物理化学,面现象习题
表面现象习题。
在293K时，把半径为10—3 m的水滴分散成半径为10—6 m小水滴，问比表面增加了多少倍？表面吉布斯能增加了多少？完成该变化时，环境至少需做功多少？已知293K时水的表面张力为0.07288 N/m.
解：
将10—6 m3油分散到盛有水的烧杯内，形成半径为10—6 m的粒子的乳状液。设油水间界面张力为62×10—3 N/m，求分散过程所需的功为多少？所增加的表面自由能为多少？如果加入微量的表面活性剂之后，再进行分散，这是油水界面张力下降到42×10—3 N/m。问此分散过程所需的功比原来过程减少多少？
解：
常压下，水的表面张力σ(N/m)与温度t (℃)的关系可表示为。
σ＝ 7.564×10—2 － 1.4×10—4t。
若在10℃时，保持水的总体积不变，试求可逆地扩大1cm2表面积时，体系的W、Q、ΔS、ΔG和ΔH。
解：
证明药粉S在两种不互溶的液体α和β中分布：（1）当σS, β σS, α + σ,α, β，S分布在液体α中。
（2）当σα, β σS, α + σS, β，S分布在液体α、β之间的界面上。
证明：药粉在两种不互溶的液体α和β中分布有三种可能状态，状态I：分布在液体α、β之间的界面上，状态II:分布在液体α中，状态III: 分布在液体β中。
5.用本章学到的理论，对下列各题进行分析或判断：
（1）两根水平放置的毛细管，管径粗细不均，管中装有少量液体，a管中为润湿性液体，b管中为不润湿液体。问两管内液体最后平衡位置在何处？为什么？
（2）在装有部分液体的毛细管中，将其一端小心加热时，问a润湿液体，b不润湿液体各向毛细管哪一端移动？为什么？
（3）在两块平行而又能完全润湿的玻璃板之间滴入水，形成一薄水层，试分析为何在垂直玻璃平面的方向上想把两块玻璃分开较为困难的原因。今有一薄水层，其厚度为10—6 m，设水的表面张力为72×10—3 N/m，玻璃板的长度l = 0.1 m，求两板之间的作用力。
解释：
（1）液体两侧表面张力相同，影响附加压力的是曲率半径。a管为凹液面，r0,Δp的方向指向液体外部，左侧曲率半径小，Δp更大些，液体向左移动，直至两侧的曲率半径相同处为最后平衡位置；b管为凸液面，r0, Δp指向液体内部，左侧曲率半径小，Δp更大些，液体向右移动，直至两侧的曲率半径相同处为最后平衡位置。
（2）毛细管的半径均匀，影响附加压力大小的是表面张力。液体的表面张力随温度的升高而降低。a管为凹液面，Δp方向指向液体外部，左侧液体受热，使σ下降，使Δp减小，所以液柱向右移动；a管为凸液面，Δp方向指向液体内部，左侧液体受热，使σ下降，使Δp减小，所以液柱向左移动；。
（3）水在两块玻璃板之间形成凹液面，r0, Δp0, 因此pl pg, 液体内部的压力小于外压，使在垂直玻璃板平面的方向把两块玻璃分离变得困难。水在玻璃板间的附加压力：
6. 汞对玻璃表面完全不润湿，若将直径为0.100mm的玻璃毛细管插入大量汞中，试求管内汞面的相对位置。已知汞的密度为1.35×104kg/m3,表面张力为0.52N/m，重力加速度g=9.8m/s2.
解：
7. 如果液体的蒸汽压符合高度分布定律,试由开尔文公式推导出毛细管上升公式。
8. 101.325kPa压力中，若水中只含有直径为10—6 m的空气泡，要使这样的水开始沸腾，需要多少度？已知水在100℃的表面张力为σ＝58.9×10—3N/m，摩尔汽化热ΔH＝40.656kJ/mol, 设水面至空气泡之间液柱的静压力气气泡内蒸汽压下降因素均可忽略不计。
解：
9.水蒸气迅速冷却至25℃会发生过饱和现象。已知25℃时水的表面张力为72.1×10—3 N/m，密度为997kg/m3,当饱和水蒸气压为水的平衡蒸汽压的4倍时，试求算最初形成的水滴半径为多少？此种水滴中含有多少个水分子？
解：
10. 已知CaCO3在500℃时的密度为3.9×103 kg/m3，表面张力为1210×10—3 N/m，分解压力为101.325 kPa。若将碳酸钙研磨成半径为30 nm的粉末，求其在500℃时的分解压力。
解：
11. 一滴油酸在20℃时，落在洁净的水面上，已知相关的界面张力数据为：σ水 ＝75×10—3 N/m，σ油酸＝32×10—3 N/m，σ油酸－水＝12×10—3 N/m，当油酸与水相互饱和后，σ油酸’＝σ油酸，σ水’＝40×10—3 N/m。据此推测，油酸在水面上开始与终了的形状。相反，如果把水滴在油酸表面上它的形状又是如何？
解：
12. 298K时，已知有关的界面张力数据如下：σ水＝72.8×10—3 N/m，σ苯＝28.9×10—3 N/m，σ汞＝471.6×10—3 N/m，σ汞－水＝375×10—3 N/m，σ汞－苯＝362×10—3 N/m，σ水－苯＝32×10—3 N/m，试问：
（1）若将一滴水滴入苯和汞之间的界面上，其接触角θ为多少？
（2）苯能否在汞或水的表面上铺展？
解：
13. 有一杀虫剂粉末，欲分散在一恰当的液体中以制成混悬喷洒剂，今有三种液体（1，2，3），测得它们与药粉及虫体表皮之间的界面张力关系如下：
解：适宜做喷洒剂的液体应符合2个条件：能润湿药粉且能润湿虫体表面。
根据润湿条件ΔG = σ液－粉 －σ粉 0，即σ粉 σ液－粉，液体1和3能润湿药粉；。
根据铺展条件ΔG = σ液 ＋ σ表皮－液 －σ表皮 0，即σ表皮 σ液 ＋ σ表皮－液，液体2和3可以润湿虫体；。
综合2个条件，选择液体3最适宜。
14. 292.15K丁酸水溶液的表面张力σ和浓度c的关系式为： σ＝ σ0 － aln(1+bc),求：
(1)写出吉布斯吸附等温式；。
(2)当a = 13.1×10—3N/m, b = 19.62dm3/mol,计算c为 0.2mol/L时的吸附量Г；。
(4)假定饱和吸附时表面上丁酸成单分子层吸附，计算在液面上每个丁酸分子的横截面积。
解：（1）。
15. 25℃测得不同浓度下氢化肉桂酸水溶液的表面张力σ的数据为：
c/kg/kg 0.0035 0.0040 0.0045 σ×103/N/m 56.0 54.0 52.0 求浓度为0.0041kg/kg及0.0050kg/kg时溶液表面的吸附量Г。
解：
以σ对c作图，得直线方程：σ ＝ 0.07 － 4c ，则：
emotionalBecause of the guerrilla forces in the surrounding area have been withdrawn, activities in the Lakes Cheng Wanjun also refuge in Japanese, Zhu Xi forces became the puppet to attack key targets Eve puppet attacking in Wuzhen, face the problem of the retreat was to meet the enemy, in a debate within the leadership, some believe that the elves, concentrate a superior force, surely do, early transfer is the best way to reduce losses.
Deputy Commander Wang Hesong impassioned statement: "Wuzhen hold, is our militarys duty!" I have win a series of victories, morale, Wuzhen battle to victory, fight this battle, a Chinese miracle in the history of guerrilla warfare."Commander Zhu Xi did not have much, but the final word. On November 5, we flew over the town for several days, bomb bursts, trembling moan tranquil town in the war. People have the feeling of a catastrophe in the town. 6th reconnaissance around the command personnel brought an urgent intelligence, town—wide panic, in the face of news of the Japanese attack town, to avoid the scourge of war, the majority of people young and old fled to the countryside in the town. Also hard to find a boat in the river. Past the bustling town just seems a deserted and desolate. 7th day in implementing low—level flights over the town, fired. That night, the Elves attack Wuzhen confirmed information. Night, bursts of gunfire coming from the distance, reportedly is Deputy Commander Wang Hesong Xu Miao came Nanxun sniper assault of the Elves. 8th, the situation is more severe in the town. One afternoon, outside East Gate and South Gate there was intense gunfire. Enemy attacks by frustrated independent battalion confronted Chen qi. At this time, the command ... 11th, as Commander of Zhu Xi—Kai Wen Yongzhi, Director of。
emotionalBecause of the guerrilla forces in the surrounding area have been withdrawn, activities in the Lakes Cheng Wanjun also refuge in Japanese, Zhu Xi forces became the puppet to attack key targets Eve puppet attacking in Wuzhen, face the problem of the retreat was to meet the enemy, in a debate within the leadership, some believe that the elves, concentrate a superior force, surely do, early transfer is the best way to reduce losses.
Deputy Commander Wang Hesong impassioned statement: "Wuzhen hold, is our militarys duty!" I have win a series of victories, morale, Wuzhen battle to victory, fight this battle, a Chinese miracle in the history of guerrilla warfare."Commander Zhu Xi did not have much, but the final word. On November 5, we flew over the town for several days, bomb bursts, trembling moan tranquil town in the war. People have the feeling of a catastrophe in the town. 6th reconnaissance around the command personnel brought an urgent intelligence, town—wide panic, in the face of news of the Japanese attack town, to avoid the scourge of war, the majority of people young and old fled to the countryside in the town. Also hard to find a boat in the river. Past the bustling town just seems a deserted and desolate. 7th day in implementing low—level flights over the town, fired. That night, the Elves attack Wuzhen confirmed information. Night, bursts of gunfire coming from the distance, reportedly is Deputy Commander Wang Hesong Xu Miao came Nanxun sniper assault of the Elves. 8th, the situation is more severe in the town. One afternoon, outside East Gate and South Gate there was intense gunfire. Enemy attacks by frustrated independent battalion confronted Chen qi. At this time, the command ... 11th, as Commander of Zhu Xi—Kai Wen Yongzhi, Director of。
emotionalBecause of the guerrilla forces in the surrounding area have been withdrawn, activities in the Lakes Cheng Wanjun also refuge in Japanese, Zhu Xi forces became the puppet to attack key targets Eve puppet attacking in Wuzhen, face the problem of the retreat was to meet the enemy, in a debate within the leadership, some believe that the elves, concentrate a superior force, surely do, early transfer is the best way to reduce losses.
Deputy Commander Wang Hesong impassioned statement: "Wuzhen hold, is our militarys duty!" I have win a series of victories, morale, Wuzhen battle to victory, fight this battle, a Chinese miracle in the history of guerrilla warfare."Commander Zhu Xi did not have much, but the final word. On November 5, we flew over the town for several days, bomb bursts, trembling moan tranquil town in the war. People have the feeling of a catastrophe in the town. 6th reconnaissance around the command personnel brought an urgent intelligence, town—wide panic, in the face of news of the Japanese attack town, to avoid the scourge of war, the majority of people young and old fled to the countryside in the town. Also hard to find a boat in the river. Past the bustling town just seems a deserted and desolate. 7th day in implementing low—level flights over the town, fired. That night, the Elves attack Wuzhen confirmed information. Night, bursts of gunfire coming from the distance, reportedly is Deputy Commander Wang Hesong Xu Miao came Nanxun sniper assault of the Elves. 8th, the situation is more severe in the town. One afternoon, outside East Gate and South Gate there was intense gunfire. Enemy attacks by frustrated independent battalion confronted Chen qi. At this time, the command ... 11th, as Commander of Zhu Xi—Kai Wen Yongzhi, Director of。