Van t Hoff factor

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,... 

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. 

We know that A7f = iK - m. For solutions of the same solvent at the same molality, the solute with the larger van t Hoff factor, /, has the lower freezing point. Therefore,... 

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

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. 

The actual value for the van t Hoff factor can be larger than the ideal value if more particles are produced than expected, e.g., a molecular compound might be considered to have /ideal = 1, but if it slightly ionizes, the /actual would be larger than 1. 

The freezing point depression is proportional to the product of the solute s molality and the van t Hoff factor. For nonelectrolytes, such as C2H5OH (0.050 m), i = 1, and thus... 

We compute the value of the van t Hoff factor, then use this value to compute the boiling point elevation. 

The boiling point must go up by 2 degrees, so ATb = 2 °C. We know that Kb = 0.512 °C/m for water. We assume that the mass of a litre of water is 1.000 kg and that the van t Hoff factor for NaCl is i = 2.00. We first determine the molality of the saltwater solution and then the mass of solute needed. 

The van t Hoff factor of NaCl most likely is not equal to 2.0, but a bit less and thus the two definitions are in fair agreement. 

This again is close to the defined freezing point of -0.52 °C, with the error most likely arising from the van t Hoff factors not being integral. 

B. In the equation At = i m - Kb, where At is the boiling-point elevation, m is the molality of the solution, and Kb is the boiling-point-elevation constant for water, i (the van t Hoff factor) would be expected to be 4 if H3B03 were completely ionized. According to data provided, i is about 1.5. Therefore, H3B03 must have a relatively low Ka. 

ATt is the number of degrees that the freezing point has been lowered (the difference in the freezing point of the pure solvent and the solution). Kt is the freezing-point depression constant (a constant of the individual solvent). The molality (m) is the molality of the solute, and i is the van t Hoff factor, which is the ratio of the number of moles of particles released into solution per mole of solute dissolved. For a nonelectrolyte such as sucrose, the van t Hoff factor would be 1. For an electrolyte such as sodium sulfate, you must take into consideration that if 1 mol of Na2S04 dissolves, 3 mol of particles would result (2 mol Na+, 1 mol SO) ). Therefore, the van t Hoff factor should be 3. However, because sometimes there is a pairing of ions in solution the observed van t Hoff factor is slightly less. The more dilute the solution, the closer the observed van t Hoff factor should be to the expected one. 

In this equation, ATb is the number of degrees that the boiling point has been elevated (the difference between the boiling point of the pure solvent and the solution), Kb is the boiling-point elevation constant, m is the molality of the solute, and i is again the van t Hoff factor. 

In this equation, u is the osmotic pressure in atmospheres, n is the number of moles of solute, R is the ideal gas constant (0.0821 Latm/K mol), T is the Kelvin temperature, V is the volume of the solution and i is the van t Hoff factor. If one knows the moles of solute and the volume in liters, n/V may be replaced by the molarity, M. It is possible to calculate the molar mass of a solute from osmotic pressure measurements. This is especially useful in the determination of the molar mass of large molecules such as proteins. 

We already have the van t Hoff factor, the Kb, and solution molality so we can simply substitute ... 

The freezing point depression and boiling point elevation techniques are useful in calculating the molar mass of a solute or its van t Hoff factor. In these cases, you will begin with the answer (the freezing point depression or the boiling point elevation), and follow the same steps as above in reverse order. 

In the preceding examples, we saw how to deal with nonelectrolytes. If the solution contains an electrolyte, there will only be one change necessary. This change will be to enter the value of the van t Hoff factor. We will see how to do this in the next example. 

From this relationship, we can see that each Na2S04 produces three ions. The production of three ions means that the van t Hoff factor, i, is 3. We need to know the molality of the solution to find our answer. To determine the molality, we will begin by determining the moles of sodium sulfate. Sodium sulfate has a molar mass of 142.04 g/mol. Thus, the number of moles of sodium sulfate present is ... 

The most common error made in colligative property problems is to forget to separate the ions of an electrolyte. The van t Hoff factor, even when not needed, is a useful reminder. 

Determine the van t Hoff factor for trichloroacetic acid (Kb for water = 0.512 K kg mof1). 

A common mistake is the assumption that the van t Hoff factor must be a whole number. This is true only for strong electrolytes at very low concentrations. 

Many errors are associated with electrolytes. The van t Hoff factor is often forgotten. The van t Hoff factor is a calculated value, not a measured value. As a calculated value, it may or may not be a whole number. 

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