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 cme depends on the substance, the solvent, and the temperature. At and above the cmc, the properties of the solution vary drastically. (a) The turbidity (the amount of light scattering) of solutions increases dramatically at the cmc. Suggest an explanation. (b) The ionic conductivity of the solution dramatically changes at the 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 cmc.

Step by step solution

01

Understanding Micelles and cmc

Micelles are structures formed by surfactants like sodium stearate in a solution when its concentration reaches a certain value called the critical micelle concentration (cmc). These micelles are composed of dozens to hundreds of molecules and can significantly change the properties of the solution at and above the cmc.

02

(a) Explaining the Increased Turbidity

Turbidity is the measure of the scattering of light in a solution. When the concentration of surfactants like sodium stearate reaches the cmc, they start to form micelle structures. This causes an increase in the number of larger particles (micelles) in the solution, leading to more light scattering. Therefore, the turbidity of the solution increases dramatically at the cmc.

03

(b) Explaining the Change in Ionic Conductivity

Ionic conductivity is the ability of a solution to allow the transport of ions. Surfactants like sodium stearate are ionic compounds, dissociating into cations (sodium ions) and anions (stearate ions). Before reaching the cmc, these ions are free to move in the solution, contributing to its ionic conductivity. At and above the cmc, when micelles are formed, the ions become part of the micelle structure, resulting in a decrease in the number of free ions available for the transport. Consequently, the ionic conductivity of the solution changes dramatically at the cmc.

04

(c) Predicting the Fluorescence Intensity

As the concentration of sodium stearate approaches the cmc, there is an increase in the number of micelles formed in the solution. When the fluorescent dye is introduced, the dye's molecules will be in a hydrophobic environment, which leads to a greater intensity of fluorescence. So, as the sodium stearate concentration increases past the cmc, the intensity of fluorescence for the dye in the solution will also increase, as more micelles provide more hydrophobic environments for the dye molecules to reside in and emit stronger fluorescence.

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