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Chapter 11: Problem 33

(a) What is the relationship between surface tension and temperature? (b) What is the relationship between viscosity and temperature? (c) Why do substances with high surface tension also tend to have high viscosities?

Short Answer

Expert verified
(a) The relationship between surface tension and temperature is generally inverse, meaning as the temperature increases, the surface tension of a liquid tends to decrease. This is due to increased molecular motion, which reduces molecular cohesion and attraction at the surface. (b) For most fluids, viscosity decreases with an increase in temperature. However, for gases, viscosity tends to increase with temperature. This is because increased molecular motion leads to more collisions between gas molecules and a reduction in internal friction for liquids. (c) Substances with high surface tension typically have strong intermolecular forces, which also determine viscosity. Strong intermolecular forces increase resistance to flow (i.e., viscosity), so substances with high surface tensions often exhibit high viscosities as both properties rely on the magnitude of intermolecular forces.

Step by step solution

01

Defining Surface Tension and Viscosity

Surface tension is the force that holds the molecules at the surface of a liquid together, causing it to form a thin film or droplet shape. It is a result of the imbalance in cohesive forces between the molecules in the interior and those at the surface of the liquid. Viscosity, on the other hand, is a measure of a fluid's resistance to flow. It describes the degree to which a fluid resists deformation by shear stress or tensile stress. In other words, it is a measure of the fluid's internal friction.
02

Relationship between Surface Tension and Temperature

The relationship between surface tension and temperature is generally inverse. As the temperature increases, the surface tension of a liquid tends to decrease. This is because an increase in temperature leads to increased molecular motion, which reduces the molecular cohesion and attraction at the surface, thereby reducing the surface tension. Mathematically, this relationship is usually represented by the Gibbs adsorption isotherm equation, which can be simplified as: \( \frac{d\gamma}{dT} = \frac{-\Gamma \Delta H}{T} \) Here, \(\gamma\) is the surface tension, \(T\) is the temperature, \(\Gamma\) is the surface excess of the solute, and \(\Delta H\) is the enthalpy change per mole of the adsorbed material.
03

Relationship between Viscosity and Temperature

For most fluids, the viscosity usually decreases with an increase in temperature. For gases, however, the viscosity tends to increase with temperature. For liquids, the explanation lies in the fact that increased temperature leads to increased molecular motion, which reduces their internal friction, and consequently, their viscosity. For gases, the increased molecular motion caused by a higher temperature means that there are more collisions between gas molecules, which results in an increase in viscosity. One of the common empirical equations to describe this behavior is the Arrhenius equation: \( \eta = Ae^{\frac{B}{T}} \) Here, \(\eta\) is the viscosity, \(T\) is the temperature, and \(A\) and \(B\) are constants for a given fluid.
04

Why Substances with High Surface Tension also Tend to Have High Viscosities

Substances with high surface tension typically have strong intermolecular forces or cohesive forces that hold the molecules together. These intermolecular forces also play a crucial role in determining the viscosity of a substance, as stronger intermolecular forces make it more difficult for the molecules to slide past one another, increasing the resistance to flow (i.e., viscosity). Therefore, it is common for substances with high surface tensions to also exhibit high viscosities, as both properties rely on the magnitude of intermolecular forces.

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Most popular questions from this chapter

Ethyl chloride \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\right)\) boils at \(12^{\circ} \mathrm{C}\). When liquid $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}$ under pressure is sprayed on a room-temperature $\left(25^{\circ} \mathrm{C}\right)$ surface in air, the surface is cooled considerably. (a) What does this observation tell us about the specific heat of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(g)\) as compared with that of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(l) ?(\mathbf{b})\) Assume that the heat lost by the surface is gained by ethyl chloride. What enthalpies must you consider if you were to calculate the final temperature of the surface?

The vapor pressure of a volatile liquid can be determined by slowly bubbling a known volume of gas through it at a known temperature and pressure. In an experiment, \(8.00 \mathrm{~L}\) of argon gas is passed through $11.7872 \mathrm{~g}\( of liquid hexane \)\mathrm{C}_{6} \mathrm{H}_{14}$ at \(30.0^{\circ} \mathrm{C}\). The mass of the remaining liquid after the experiment is \(4.875 \mathrm{~g}\). Assuming that the gas becomes saturated with hexane vapor and that the total gas volume and temperature remain constant, what is the vapor pressure of hexane in atm?

Describe the intermolecular forces that must be overcome to convert these substances from a liquid to a gas: (a) \(\mathrm{CF}_{4}\), (b) \(\mathrm{NH}_{3}\) (c) \(\mathrm{BCl}_{3}\)

It often happens that a substance possessing a smectic liquid crystalline phase just above the melting point passes into a nematic liquid crystalline phase at a higher temperature. Account for this type of behavior.

Propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) is pressurized into liquid and stored in cylinders to be used as a fuel. The normal boiling point of propane is listed as \(-42^{\circ} \mathrm{C}\). (a) When converting propane into liquid at room temperature of \(25^{\circ} \mathrm{C},\) would you expect the pressure in the tank to be greater or less than atmospheric pressure? How does the pressure within the tank depend on how much liquid propane is in it? (b) Suppose the fuel tank leaks and a few liters of propane escape rapidly. What do you expect would happen to the temperature of the remaining liquid propane in the tank? Explain. (c) How much heat must be added to vaporize $20 \mathrm{~g}\( of propane if its heat of vaporization is \)18.8 \mathrm{~kJ} / \mathrm{mol} ?\( What volume does this amount of propane occupy at \)100 \mathrm{kPa}\( and \)25^{\circ} \mathrm{C} ?$
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