Van’t Hoff i factor

Here, i, the van t Hoff i factor, is determined experimentally. In a very dilute solution (less than about 10 3 mol-I. ), when all ions are independent, i = 2 for MX salts such as NaCl, i = 3 for MX2 salts such as CaCl2, and so on. For dilute nonelectrolyte solutions, i =l. The i factor is so unreliable, however that it is best to confine quantitative calculations of freezing-point depression to nonelectrolyte solutions. Even these solutions must be dilute enough to be approximately ideal. 

A 1.00% by mass NaCI(aq) solution has a freezing point of —0.593°C. (a) Estimate the van t Hoff i factor from the data, (b) Determine the total molality of all solute species. 

Interpret a measured value of the van t Hoff i factor, Self-Test 8.12. 

A 1.00% NaCl(aq) by mass solution has a freezing point of —0.593°C. (a) Estimate the van t Hoff i factor from the data, (b) Determine the total molality of all solute species, (c) Calculate the percentage dissociation of NaCl in this solution. (Hint The molality calculated from the freezing-point depression is the sum of the molalities of the undissociated ion pairs, the Na+ ions, and the Cl ions.)... 

The freezing point of a 5.00% by mass CH3COOH(aq) solution is — 1.576°C. Determine the experimental van t Hoff i factor for this solution. Account for its value on the basis of your understanding of intermolecular forces. 

Hantzsch s work said his conclusions have lately been revised and criticized. In his extensive work published in 1941, Titov [35] drew attention to the fact that none of the existing view about the action of sulphuric acid on nitric acid explained Hantzsch s observation that the value of the van t Hoff i-factor for nitric acid dissolved in sulphuric acid may be close to 4. 

Using more precise methods of ciyometric measurements Ingold [37] and coworkers had already found in 1946 that the value of van t Hoff i-factor for HN03 in sulphuric acid is 4.4. Ingold explained this by eqn. (18). 

For an electrolyte that dissociates into two ions, the van t Hoff i factor will be 1 plus the degree of dissociation, in this case 0.075. This can be readily seen for the general case MX. Let A = initial concentration of MX (if none is dissociated) and let Y = the concentration of MX that subsequently dissociates ... 

NH4S0 4 S0"4+NH 4, and unless the first stage be completed, the calculation cannot easily be made. From the conductivity and f.p. measurements of a normal soln., S. Arrhenius calculated for the ternary ionization, (NH4)2S04 2NH 4+SO"4, the value 2 17 for J. H. van t Hoff s factor i but the result is not probable. H. Koppe calculated i=2 00 for the W-soln. from his osmotic measurements. The effect of additions of non-conductors to the soln. was studied by S. Arrhenius. The degree of ionization with a W-soln., at 25°, Is 0 0185 with methyl alcohol 0 0249 with ethyl alcohol 0 0267 with isopropyl alcohol 0 0212 with ether and 0 0171 with acetone. 

This relation must hold if the mass law is obeyed By eliminating C, and C from this equation and from the thermodynamic equation (i), (viz 2dirJC, - dirujCu = o), it is seen that the necessary and sufficient condition that the law of mass action should hold is that at all concentrations dmUC = dirJdCu Now the computation of van t Hoff s factor i from freezing-point data, and the consequent calculation of the degree of ionisation on this basis assumes that the ions and the undissociated molecules are normal That is, it assumes dirJdC, = dirJdCu = RT... 

Fischer and Walach i showed that if Knorr s pyrrole is dissolved in concentrated sulphuric acid at 40° and the solution then poured on ice, 2-ethoxycarbonyl-3,5-dimethylpyrrole-4-carboxylic acid results. Probably, dissolution of the diester in concentrated sulphuric acid generates the acylium ion (77) evidence for this is the van t Hoff cryoscopic factor of 3 5 observed for such solutions a xhe process cannot be complete at the freezing point, for complete acylization would give s factor of 5. Acyli-zation 184 AacI > will be facilitated by electron-releasing substituents and will not be subject to steric factors. In the pyrrole series, a balance has to be struck between the facilitation caused by increasing alkyl substitution in the nucleus and the retardation which would accompany salt formation by... 

The same van t Hoff responsible for the i factor showed that the osmotic pressure of a solution is related to the molarity, c, of the solute in the solution ... 

A theory close to modem concepts was developed by a Swede, Svante Arrhenins. The hrst version of the theory was outlined in his doctoral dissertation of 1883, the hnal version in a classical paper published at the end of 1887. This theory took up van t Hoff s suggeshons, published some years earlier, that ideal gas laws could be used for the osmotic pressure in soluhons. It had been fonnd that anomalously high values of osmotic pressure which cannot be ascribed to nonideality sometimes occur even in highly dilute solutions. To explain the anomaly, van t Hoff had introduced an empirical correchon factor i larger than nnity, called the isotonic coefficient or van t Hoff factor,... 

Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

The ideal value for the van t Hoff factor, i, for strong electrolytes at infinite dilution is the total number of ions present in a formula unit. 

The value for the van t Hoff factor, i, for strong electrolytes in dilute solution approximates the total number of ions present in a formula unit. So, / = 2 for KC103 and / = 3 for CaCl2. The value of / for the weak electrolyte such as CH3COOH is between 1 and 2. The value of / for a nonelectrolyte such as CH3OH is 1. 

Note The van t Hoff factor, i, must be included in all calculations involving colligative properties, including... 

We know that APf = iKf m. For solutions of the same solvent at the same molality, the solute with the larger van t Hoff factor, i, has the lower freezing point. 

The true molecular weight of acetic acid is 60.05 g/mol. Acetic acid is a weak acid and dissociates very slightly in water the van t Hoff factor, i, is then only slightly larger than 1. The behavior of acetic acid approximates that of a nonelectrolyte in water. 

---