Van t Hoffs equation

The enthalpies of complexation of 3.8c to the copper(lf) - amino acid ligand complexes have been calculated from the values of at 20 C, 25 1C, 30 1C, 40 1C and 50 1C using the van t Hoff equation. Complexation entropies have been calculated from the corresponding Gibbs energies and enhalpies. 

The molecular weight analysis presented above is a purely thermodynamic result and is independent of any model. The procedure requires dilute solutions, but is not based on the assumption of ideality, even though Eq. (8.88) is a variation of the van t Hoff equation. 

The solute molecular weight enters the van t Hoff equation as the factor of proportionality between the number of solute particles that the osmotic pressure counts and the mass of solute which is known from the preparation of the solution. The molecular weight that is obtained from measurements on poly disperse systems is a number average quantity. 

When B = 0, the solution behaves ideally, at least through second-order effects. This means that deviations from ideality might be observed at still higher concentrations, but that the van t Hoff equation applies at least in dilute solutions for systems with B = 0. 

Neglecting the higher-order terms, we can write the osmotic pressure for this three-component system in terms of the van t Hoff equation ... 

Note that if z = 0, the entire quantity in the brackets would equal m2, and Eq. (8.126) would be the van t Hoff equation applied to an ordinary polymer. 

A correct value of the molecular weight is obtained for the charged polymer by the van t Hoff equation, provided that a large excess of indifferent electrolyte is present. These high concentrations are described as swamping electrolyte conditions. 

Van t Hoffs equation Vantocil Vantocil IB Vantol Vapam... 

For example, the measurements of solution osmotic pressure made with membranes by Traube and Pfeffer were used by van t Hoff in 1887 to develop his limit law, which explains the behavior of ideal dilute solutions. This work led direcdy to the van t Hoff equation. At about the same time, the concept of a perfectly selective semipermeable membrane was used by MaxweU and others in developing the kinetic theory of gases. 

For many years, it was thought that the macro solute forms a new phase near the membrane—that of a gel or gel-like layer. The model provided good correlations of experimental data and has been widely used. It does not fit known experimental facts. An explanation that fits the known data well is based on osmotic pressure. The van t Hoff equation [Eq. (22-75)] is hopelessly inadequate to predict the osmotic pressure of a macromolecular solution. Using the empirical expression... 

The effeet of temperature on equilibrium eomposition ean be eal-eulated using the van t Hoff equation. Sinee the standard heat of reaetion is negative (-AH[ ) for an exothermie reaetion, an inerease in temperature results in a deerease in K and a subsequent deerease in eonversion. Therefore, an exothermie reaetion must be performed at as low a temperature as possible. An endothermie reaetion (+AH] ) is positive and K inereases with an inerease in temperature, as does the equilibrium eonversion. Therefore, an endothermie reaetion must be performed at an elevated temperature. 

Here Q is the solute concentration and R the gas constant. This is in fact obeyed over a rather wide range of concentrations, almost up to solute mole fractions of 0.61, with an error of only 25 percent. This is remarkable, since the van t Hoff equation is rigorous only in the infinitely dilute limit. Even in the case of highly nonideal solutions, for example a solution with a ratios of 1.5 and e ratios of 4, the van t Hoff equation is still obeyed quite well for concentrations up to about 6 mole percent. It appears from these results that the van t Hoff approximation is much more sensitive to the nonideality of the solutions, and not that sensitive... 

The most widely used transient method is the temperature-jump (T-jump) method. This is based on the van t Hoff equation, which describes the temperature dependence of the equilibrium constant. 

As pointed out earlier, the equilibrium constant of a system changes with temperature. The form of the equation relating K to T is a familiar one, similar to the Clausius-Clapeyron equation (Chapter 9) and the Arrhenius equation (Chapter 11). This one is called the van t Hoff equation, honoring Jacobus van t Hoff (1852-1911), who was the first to use the equilibrium constant, K. Coincidentally, van t Hoff was a good friend of Arrhenius. The equation is... 

Thermodynamic quantities for a system may be determined from the van t Hoff equation Eq.(3), which defines the equilibrium constant, K, in terms of the reaction enthalpy, AH and the temperature, T. 

The composite rate constant is k = k2Ka. To explore its temperature profile we write a transition state equation, or Arrhenius equation, for the rate constant k2, and the van t Hoff equation for Ka. In the TST notation, the rate constant for Eq. (7-20) becomes... 

The size of the equilibrium displacement depends on AT and AH for the equilibrium. The sign of AH determines the direction of the shift in accord with the van t Hoff equation. A typical apparatus might discharge 10-25 kV in 1 cm3 of solution. This voltage discharge produces about 45 J in 10-6 s, which corresponds to 4.5 x 107 W. A temperature rise of 5-10 °C might ensue. 

The expression that we have just derived is a quantitative version of I.e Chate-lier s principle for the effect of temperature. It is normally rearranged (by multiplying through by —1 and then using In a — In h = In (alb)) into the van t Hoff equation ... 

What does this equation tell us Suppose that the reaction is endothermic, then AH° is positive. If T2 > T, then 1/T2 < 1/T, and the term in braces is also positive. Therefore, In (K2/K,) is positive, which implies that K,/K, > 1 and therefore that K2 > K,. In other words, an increase in temperature favors the formation of product if the reaction is endothermic. We predict the opposite effect for an exothermic reaction because AHr° is then negative. Therefore, the van t Hoff equation accounts for Le Chatelier s principle for the effect of temperature on an equilibrium. 

One word of warning when using the van t Hoff equation for reactions involving gases, the equilibrium constants must be K, not K(.. If we want a new value for Kc for a gas-phase reaction, we convert from K(. into K at the initial temperature (by using Eq. 12), use the van t Hoff equation to calculate the value of K at the new temperature, and then convert that K into the new Kc by using Eq. 12 at the new temperature. 

STRATEGY The synthesis of ammonia is exothermic, and so we expect the equilibrium constant to be smaller at the higher temperature. To use the van t Hoff equation, we need... 

The vaporization of a liquid can be treated as a special case of an equilibrium. How does the vapor pressure of a liquid vary with temperature Hint Devise a version of the van t Hoff equation that applies to vapor pressure by first writing the equilibrium constant K for vaporization. 

The van t Hoff equation describes the temperature dependence of the equilibrium constant. 

To calculate the equilibrium composition of a mixture at a given temperature, we first need to calculate the equilibrium constant from thermodynamic data valid under the standard conditions of 298 K and 1 bar, as in Tab. 2.2. Differentiating Eq. (22) and using AG° = A - TAS° we obtain the Van t Hoff equation ... 

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