#### Chemical Potential: Screencasts

Shows how the chemical potentials of a solid and a liquid change at constant temperature as pressure increases over a narrow pressure range for a single-component. The different behaviors for water and ethanol are demonstrated.

We suggest you list the important points in this screencast as a way to increase retention.

Shows how the chemical potentials of a solid and a liquid change at constant pressure as temperature increases over a narrow temperature range for a single component.

We suggest you list the important points in this screencast as a way to increase retention.

Optional screencast: What is Chemical Potential? Multi-Component

##### Important Equations:

Chemical potential definition for a mixture:

\[\mu _i \equiv \left( \frac{\partial \underline{G}}{\partial n_i} \right) _{P,T,n_{j\neq i}} \]

where \(\mu _i\) is the chemical potential of component \(i\)

\(\underline{G}\) is the total Gibbs free energy (nG) for the mixture

\(n_i\) is the number of moles of component \(i\)

For a pure fluid:

\[d\mu = dG = -SdT + VdP\]

where \(\mu\) is the chemical potential (kJ/mol)

\(G\) is the molar Gibbs free energy (kJ/mol)

\(S\) is the molar entropy (kJ/mol-K)

\(T\) is the temperature (K)

\(V\) is the molar volume (m^{3}/mol)

\(P\) is the pressure (bar).

For mixtures:

\[d\underline{G} = \underline{V}dP – \underline{S}dT + \sum _i \mu _i dn_i\]

where \(\underline{G}\), \(\underline{V}\), and \(\underline{S}\) are extensive variables

\(\mu _i\) is the chemical potential of component \(i\)

\(n_i\) is the number of moles of component \(i\)

The summation is over all components in the mixture.

At vapor-liquid equilibrium for a binary system:

\[\mu ^V _1 = \mu ^L _1 \hspace{1cm} \mu ^V _2 = \mu ^L _2\]

For component \(i\) in a mixture:

\[\mu _i – \mu _{i,pure} = RTln\left( \frac{\hat{\,\,\,f_i}}{f_i} \right)\]

where \(\hat{\,f_i}\) is the fugacity of component \(i\) in the mixture

\(f_i\) is the pure component fugacity at the same temperature and pressure

For component \(i\) in an ideal-gas mixture:

\[\mu ^{ig} _i = G^{ig} _i + RTln(y_i)\]

where \(\mu ^{ig} _i\) is the chemical potential of component \(i\) in the mixture

\(G^{ig} _i\) is the Gibbs free energy of the pure-component ideal gas

\(R\) is the ideal gas constant

\(T\) is the absolute temperature

\(y_i\) is the mole fraction of component \(i\) in the mixture.