Question

A real solution in which the molecules of component 1 and 2 are nearly the same size is known as a regular solution. For such a solution, the total mixing free energy is

where n_i is the moles of component I and x is a constant parameter that corrects for the non-ideal behavior.

1. Prove that the change in chemical potential for component 1 can be expressed as
2. Derive the activity coefficient for component 1.

A real solution in which the molecules of component 1 and component 2 are nearly the same size is known as a regular solution. For such a solution, the total mixing free energy is AG=RT(mi in ne me = n, in 1,mm +n + n n ,+ na where ni is the moles of component i and x is a constant parameter that corrects for the non-ideal behavior. (a) (8%) Prove that the change in chemical potential for component 1 can be expressed as On) A4, = RT In- A4 = rrbandma () m+h (2+2 (b) (7%) Derive the activity coefficient for component 1.

Answer 1

component 2 ₂ moles component 0 ni moles = mole fractional Component of W2 = mole component fractional ② ท X = И. nitn2 n- nith me know it Asmix = -R [ Mi enni + 1₂ lnx2] Da= SH-TAS Damix = Dimix - TDS mix zero for the case of mixing for ideal 1. A mix = - TOSmix - - putting the value foram eq samix - RT [ni en x + na ln x2] Samix = RT (n. ln (m + n ln (n27 for Non ideal nith hithan pamix = RT (m, en (69) + 4 () Y 7 2 hth2

@ 29 = VdP - SUT & Elidni 26= Vap-SIT + Midni + (My drea 20 ni - HRT wenn al = 29 m2 Entennithe) + Om the ** mitha ni th M M RT In nitha