Practice Problems

P12.1. Acrolein + water exhibits an atmospheric (1 bar) azeotrope at 97.4 wt% acrolein and 52.4°C.

a. Determine the values of A_ij for the van Laar equation that match this bubble-point pressure at the same liquid and vapor compositions and temperature. (ANS. 2.97, 2.21)

(You may use the shortcut vapor pressure equation for acrolein: T_c = 506 K; P_c = 51.6 bar; and ω = 0.330; MW = 56.)

b. Tabulate P at 326.55 K and x = {0.1,0.3,0.5} via the van Laar equation using the A₁₂ and A₂₁ determined above. (ANS. P = {1.11, 1.15, 1.03}

P12.2. The system α-epichlorohydrin(1) + n-propanol(2) exhibits an azeotrope at 760 mmHg and 96°C containing 16 mol% epichlorohydrin. Use the van Laar theory to estimate the composition of the vapor in equilibrium with a 90 mol% epichlorohydrin liquid solution at 96°C. (α-epichlorohydrin has the formula C₃H₅ClO, and IUPAC name 1-chloro-2,3-epoxypropane. Its vapor pressure can be approximated by: log₁₀P^sat = 8.0270–2007/T, where P^sat is in mmHg and T is in Kelvin. You can use the shortcut vapor pressure equation for n-propanol.) (ANS. 0.72, 0.63 bar)

P12.3. The following free energy model has been suggested for a particularly unusual binary liquid-liquid mixture. Derive the expression for the activity coefficient of component 1,

where,  and .

(ANS. )

P12.4. The Scatchard-Hildebrand model can be extended to multicomponent mixtures in the following manner. Setting a_ij = (a_iia_jj)^½ and a_ii/V_i = V_iδ² Eqn. 12.7 can be rewritten as

Recognizing that the quadratic term is separable and simplifying the square-root of the square:

where <δ> ≡ Σx_iV_iδ_i/V ≡ ΣΦ_iδ_i and V ≡ Σx_iV_i.

This result can be made even simpler by adding and subtracting V<δ>² and rearranging to obtain:

where we have substituted the definition of <δ> in the second term and the definition of V in the third.

Collecting all terms in a common summation, we obtain:

This is a remarkably simple result. Derive an equally simple expression for the activity coefficient of a component in a multicomponent mixture. (Hint: It is easier to start with Eqn. 12.65.) (ANS. Eqn. 12.54)