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The graduated flask, Fig. 54, which may have a capacity of 20 to 50 cubic centimetres, according to the size of the polariscopetube, should not be wider in the neck than 8 millimetres at the most, and the mark should be pretty far down, so as to avoid any want of uniformity in the solution. The solution having been prepared approximately in the flask, or in some other vessel from which it can be removed to the flask, a thermometer is inserted before finally adjusting to the mark, and the temperature brought to the standard (20° Cent.) by warming with the hand or some form of water-bath. When the temperature stands at 20° Cent, the thermometer should be removed, washed down with a little of the solvent employed, and the liquid then brought accurately to the mark
From the weight of the known volume of solution so prepared we have at the same time approximately the specific weight, and by applying, as in $ 69, the reduction to vacuum, we may obtain a more accurate value for the percentage composition of the solution.
$ 73. Standardising the Flasks. — The volume of the graduated terms of flasks must be determined accurately in the true cubic centimetre (the space, that is, occupied by 1 gramme of water weighed in vacuo at a temperature of 4o Cent.). If the measure is already marked, it should be filled almost to the mark with distilled water, a thermometer inserted, and the liquid warmed or cooled to the normal temperature at which the vessel is to be used (17-5° or 20° Cent.). Then withdrawing the thermometer, water should be added until the mark appears, to an eye looking horizontally, tangential to the concave surface of the liquid. The neck of the flask must be freed of all adhering drops, and the weight of water determined. The reduction to vacuum may then be made with sufficient accuracy, if we are using brass weights, by taking each gramme of water weighed in air as 1 milligramme too light. For p grammes of water, the corrected weight P will thus be P = p + 0·001 p. If now the density Q of water at the temperature of the experiment t°, relative to water at 4° taken as unity, or, in other words, if the weight in grammes of 1 cubio centimetre of water at the temperature to is known, the volume in
1 Provided, that is, the weight of water does not exceed about 100 grammes. For larger quantities, the value 0.00106 gramme or 1:06 milligrammes given in § 69 must be employed
cubic centimetres V. contained in the measure at the temperature to is given by the equation
Q The density of water at different temperatures is shown in the annexed table, prepared by Rosetti from the results obtained by various observers (Kopp, Despretz, Hagen, Matthiessen, and Rosetti). The values are given from 0° to 50° Cent., so as to allow the capacities of graduated flasks or pycnometers to be calculated at any of these temperatures.
1 Rosetti: Pogg. Ann., Erg. Bd. 5, 268.
Take the case of a flask holding 25.065 grammes of water at a temperature of 20° Cent., then the weight in vacuo P = 25.065 + 0.025 = 25.09 grammes, and the capacity at 20° Cent. will be 25.09
= 25.13 cubic centimetres. 0.99826
With a width of neck of 7 or 8 millimetres, there will be variations in the results of successive determinations, no matter how carefully performed, amounting to about 0.05 cubic centimetre. For example, three subsequent measurements of the above flask gave instead of 25.13 cubic centimetres, the values 25:16, 25:11, 25:17 respectively. Now' a difference of 0.05 cubic centimetre has an appreciable effect on the determination of the amount of substance in 100 cubic centimetres. For instance, suppose the flask to hold 25 cubic centimetres, and to contain 5 grammes of active substance, so that the concentration c = 20 grammes, then a variation of 0.05 cubic centimetre in volume will represent a variation of 0.84 gramme in weight. The amount of error due to this source decreases the larger the flask, and the less the concentration, so that in a 50 cubic centimetre solution containing 5 grammes of active substance, or c= 10, the variation only amounts to 0.01 gramme. The degree to which this error in the determination of the concentration of solutions affects the value of specific rotation is stated in a subsequent section (§ 75).
To graduate a flask for a particular volume, the corresponding weight of water is weighed into it, and the level marked upon its neck by a line. The under-surface of the concavity of the fluid-meniscus is taken as the reference level. For example, to graduate a flask to hold exactly 50 cubic centimetres at a temperature of 20° Cent., there will be required-inasmuch as the previous table shows that 1 cubic centimetre of water at 20° Cent. weighs 0.99826 gramme 50 X 0.99826 = 49.913
grammes of water to give the desired volume. Again, correcting for weighing in air, this amount will be reduced by one-thousandth, so that 49.863 grammes of water at 20° Cent. must be weighed into the previously tared flask. Since, however, the volume so determined is based on a single experiment only, it is necessary, if we wish to be strictly accurate, to fill the flask several times afterwards up to the mark, and take the mean of the several weights. The result so obtained almost invariably differs from a whole number, and since in this way the simplicity of even numbers in the calculations of concentration is lost, it
is of no importance to bestow special care on accurate drawing of the mark.
When a measure is used at some temperature ť other than that at which it has been graduated t, allowance must be made for the cubic expansion of glass, the coefficient of which may be taken as 0.000025 for 1° Cent. In calculating the volume at t, the capacity at the temperature of graduation being represented by Vt, we have
V t = V [1 + 0.000025 (ť – t)] where t'>t.
0.000025 (t – t)] where ť <t.
No account, however, need be taken of these variations in volume unless the difference of temperature is considerable and the measures of large size.
8 74. Mohr’sl method of graduating measures used in titration is different. For example, in the case of a 100 cubic centimetre flask, 100 grammes of water at a temperature of 17-5° Cent. are weighed into the flask, and the resulting volume marked as 100 cubic centimetres, the reductions to volume at 4° Cent. and weight in vacuo being omitted.
The cubic centimetres thus obtained are somewhat larger than the true volumes, and, as the density of water at 17.5° Cent. = 0:99875, and a deduction of 0.00105 gramme has to be made for weighing in air, the ratio between the two will be 1 : 0.9977. Hence, to reduce Mohr's cubic centimetres to their true value, they must be divided by 0.9977. If, therefore, we use Mohr's measures to determine the concentration-values of solutions, the values obtained will be greater, and so the specific rotations less than when true centimetre measures are employed, and this in the above-stated proportions. Accordingly, concentrations estimated in Mohr's cubic centimetres should be multiplied by 0.9977, and specific rotations calculated therefrom should be divided by 0.9977, to bring them to their proper values for true centimetres.
The definition of specific rotation presupposes the use of the true centimetre, and upon this supposition all scientific data thereto relating are based.
| Mohr: Lehrbuch der Titrirmethode, 4 Aufl. S. 37.
F. Influence of the several Observation-Errors on
Specific Rotation Values.
$ 75. All the factors entering into the formula [a]
are severally subject to observation-errors, the effects of which may be estimated as below :
1. As regards the angle of rotation a, the experiments given in $ 60 show that the values obtained by different observers with different instruments do not in general vary by more than the hundredth part of a degree, and that the mean error for a single observation may be taken as + 0.025. In the calculations following a maximum error of 0.05° has been allowed:
2. The length L of the tubes can easily be determined by the method described in $ 66, so that the variation in a length of 100 millimetres never exceeds 0.05 millimetre.
3. The specific gravity d of solutions can be found accurately to four places of decimals by means of the pycnometer (see $$ 70 and 71). The maximum error here, which may occur when the normal temperature has been taken more than 1° wrong, or, in particular cases, when the correction in vacuo has been omitted, may be taken as 0.001.
4. As regards the percentage composition p of solutions, neglect to reduce the weighings may involve an error of about 0:01. In cases, however, where filtering is necessary (see $ 68), the percentage may be increased by evaporation to the amount of 0.005 in aqueous solutions, and 0-02 to 0.05 in alcoholic solutions for each 10 per cent. of active substance. In choosing a value as nearly as possible applicable to all liquids, 0.02 has been allowed in what follows as error under this heading.
5. In determining the concentration c (see $ 73), an error of 0:04 gramme may occur in solutions containing 20 grammes of active substance.
This amount has been taken as a mean. In order approximately to estimate the actual influence of these errors individually on the value obtained for specific rotation, the following examples have been tabulated for substances having unequal rotatory powers in solutions of different degrees of concentration.