Entropy change, for

The most fiindamental of cluster properties are the bond strengths and entropy changes for the process [125]... 

The standard entropy change for the atom-molecule reactions is in the range 5-20 mole and the halogen molecule dissociation has an eiiU opy change of about 105 e.u. The halogen molecule dissociation energy decreases from chlorine to iodine, but the atom-molecule reactions become more endothermic from chlorine to iodine, and this latter effect probably influences the relative contributions to the mechanism from chain reaction and biinolecular reaction. 

This is die entropy change for a complete conversion to NH3 where 1 kmol of N2 is converted. The entropy change at 428 K is ... 

It can be shown - p- that if an LFER is observed over a range of temperatures, and if the enthalpy and entropy changes are temperature independent, then the enthalpy changes must be directly proportional to the entropy changes for the reaction series. Let us start with the proposition that a real effect of this type has been demonstrated for a reaction series we write this as... 

If the heat capacity can be evaluated at all temperatures between 0 K and the temperature of interest, an absolute entropy can be calculated. For biological processes, entropy changes are more useful than absolute entropies. The entropy change for a process can be calculated if the enthalpy change and free energy change are known. 

An important question for chemists, and particularly for biochemists, is, Will the reaction proceed in the direction written J. Willard Gibbs, one of the founders of thermodynamics, realized that the answer to this question lay in a comparison of the enthalpy change and the entropy change for a reaction at a given temperature. The Gibbs free energy, G, is defined as... 

The ease of dissociation of the X2 molecules follows closely the values of the enthalpy of dissociation since the entropy change for the reaction is almost independent of X. Thus F2 at 1 atm pressure is 1% dissociated into atoms at 765°C but a temperature of 975°C is required to achieve the same degree of dissociation for CI2 thereafter, the required temperature drops to 775°C for Br2 and 575°C for I2 (see also next section for atomic halogens). 

Adding together the values for the two stages, we may obtain the entropy change for the whole process... 

Notice that the second law refers to the total entropy change, involving both system and surroundings. For many spontaneous processes, the entropy change for the system is a negative quantity. Consider, for example, the rusting of iron, a spontaneous process ... 

In principle, the second law can be used to determine whether a reaction is spontaneous. To do that, however, requires calculating the entropy change for the surroundings, which is not easy. We follow a conceptually simpler approach (Section 17.3), which deals only with the thermodynamic properties of chemical systems. 

To derive an expression for the change in entropy when a system is heated, we first note that Eq. 1 applies only when the temperature remains constant as heat is supplied to a system. Except in special cases, that can be true only for infinitesimal transfers of heat so we have to break down the calculation into an infinite number of infinitesimal steps, with each step taking place at a constant but slightly different temperature, and then add together the infinitesimal entropy changes for all the steps. To do this is we use calculus. For an infinitesimal reversible transfer dgrev at the temperature T, the increase in entropy is also infinitesimal and, instead of Eq. 1, we write... 

Some changes are accompanied by a change in volume. Because a larger volume provides a greater range of locations for the molecules, we can expect the positional disorder of a gas and therefore its entropy to increase as the volume it occupies is increased. Once again, we can use Eq. 1 to rum this intuitive idea into a quantitative expression of the entropy change for the isothermal expansion of an ideal gas. 

A note on good practice Note that the entropy change for 1 mol of a substance is reported differently from the entropy change per mole the units of the former are joules per kelvin (J-K ), those of the latter are joules per kelvin per mole (J-K -mol ). 

To use Eq. 1 to calculate the entropy change for a substance undergoing a transition from one phase to another at its transition temperature, we need to note three facts ... 

Self-Test 7.12A Without doing any calculations, estimate the sign of the entropy change for the reaction N2(g) + 3 H2(g) - 2 NH,(g) and explain your answer. 

EXAMPLE 7.12 Calculating the total entropy change for the expansion of an ideal gas... 

Calculate the entropy change for reversible heat transfer (Example 7.1). 

Use data in Table 7.3 or Appendix 2A to calculate the standard entropy change for each of the following reactions at 25°C. For each reaction, interpret the sign and magnitude of the reaction entropy, (a) The synthesis of carbon disulfide from natural gas (methane) CH4(g) + 4 S(s, rhombic) - CS2(1) +... 

---