Molar freezing point depression

Nitric acid alone fails to nitrate benzene and sulfuric acid also does not readily react with it, yet the mixed acid is an efficient nitrating reagent. Solutions of nitric acid in sulfuric acid show an approximately four-fold molar freezing-point depression and this has been attributed to the generation of four ions, as shown in equation (1) ... 

That the amide might be dehydrated by the sulfuric acid reaction mixture seems to be ruled out by the fact that benzamide shows a molar freezing point depression of two in sulfuric acid solution. Dehydration would cause a molar freezing point depression of four. Accordingly, it seems more likely58 that dehydration of the intermediate XC occurs before rearrangement since a series of steps similar to those outlined in equations 25 to 29 would lead to the nitrile directly ... 

In considering the acid hydrolysis of esters, we should remember that esters are weak bases. Most of them show a molar freezing point depression of two when they are dissolved in 100 per cent sulfuric acid. Presumably the two species arise from the reaction (see p. 36) ... 

II. Unimolecular Acid-Catalyzed Reactions Involving Acyl-Oxygen Fission. At least one instance is known in which decomposition of the protonated complex does not seem to depend upon the attack of water or an alcohol molecule. It is the formation or hydrolysis of esters of 2,4,6-trimethylbenzoic acid in sulfuric acid solution. Since cryoscopic studies have shown that the acid gives a molar freezing point depression of four (p. 39), and the ester five (p. 225), we must conclude that decomposition of the protonated complex to the acyl carbonium ion 0... 

The constitution of the thorium(lV) carbonate complex formed at high carbonate concentration has been determined by cryoscopy. This is a method that provides information about the number of solute particles in solution and for the case of complex formation reactions, the change in this number as a result of complex formation, e.g. for the reaction Th" + 5CO3 Th(C03)5 there is a decrease of five. The authors have determined the molar freezing point depression and this is used to test the stoichiometry of the complexes formed. One important conclusion from this study is that the experimental data are only consistent with the stoichiometry Th(C03)j". Experimental data of this type caimot be made in a medium of constant ionic strength and it is also not possible to determine equilibrium constants. However, the proposed stoichiometiy is in agreement with that proposed in a large number of other studies. 

The molar freezing point depression of water is 1.86 ° C. Blood freezes on average at -0.54 ° C. Plasma and tear fluid have the same freezing point. The osmolarity of blood, plasma and tear fluid is thus equal to ... 

Colligative properties, particularly freezing point depression, can be used to determine molar masses of a wide variety of nonelectrolytes. The approach used is illustrated in Example 10.9. 

In carrying out a molar mass determination by freezing point depression, we must choose a solvent in which the solute is readily soluble. Usually, several such solvents are available. Of these, we tend to pick one that has the largest kf. This makes ATf large and thus reduces the percent error in the freezing point measurement From this point of view, cyclohexane or other organic solvents are better choices than water, because their kf values are larger. 

The presence of a solute lowers the freezing point of a solvent if the solute is nonvolatile, the boiling point is also raised. The freezing-point depression can be used to calculate the molar mass of the solute. If the solute is an electrolyte, the extent of its dissociation, protonation, or deprotonation must also be taken into account. 

Colligative properties can be sources of insight into not only the properties of solutions, but also the properties of the solute. For example, acetic acid, CH.COOH, behaves differently in two different solvents, (a) The freezing point of a 5.00% by mass aqueous acetic acid solution is — l.72°C. What is the molar mass of the solute Explain any discrepancy between the experimental and the expected molar mass, (b) The freezing-point depression associated with a 5.00% by mass solution of acetic acid in benzene is 2.32°C. Whar is the experimental molar mass of the solute in benzene What can you conclude about the nature of acetic acid in benzene ... 

Colligative1 properties of dilute polymer solutions depend only on the number of dissolved molecules and not on properties of the molecules themselves, such as mass or size. Osmotic pressure, freezing point depression, boiling point elevation, and vapour pressure lowering are the most prominent examples. These methods essentially allow one to count the number n of solute molecules. From n and the known total mass m of the solute the molar mass M is readily obtained as... 

The freezing-point depression data are used to determine the molar mass. 

Determination of molar mass by freezing-point depression... 

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. 

The freezing-point depression technique is also commonly used to calculate the molar mass of a solute. 

When using the freezing-point depression method of determining the molar mass of a nonelectrolyte, what information is needed in addition to the above ... 

D—To calculate the molar mass, the mass of the solute and the moles of the solute are needed. The molality of the solution may be determined from the freezing-point depression, and the freezing-point depression constant (I and II). If the mass of the solvent is known, the moles of the solute may be calculated from the molality. These moles, along with the mass of the solute, can be used to determine the molar mass. 

Experiment 4 Molar Mass by Freezing-Point Depression... 

Kf = molal freezing-point depression constant Kt,= molal boiling-point elevation constant A = absorbance a= molar absorptivity b = path length c= concentration Q = reaction quotient /= current (amperes) q= charge (coulombs) f= time (seconds)... 

The method is based on the principle that a solution of lactose specifically hydrolyzed will show a freezing point depression directly proportional to the molarity of the lactose. Doubling of the number of molecules by hydrolysis theoretically will double the effect that the carbohydrate would have on the freezing point. The method was most sensitive in the region of lactose concentration of 1.0 to 3.5% ( 0.05% lactose). 

ACTIVITY COEFFICIENT. A fractional number which when multiplied by the molar concentration of a substance in solution yields the chemical activity. This term provides an approximation of how much interaction exists between molecules at higher concentrations. Activity coefficients and activities are most commonly obtained from measurements of vapor-pressure lowering, freezing-point depression, boiling-point elevation, solubility, and electromotive force. In certain cases, activity coefficients can be estimated theoretically. As commonly used, activity is a relative quantity having unit value in some chosen standard state. Thus, the standard state of unit activity for water, dty, in aqueous solutions of potassium chloride is pure liquid water at one atmosphere pressure and the given temperature. The standard slate for the activity of a solute like potassium chloride is often so defined as to make the ratio of the activity to the concentration of solute approach unity as Ihe concentration decreases to zero. 

When determining a molar mass from freezing-point depression, it is possible to make each of the following errors (among others). In each case, predict whether the error would cause the reported molar mass to be greater or less than the actual molar mass. 

X V iution), the determination of the molar mass of a solute requires a measurement of mass, volume, temperature, and osmotic pressure. Osmotic pressures are generally large and can be determined quite accurately, thus yielding accurate molar masses. Boiling-point elevations and freezing-point depressions are usually small and not very accurate, so molar mass determinations based on those measures often are not accurate. 

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