Compounds like sodium stearate, called "surfactants" in general, can form structures known as micelles in water, once the solution concentration reaches the value known as the critical micelle concentration (cmc). Micelles contain dozens to hundreds of molecules. The cmc depends on the substance, the solvent, and the temperature. At and above the \(\mathrm{cmc}\), the properties of the solution vary drastically. (a) The turbidity (the amount of light scattering) of solutions increases dramatically at the \(\mathrm{cmc}\). Suggest an explanation. (b) The ionic conductivity of the solution dramatically changes at the \(\mathrm{cmc}\). Suggest an explanation. (c) Chemists have developed fluorescent dyes that glow brightly only when the dye molecules are in a hydrophobic environment. Predict how the intensity of such fluorescence would relate to the concentration of sodium stearate as the sodium stearate concentration approaches and then increases past the \(\mathrm{cmc}\).

Step by step solution

01

Part (a): Turbidity Increase Explanation

When the concentration of sodium stearate reaches the critical micelle concentration (cmc), micelles start to form. Micelles are aggregates of amphiphilic surfactant molecules (like sodium stearate), with hydrophobic tails facing inward and hydrophilic heads facing outward towards the water. The formation of micelles can cause a significant increase in turbidity (light scattering) because the aggregated micelles are larger than individual sodium stearate molecules, and therefore scatter more light.

02

Part (b): Ionic Conductivity Change Explanation

The ionic conductivity of a solution is related to the number of free ions that can move and carry an electrical charge. Below the cmc, sodium stearate is dissolved as individual ions (sodium and stearate), which can readily move and contribute to higher ionic conductivity. However, at and above the cmc, a notable portion of the sodium stearate forms micelles. In the micelles, the sodium ions are "trapped" as they are associated with the stearate ions, which reduces their contribution to the ionic conductivity. That's why the ionic conductivity dramatically changes at the cmc.

03

Part (c): Fluorescence Intensity Prediction

In the presence of sodium stearate, a fluorescent dye will glow brightly only when it is in a hydrophobic environment. Since the interior of micelles is formed by the hydrophobic tails of sodium stearate molecules, it provides a hydrophobic environment for the dye to fluoresce. As the sodium stearate concentration approaches the cmc, the number of micelles starts to increase, providing more hydrophobic environments for the dye to fluoresce in. So, the intensity of fluorescence will increase. Once the concentration surpasses the cmc, micelles are more abundant, and the fluorescence intensity will be higher. However, as the overall micelle concentration increases past the cmc, the increase in intensity may not be as rapid as it was below the cmc since more micelles are already present to accommodate dye molecules.

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