole fraction | x |
xA =
nA
∑ni
|
Mole fraction, or the amount fraction of component A, is equal to the ratio between the amount of solute A and the sum of amounts of all substances within the solution or mixture. | |
| Mass fraction | w |
wA =
mA
∑mi
|
Mass fraction or weight fraction of component A is the mass ratio between the solute A and the sum mass of all substances within the solution or mixture. | |
| Volume fraction | φ |
φA =
VA
∑Vi
|
Volume fraction of component A is the volume ratio between the solute A and the sum volume of all substances in the solution. | |
| Mole ratio |
nA
nB
|
Mole, or amount ratio, is the ratio between the number of moles of any two components in a solution or mixture. | ||
| Mass ratio |
mA
mB
|
Mass ratio is the ratio between the masses of any two components in a solution or mixture. | ||
| Volume ratio |
VA
VB
|
Volume ratio is the ratio between the volumes of two solution components. | ||
| Molality | b |
bA =
nA
mS
|
mol kg-1 | Molality of component A is equal to the ratio between the number of moles of solute A and the mass of solvent S. |
Citing this page:
Generalic, Eni. "Quantitative expression of composition of mixtures and solutions." EniG. Periodic Table of the Elements. KTF-Split, 18 Jan. 2024. Web. {Date of access}. <https://www.periodni.com/quantitative_expression_of_composition_of_solutions.html>.
