#### 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 (m3/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.