Now we are going to start looking at models for the chemical potential  i of a given component i in a mixture The first model is the ideal gas mixture The second model is the ideal solution As you study this, think about the differences, not only mathematical but also the physical differences of these models

The ideal-gas mixture model EOS for an ideal gas Calculate the partial molar volume for an ideal gas component of an ideal gas mixture

For an ideal gas mixture

For any partial molar property other than volume, in an ideal gas mixture:

Partial molar entropy (igm)

Partial molar Gibbs energy Chemical potential of component i in an ideal gas mixture This is  for a pure component !!! *******************************************************************************

Problem What is the change in entropy when 0.7 m 3 of CO 2 and 0.3 m 3 of N 2, each at 1 bar and 25 o C blend to form a gas mixture at the same conditions? Assume ideal gases. We showed that:

solution n = PV/RT= 1 bar 1 m 3 / [R x 278 K]  S = J/K

Problem What is the ideal work for the separation of an equimolar mixture of methane and ethane at 175 o C and 3 bar in a steady-flow process into product streams of the pure gases at 35 o C and 1 bar if the surroundings temperature T  = 300K? 1)Read section 5.8 (calculation of ideal work) 2)Think about the process: separation of gases and change of state First calculate  H and  S for methane and for ethane changing their state from P 1, T 1, to P 2 T 2 Second, calculate  H for de-mixing and  S for de-mixing from a mixture of ideal gases

solution = J/mol = J/mol K W ideal =  H – T   S = J/mol

Problem A vessel, divided into two parts by a partition, contains 4 mol of N 2 gas at 75 o C and 30 bar at one side of the partition and 2.5 mol of Ar at 130 o C and 20 bar on the other. If the partition is removed and the gases mix adiabatically and completely, what is the change in entropy? Assume N 2 to be an ideal gas with C v =(5/2)R and Ar to be an ideal gas with C v =(3/2)R