Composition vs Concentration

It is useful to reiterate the definitions of concentration and composition.

Concentration is the number of something per unit volume:¹

$$\mbox{Molar Concentration of Species $j$} = \frac{n_j}{\ensuremath{{V}^{\mbox{total}}}}$$ (05-3)

where $n_j$ is the number of moles of $j$:

$${n_j} \equiv \frac{N_j}{\ensuremath{\mbox{N}_{\mbox{avag.}}}\newc... ...}{\ensuremath{\mbox{mole}^{-1}}} \newcommand {\mole}{\ensuremath{\mbox{mole}}}}$$ (05-4)

where $N_j$ is the number of $j$-type atoms or molecules.

Mole fractions or number fractions are defined by:

$$\ensuremath{\overline{N_j}}= \frac{N_j}{N_{\mbox{total}}} \equiv X_j$$ (05-5)

Mole fractions are unit-less--they are just numbers and each must satisfy $0 \leq X_j \leq 1$ and their sum must satisfy:

$$1 = \ensuremath{\sum_{j=1}^{C}}X_j$$ (05-6)

Composition describes the molar chemical complexion of a system--it is the set of mole fractions: $( X_1 , X_2 , \ldots , X_C ) = \frac{1}{N_{\mbox{total}}} ( N_1 , N_2 , \ldots , N_C )$.

In the special case of the binary alloys (those that have only two possible components $A$ and $B$), the composition can be identified with a single variable $X=X_B$ because $X_A$ is fixed by the relation $X_A + X_B = 1$.