![]() ![]() Here we further explore the nature of this state function and define it mathematically. In Chapter 13, we introduced the concept of entropy in relation to solution formation. Mathematically, the symbol for the internal enthalpy change is 'H' and the symbol for the internal entropy change is 'S.' Free energy is symbolized by 'G,' and the relationship is given by the following expression: G H TS. To help explain why these phenomena proceed spontaneously in only one direction requires an additional state function called entropy (S), a thermodynamic property of all substances that is proportional to their degree of "disorder". Free energy is just a way to keep track of the sum of the two effects. Moreover, the molecules of a gas remain evenly distributed throughout the entire volume of a glass bulb and never spontaneously assemble in only one portion of the available volume. For example, after a cube of sugar has dissolved in a glass of water so that the sucrose molecules are uniformly dispersed in a dilute solution, they never spontaneously come back together in solution to form a sugar cube. For a full video: see Thus enthalpy is not the only factor that determines whether a process is spontaneous. ![]() For instance, the solubility of methane in water decreases with increasing temperature at low temperatures (after reaching a minimum at about 350 K, the solubility increases with higher temperature 31 ). When water is placed on a block of wood under the flask, the highly endothermic reaction that takes place in the flask freezes water that has been placed under the beaker, so the flask becomes frozen to the wood. The hydrophobic interaction is entropy-driven and thus intrinsically temperature sensitive. ![]() The reaction of barium hydroxide with ammonium thiocyanate is spontaneous but highly endothermic, so water, one product of the reaction, quickly freezes into slush. ![]()
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