Raoult + Activity Combined
Why combine Raoult and activity?
For ideal mixtures, a first approximation is \(P_i=x_iP_i^\circ\). Real mixtures deviate, especially when component interactions are strong. The activity coefficient \(\gamma_i\) corrects this non-ideality.
\[P_i = x_i\,\gamma_i\,P_i^\circ\]
With \(\gamma_i=1\), behavior is ideal. Values \(\gamma_i>1\) indicate positive and \(\gamma_i<1\) negative deviations from Raoult’s law.
- Process-oriented vapor pressure estimates for real mixtures
- Direct comparison of ideal vs real predictions
- Back-calculation of \(\gamma_i\) from measurements
Crosslink: For \(\gamma\) background, use the Activity Coefficient calculator.
Formulas (MathJax)
\[P_i = x_i\gamma_i P_i^\circ\]
\[\gamma_i = \frac{P_i}{x_iP_i^\circ}\]
\[P_{total}=\sum_i x_i\gamma_iP_i^\circ\]
Formula symbol legend
- \(P_i\): partial pressure of component \(i\)
- \(x_i\): liquid-phase mole fraction
- \(\gamma_i\): activity coefficient
- \(P_i^\circ\): pure-component saturation pressure
- \(P_{total}\): total vapor pressure
Detailed examples
Example 1: \(x_i=0.35\), \(\gamma_i=1.18\), \(P_i^\circ=0.620\,\mathrm{bar}\). Then \(P_i=0.35\cdot1.18\cdot0.620\approx0.256\,\mathrm{bar}\).
Example 2: Measured \(P_i=0.256\,\mathrm{bar}\), known \(x_i=0.35\), \(P_i^\circ=0.620\,\mathrm{bar}\). Then \(\gamma_i\approx1.18\) (positive deviation).
Example 3 (binary): \(P_A=x_A\gamma_AP_A^\circ\), \(P_B=x_B\gamma_BP_B^\circ\), \(P_{total}=P_A+P_B\). This yields practical estimates for non-ideal boiling/evaporation conditions.
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