Dalton Model

Mixture of Ideal Gases

Partial Pressures:

• Pressure of component $i$ occupying volume $V$ at temperature $T$
• For ideal gases, $P_{i}V=n_{i}RT$

Dalton's Law:

• $P=\sum _i{P}_i$

In layman's terms: Mixture of ideal gases is an Ideal Gas

• $PV=\sum _i{P}_{i}V=\sum _i{n}_{i}RT=nRT$

Key relations:

$P_i=X_{i}P$ $X_i=\frac{P_i}{P}$

Entropy of Mixing:

(Recall) Key Relations:

• Gibbs Equation: $du=Tds-Pdv$
• Entropy change: $ds=C_p\frac{dT}{T}-R\frac{dP}{P}$
• Integrated form: $s_i=s_{i,ref}^0+C_p\ln \left(\frac{T}{T_{r}ef}\right)-R\ln \left(\frac{P_i}{P_0}\right)$

Mixing of Ideal Gases:

• Initial state: each gas separated at $T$ and $P$
• Final state: all mixed at $T$ and $P$
• Per component: $\mathrm{\Delta }{s}_i=-R\ln X_i$
• For mixture: $\mathrm{\Delta }S=\sum _i{m}_i\mathrm{\Delta }{s}_i=-nR\sum _i{X}_i\ln X_i$