(b) Write a brief account of the Gibbs adsorption isotherm. Include in your answer the validity of any assumptions made and explain clearly how one may use such an isotherm to estimate molecular cross sectional areas for adsorbed species.
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∻Solution∻ ‖ 1 ⋮ **Understand Gibbs Adsorption Isotherm**: The Gibbs adsorption isotherm describes how the concentration of a substance adsorbed on a surface changes with its concentration in the adjacent phase. ‖ ‖ 2 ⋮ **Assumptions**: The main assumption is that the surface layer is in equilibrium with the bulk phase, and the temperature is constant. The surface is also assumed to be perfectly flat and the adsorbed layer is considered to be monomolecular. ‖ ‖ 3 ⋮ **Gibbs Adsorption Equation**: The isotherm is given by the equation $-\Gamma = \left(\frac{\partial \gamma}{\partial \ln C}\right)_T$, where $\Gamma$ is the surface excess concentration, $\gamma$ is the surface tension, $C$ is the concentration of the adsorbing species, and $T$ is the temperature. ‖ ‖ 4 ⋮ **Estimating Molecular Cross-Sectional Areas**: By measuring the change in surface tension with concentration, one can calculate the surface excess concentration. Knowing the number of molecules in the surface excess allows for the estimation of the molecular cross-sectional area using the equation $A = \frac{1}{\Gamma N_A}$, where $A$ is the molecular cross-sectional area and $N_A$ is Avogadro's number. ‖ ∻Answer∻ ⚹ The Gibbs adsorption isotherm can be used to estimate molecular cross-sectional areas for adsorbed species by measuring the change in surface tension with concentration and applying the equation $A = \frac{1}{\Gamma N_A}$. ⚹ ∻Key Concept∻ ⚹ Gibbs adsorption isotherm ⚹ ∻Explanation∻ ⚹ It relates the change in surface tension to the concentration of the adsorbed species, allowing for the estimation of molecular cross-sectional areas. ⚹◊What is the relationship between surface tension and the Gibbs adsorption isotherm in the context of molecular cross sectional areas for adsorbed species⍭ Generate me a similar question◊

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