 Standard-state activity conversion

Standard-state activity conversion changes the numerical thermodynamic activity assigned to a fixed physical state when its reference chemical potential changes. The observable equilibrium and physical chemical potential stay the same. The activity and its standard chemical potential must therefore be converted together.

At fixed temperature $T$, writeIf ${\delta }_i={\tilde{\mu }}_i^{\circ }-{\mu }_i^{\circ }$, subtraction givesHere $R$ is the molar gas constant. This follows from the IUPAC definition of relative activity and its specified standard state.^[ref] Changing just the activity in the first equation would instead change the calculated physical chemical potential.

For an invented conversion ${\tilde{a}}_i=10a_i$, the compensating reference shift is ${\delta }_i=-RT\ln 10$. An old activity $0.03$ becomes $0.30$; the two expressions for ${\mu }_i$ are identical. An activity of one consequently identifies a reference condition under the chosen convention, not an invariant amount of material.

An activity conversion of an equilibrium constant follows the same logic. For the reaction A $\rightleftharpoons$ B, take $K=a_B/a_A$ at equilibrium and convert by ${\tilde{a}}_A=10a_A$, ${\tilde{a}}_B=2a_B$. Then $\tilde{K}=K/5$. If $K=5$, the converted value is $1$, whilebecause originally ${\Delta }_r{G}^{\circ }=-RT\ln 5$. For any physical composition, the corresponding reaction quotient also changes by $1/5$, so ${\Delta }_r{G}^{\circ }+RT\ln Q$ remains unchanged. These are reference changes, not altered reaction chemistry.

The same requirement governs activity equality for coexisting liquids: compare activities only after identifying their standard states, composition scales and reference conventions. Equal numerical values expressed under incompatible conventions do not, by themselves, establish liquid-liquid equilibrium.