1. 加入 (a) 10 ml, (b) 1ml 和 (c) 0.1ml 己烷制备三种己烷水溶液

(1) 根据自由能描述每种溶液（混合或分离）的平衡状态

(2)向溶液(b)中逐渐加入表面活性剂。当表面活性剂的浓度

2、表中为苯酚溶液在30摄氏度时的表面张力。计算表面

3.假设你要混合液体A和B。在混合过程中，总体积保持不变，

(A) 如果 x 参数由 x ൌ 500/x 给出（T 是以开尔文为单位的温度）：
(1) 计算临界点 x௖ ，高于该临界点，溶液独立于

(2) 描述共存成分在 273 K 时的体积分数。
(3) 给出 273 K 处的旋节线上的体积分数。

(B) 在 x 参数取大正值的情况下：
(4) 假设 x≫1 和 B 液浓度 x≪1 ，推导出近似值

(5) 假设水和直链烃之间的 x 参数值近似为
x 3.04 ൅ 1.37x，其中 x 是碳氢化合物中的碳原子数。使用公式

1. Three aqueous solutions of hexane are prepared by adding (a) 10 ml, (b) 1ml and (c) 0.1ml of hexane
to 1 liter of water, respectively. The interfacial tension between water and hexane is 40 mN/m at room
temperature.
(1) Describe the equilibrium state of each solution (mixed or separated), based on the free energy when
the hexane is divided into N droplets.
(2) To the solution (b), a surfactant was gradually added. When the concentration of the surfactant
exceeded a certain value, the solution became turbid. The molecular length and the packing parameter
of the surfactant are 10 nm and 0.2, respectively. Assuming that all the surfactant molecules are
adsorbed on the water-hexane interface, calculate the threshold concentration of the surfactant, above
which the light scattering can be observed.

2. The table shows the surface tension of phenol solutions at 30 degrees Celsius. Calculate the surface
adsorption of phenol molecules in 0.100 wt% solution. You can use Gibbs adsorption isotherm
equation.
Concentration of phenol (wt%) 0.024 0.047 0.118 0.471
Surface tension (mN/m) 72.6 72.2 71.3 66.5

3. Suppose that you will mix liquids A and B. In the mixing process, the total volume is maintained,
and no chemical reactions take place. Consider the two cases and answer the questions.
(A) In the case that x-parameter is given by x ൌ 500/x (T is the temperature in kelvin):
(1) Calculate the critical point x௖ , above which the solution is uniformly mixed independently of
mixing ratios.
(2) Describe the volume fraction of the coexisting compositions at 273 K.
(3) Give the volume fraction on the spinodal line at 273 K.

(B) In the case that x-parameter takes a large positive value:
(4) Assuming that x≫1 and the concentration of B-liquid x≪1 , derive an approximate
expression for the limit of solubility of liquid B in liquid A.
(5) Suppose that the value of x-parameter between water and linear hydrocarbons is approximated as
x 3.04 ൅ 1.37x, where x is the number of carbon atoms in the hydrocarbons. Using the formula
derived in (4), calculate the limiting solubilities of hexane(C6H14), octane (C8H18) and decane (C10H22)
in water. (You can compare the calculated values with the experimental data as 13 mg/L (C6H14), 0.66
mg/L (C8H18), and 0.052 mg/L(C10H22).)