24.8: Activities are Calculated with Respect to Standard States

Need to define a new variable. The thermodynamic activity, \(a\), is the effective concentration of a species in a mixture. It is a dimensionless quantity that are calculated with respect to standard states. For a gas, this would be related to the fugacity and for a solution, to the concentration. The activity for a real gas:

\[a_i=\frac{f_i}{P^{\circ}}=\frac{\phi_iP_i}{P^{\circ}}=\frac{\phi_i(y_iP)}{P^{\circ}} \nonumber \]

For systems where we treat the gases as ideal:

\[ \phi_i=1 \nonumber \]

\[ a_i=\frac{P_i}{P^{\circ}}=y_i\frac{P}{P^{\circ}} \nonumber \]

The activity for a solution:

\[ a_i=\gamma i\sf\frac{[A]}{1\;\underline{M}} \nonumber \]

General chemistry and organic chemistry use ideal reactants where \(\gamma_i=1\):

\[ a_i=\sf\frac{[A]}{1\;\underline{M}} \nonumber \]

The activity for a solid or liquid:

\[ a_i=1 \nonumber \]

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