Faculty of Chemistry and Technology in Split
The relative atomic mass (A_{r}) 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 ^{12}C. The relative molecular mass (M_{r}) 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, M_{r}(H_{2}SO_{4}) is equal to:
M_{r}(H_{2}SO_{4})
= 2*A_{r}(H) + A_{r}(S) + 4*A_{r}(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 = 6.022045·10^{23} mol^{1})
The molar mass of a substance (M) is the weight of one mole of the substance, or rather the mass of 6.022045·10^{23} 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(H_{2}SO_{4}), 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:
Unless specified otherwise, the ratio referes to the mass ratio.
Molar, weight, and volume fractions are numbered, dimensionless units most commonly expressed as a:
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 
c_{A} =
n_{A}
/
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 
γ_{A} =
m_{A}
/
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 
σ_{A} =
V_{A}
/
V

m^{3} 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 
x_{A} =
n_{A}
/
∑n_{i}

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 
w_{A} =
m_{A}
/
∑m_{i}

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 
φ_{A} =
V_{A}
/
∑V_{i}

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 
n_{A}
/
n_{B}

Mole, or amount ratio, is the ratio between the number of moles of any two components in a solution or mixture.  
Mass ratio 
m_{A}
/
m_{B}

Mass ratio is the ratio between the masses of any two components in a solution or mixture.  
Volume ratio 
V_{A}
/
V_{B}

Volume ratio is the ratio between the volumes of two solution components.  
Molality  b 
b_{A} =
n_{A}
/
m_{S}

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. KTFSplit, 29 May 2017. Web. {Date of access}. <http://www.periodni.com/quantitative_expression_of_composition_of_solutions.html>.
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