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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 can be described by the Eötvös Rule, which states that surface tension decreases linearly with temperature: \(T(\gamma - \gamma_0) = k(T - T_0)\). (b) The relationship between viscosity and temperature varies for gases and liquids. For gases, viscosity increases with temperature, while for liquids, it generally decreases. The Arrhenius equation models this relationship for liquids: \(\eta = \eta_0 e^{(\frac{-E_a}{RT})}\). (c) Substances with high surface tension tend to have high viscosities because both properties are influenced by the same factors: the strength of intermolecular forces and molecular size or shape. Stronger intermolecular forces result in stronger cohesion between fluid particles, leading to higher surface tension and greater resistance to flow (viscosity).

Step by step solution

01

(Part (a) - Relationship between Surface Tension and Temperature)

Surface tension is the property of liquids which causes the surface to contract, allowing it to resist an external force. It occurs because of the unequal force distribution between the particles at the surface and in the interior of the liquid. The relationship between surface tension and temperature can be explained using the Eötvös Rule, which states that for most liquids, surface tension decreases linearly with temperature. Mathematically, the Eötvös Rule can be written as: \(T(\gamma - \gamma_0) = k(T - T_0)\) Here, \(\gamma\) is the surface tension at temperature T, \(\gamma_0\) is the reference surface tension at temperature \(T_0\), and k is a constant.
02

(Part (b) - Relationship between Viscosity and Temperature)

Viscosity is the measure of a fluid's resistance to flow. It is mainly dependent on the type of fluid and its temperature. For gases and liquids, the relationship between viscosity and temperature can vary significantly. For gases, viscosity generally increases with increasing temperature due to molecular interactions. For liquids, viscosity usually decreases with increasing temperature. This is because, at higher temperatures, the intermolecular forces between the liquid particles become weaker, and the particles are more likely to move freely. The relationship between viscosity and temperature can be modeled using the Arrhenius equation for liquids: \(\eta = \eta_0 e^{(\frac{-E_a}{RT})}\) Here, \(\eta\) is the viscosity, \(\eta_0\) is the pre-exponential factor, \(E_a\) is the activation energy, R is the gas constant, and T is the temperature.
03

(Part (c) - High Surface Tension and High Viscosities)

Substances with high surface tension tend to have high viscosities because both of these properties are influenced by the same factors: the strength of intermolecular forces (such as van der Waals forces, hydrogen bonding, or ionic interactions) and molecular size or shape. Stronger intermolecular forces generally result in stronger cohesion between the fluid particles, leading to a higher surface tension and a greater resistance to flow (i.e., viscosity). In summary, substances with stronger intermolecular forces and complex molecular structures may display high surface tension and high viscosities.

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