(e) Mixing of non-identical gases

A rigid insulated container is divided into two compartments by a partition.

Figure 22.2

Refer to Figure 22.2. One compartment contains mol of an ideal gas A at pressure P and temperature T while the second compartment contains mol of an ideal gas B at the same pressure and temperature. The partition is removed and the gases are allowed to mix. To evaluate the entropy change on mixing, let us device the following reversible process.

Let the gases A and B expand reversible and isothermally to their final partial pressures and respectively. Then the gases are introduced through semi-permeable membranes into a container in which the partial pressure of gas A is and the partial pressure of gas B is . The reversible mixing process is, therefore, accomplished in the following two steps.

• Reversible isothermal expansion of gases to their respective partial pressures.
• Forcing the gases reversibility through semi permeable membranes.

For gas A,

ln	(22.20)

Similarly, for gas B,

ln

(22.21)

Where, and

Here and are the mole fractions of gases A and B respectively, in the final mixture.

Hence,

ln   ln  and

(22.22)

Therefore, the entropy change associated with the mixing of non-identical gases is

In - R In

(22.23)

or,

In − In	(22.24)
In	(22.25)

Where is the molar entropy. Since , is always positive.