Mole Fractions

Definitions

For a mixture with species $i=1,\dots ,N$ and total moles $n={\sum }_i{n}_i$:

• mole fraction: $x_i\equiv \frac{n_i}{n}$, so ${\sum }_i{x}_i=1$.
• mixture molecular weight: $\bar{W}={\sum }_i{x}_i{W}_i$, with $W_i$ species molecular weights.
• mixture gas constant: $R=\frac{R_u}{\bar{W}}$.

For ideal gas mixtures:

• Dalton’s law: $p_i=x_{i}p$, so $x_i=\frac{p_i}{p}$.
• mixture enthalpy (frozen comp.): $h={\sum }_i{Y}_i{h}_i(T)$ with mass fractions $Y_i=\frac{x_i{W}_i}{\bar{W}}$.

Useful Identities

• Convert $x_i\leftrightarrow Y_i$: $Y_i=\frac{x_i{W}_i}{\bar{W}}$, $x_i=\frac{Y_i/W_i}{{\sum }_j{Y}_j/W_j}$.
• For reacting systems, $x_i$ and thus $\bar{W}$ depend on composition (e.g., equilibrium), which in turn feeds $R=R_u/\bar{W}$ into nozzle/performance formulas.