Entropies of vaporization

Por most normal liquids the constant has a value of approx. 88JmolK" . Associated liquids show marked variations from this value. The Trouton constant is the molar entropy of vaporization. 

Thus the new thermodynamic heats and entropies of adsorption differ from the preceding ones by the heats and entropies of vaporization of liquid adsorbate. 

Equation (3.7) gives a simple procedure for evaluating the entropy change accompanying a change of state. At the normal boiling point of a liquid, for example, the heat is absorbed reversibly and equals the heat of vaporization AH,. Since T is constant, the entropy of vaporization is AH,/T. For benzene, for example, AS, = (30.8 k J mol" )/353 = 87 J K mol. ... 

A great many liquids have entropies of vaporization at the normal boiling point in the vicinity of this value (see benzene above), a generalization known as Trouton s rule. Our interest is clearly not in evaporation, but in the elongation of elastomers. In the next section we shall apply Eq. (3.21) to the stretching process for a statistical—and therefore molecular—picture of elasticity. 

It is equivalent to say that entropy of vaporization is a constant value for non-associating Hquids. Associating Hquids, eg, ammonia, water, methanol, and ethanol, do not obey the rule of Pictet and Trouton. Despite its simplicity, the Pictet-Trouton view of Hquid vaporization (19) is an exceUent example of the many rules of thumb that have been useful aids in engineering calculations for decades (5,7,8,9,21). However, proper appHcation requires an understanding of the physical reasoning behind each rule. 

Values for many properties can be determined using reference substances, including density, surface tension, viscosity, partition coefficient, solubihty, diffusion coefficient, vapor pressure, latent heat, critical properties, entropies of vaporization, heats of solution, coUigative properties, and activity coefficients. Table 1 Hsts the equations needed for determining these properties. 

Conventional Partial Molal Entropy of (H30)+ and (OH)-. Let us now consider the partial molal entropy for the (1I30)+ ion and the (OH)- ion. If we wish to add an (HsO)+ ion to water, this may be done in two steps we first add an H2O molecule to the liquid, and then add a proton to this molecule. The entropy of liquid water at 25°C is 16.75 cal/deg/mole. This value may be obtained (1) from the low temperature calorimetric data of Giauque and Stout,1 combined with the zero point entropy predicted by Pauling, or (2) from the spectroscopic entropy of steam loss the entropy of vaporization. 2 Values obtained by the two methods agree within 0.01 cal/deg. 

The entropy of vaporization, ASvap, is the change in entropy per mole of molecules when a substance changes from a liquid into a vapor. The heat required per mole to vaporize the liquid at constant pressure is equal to the enthalpy of vaporization (A//vap, Section 6.11). It then follows from Eq. 1, by setting = AH, that the entropy of vaporization at the normal boiling point is... 

When the liquid and the vapor are in their standard states (both pure, both at 1 bar) and the boiling temperature is for 1 bar, we refer to the standard entropy of vaporization and write it ASvap°. Because all standard entropies of vaporization are positive, they are normally reported without their positive sign. 

EXAMPLE 7.6 Sample exercise Calculating the standard entropy of vaporization... 

What is the standard entropy of vaporization of acetone at its normal boiling point of 56.2°C ... 

Self-Test 7.6A Calculate the standard entropy of vaporization of argon at its boiling point (see Table 6.3). 

Table 7.1 lists the standard entropies of vaporization of a number of liquids. These and other data show a striking pattern many values are close to 85 J-K 1-mol h This observation is called Trouton s rule. The explanation of Trouton s rule is that approximately the same increase in positional disorder occurs when any liquid is converted into vapor, and so we can expect the... 

TABLE 7.1 Standard Entropy of Vaporization at the Normal Boiling Point ... 

Self-Test 7.17B Confirm that liquid benzene and benzene vapor are in equilibrium at the normal boiling point of benzene. 80.1°C, and 1 atm pressure. The enthalpy of vaporization of benzene at its boiling point is 30.8 kj-mol 1 and its entropy of vaporization is 87.2 J-K -mol. ... 

The standard entropy of vaporization of benzene is approximately 85 J-K -mol-1 at its boiling point, (a) Estimate the standard enthalpy of vaporization of benzene at its normal boiling point of 80.°C. (b) What is the standard entropy change of the surroundings when 10. g of benzene, CfiHfi, vaporizes at its normal boiling point ... 

Calculate the standard entropy of vaporization of water at 85°C, given that its standard entropy of vaporization at 100.°C is 109.0 J-K -mol 1 and the molar heat capacities at constant pressure of liquid water and water vapor are 75.3 J-K -mol 1 and 33.6 J-K -mol, respectively, in this range. 

At this point we can use AGvap° = AHvap° — TAS °, where AHrap° and ASvap° are the standard enthalpy and entropy of vaporization, respectively, and obtain... 

Neither the enthalpy nor the entropy of vaporization varies much with temperature so, for a given substance, ASvap° and AHtl )° can both be treated as approximately constant. It follows that the vapor pressures P, and P2 at any two temperatures T, and T2 are related by writing this equation for two temperatures and subtracting one from the other. In the process, the entropy terms cancel ... 

C. Using these data, calculate (a) the standard enthalpy of vaporization (b) the standard entropy of vaporization ... 

The vapor pressure of chlorine dioxide, Cl02, is 155 Torr at —22.75°C and 485 Torr at ().()0°C. Calculate (a) the standard enthalpy of vaporization (b) the standard entropy of vaporization (c) the standard Gibbs free energy of vaporization (d) the normal boiling point of C102. 

It is standard practice in chemical laboratories to distill high-boiling-point substances under reduced pressure. Trichloroacetic acid has a standard enthalpy of vaporization of 57.814 kj-mol 1 and a standard entropy of vaporization of 124 J-K 1-mol. Use this information to determine the pressure that one would need to achieve to distill trichloroacetic-acid at 80.°C. 

A change in entropy is equal to the heat supplied reversibly to a system divided by the temperature at which the transfer takes place, entropy of vaporization (AS ) The entropy change per mole accompanying vaporization (the conversion of a substance from the liquid state into the vapor state). 

Trouton s rule The empirical observation that the entropy of vaporization at the boiling point (the enthalpy of vaporization divided by the boiling temperature) is approximately 85 J-K—1 -mol 1 for many liquids. 

According to Trouton s rule, the entropy of vaporization of an organic liquid is a constant of approximately 85 J-mol 1 -K 1. The relationship between entropy of fusion, enthalpy of fusion, and melting point is given by... 

We apply the condensed form of the seven-step strategy. To calculate a vapor pressure, we need the enthalpy and entropy of vaporization. Then we can apply Equation. ... 

C14-0051. Table lists molar enthalpies of vaporization of several substances. Calculate the molar entropy of vaporization at its normal boiling point for each of the following (a) molecular oxygen (b) ethane (c) benzene and (d) mercury. 

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