Positive entropy change

Any change taking place which results in an increase in entropy has a positive entropy change (AS). Most spontaneous thermodynamic processes are accompanied by an increase in entropy. Entropy has units of Joules per degree K per mole. For representative values see table on p. 393. 

STRATEGY We expect a positive entropy change because the thermal disorder in a system increases as the temperature is raised. We use Eq. 2, with the heat capacity at constant volume, Cv = nCV m. Find the amount (in moles) of gas molecules by using the ideal gas law, PV = nRT, and the initial conditions remember to express temperature in kelvins. Because the data are liters and kilopascals, use R expressed in those units. As always, avoid rounding errors by delaying the numerical calculation to the last possible stage. 

The decomposition of N2 O4 requires a bond to break. This is the reason why the decomposition has a positive A 77 °. At the same time, the number of molecules doubles during decomposition, which is the reason AS° has a positive value. The positive enthalpy change means that energy Is removed from the surroundings and constrained, whereas the positive entropy change means that matter is dispersed. At temperatures below 315 K, the enthalpy term dominates and decomposition is not spontaneous, but at temperatures above 315 K, the entropy term dominates and decomposition is spontaneous. 

Solid ammonium nitrate is an orderly, crystalline substance, a state considerably less random than a solution of ions in water. In this case, the positive entropy change outweighs the enthalpy change. That is TAS > AH. The Gibbs free energy change is negative, so the process will proceed spontaneously. 

Thermodynamic analysis of the binding constants of BSA and procyanidin dimer and trimer from the Van t Hoff equation (29) indicates a reaction with a positive entropy change, a positive... 

As noted in table 11.1, the ability of THFTCA to separate LJO from trivalent lanthanide ions is mainly of enthalpic origin. Reaction 11.33 has a considerably more unfavorable enthalpic contribution than reaction 11.32. The complexation is, however, predominantly entropy driven because the T ArS° term dominates the ArH° contribution for all systems. The large positive entropy changes observed for reactions 11.32 and 11.33 result from the release of water molecules coordinated to the metal on complexation with the tridentate THFTCA2- ligand. Note that a negative entropy contribution would be expected if these reactions were truly 2 particle = 1 particle reactions [226]. 

A reversible adiabatic expansion of an ideal gas has a zero entropy change, and an irreversible adiabatic expansion of the same gas from the same initial state to the same final volume has a positive entropy change. This statement may seem to be inconsistent with the statement that 5 is a thermodynamic property. The resolution of the discrepancy is that the two changes do not constitute the same change of state the final temperature of the reversible adiabatic expansion is lower than the final temperature of the irreversible adiabatic expansion (as in path 2 in Fig. 6.7). 

Yeager suggests that the major factor involved in the ion exchange selectivity of Nafion is the positive entropy change associated with the replacement of H+ with the metal ion, which is accompanied by water release and polymer contraction. 

In the preceding section, the positive entropy change observed in many complexation reactions has been related to the release of a larger number of water molecules than the number of bound ligands. As a result, the total degrees of freedom of the system are increased by complexation and results in a positive... 

The enthalpy value of Eq. (3.23) is very small as might be expected if two Cd-N bonds in Cd(NH3) 2 are replaced by two Cd-N bonds in Cd(en). The favorable equilibrium constants for reactions [Eqs. (3.22) and (3.23)] are due to the positive entropy change. Note that in reaction, Eq. (3.23), two reactant molecules form three product molecules so chelation increases the net disorder (i.e., increase the degrees of freedom) of the system, which contributes a positive AS° change. In reaction Eq. (3.23), the AH is more negative but, again, it is the large, positive entropy that causes the chelation to be so favored. 

This positive entropy change means that there is greater disorder in the product (HjO gas) than the reactant (HjO liquid). In terms of just entropy, the increase in entropy drives the reaction to the right, toward a condition of higher entropy. 

In aqueous systems, the enthalpy change due to micellization is usually positive, and micelliza-tion is driven by entropy change. Explain the reason for the positive entropy change. 

Reactions with a large, positive entropy change also favor product formation (large Kp). For example, a reaction with a net increase in the number of moles of gas-phase species has a very positive A S°, from the translational entropy gain associated with the additional species. If AS° > 0, high temperatures increase Kp and drive the reaction toward completion (toward the products). If A5° < 0, Kp will increase as the temperature goes down. 

Since AG° = AH0- TAS° (see Chapter 6), it follows that the negative value of AG° for hydrophobic interactions must result from a positive entropy change, which may arise from the restricted mobility of water molecules that surround dissolved hydrophobic groups. When two hydrophobic groups come together to form a "hydrophobic bond," water molecules are freed from the structured region around the hydrophobic surfaces and the entropy increases. The AS° for Eq. 2-9 is about 12 J deg 1 mol-1. Attempts have been made to relate this value directly to the increased number of orientations possible for a water molecule when it is freed from the structured region.64 However, interpretation of the hydrophobic effect is complex and controversial.65-713... 

As you might expect, there is a large positive entropy change, corresponding to a large increase in randomness, on converting water from a liquid to a gas. 

The mixing of two gaseous substances, or of two non-polar liquids, are further examples of entropy-driven processes. These involve negligible enthalpy changes (no strong chemical bonds are formed or broken) but the increased randomness and disorder in the system lead to a positive entropy change. 

---