A sugar laboratory should be provided with three balances of the follow- ing general types—
(1) An analytical balance for accurate work;
(2) A sampling balance for work of moderate accuracy;
(3) A balance of higher capacity for coarse weighing of large masses.
The Analytical Balance
This balance is required for all analytical purposes, for determination of specific rotations, for calibration of small items of volumetric glassware,
Fig. 30—-A modern single pan constant load balance (Sartorius).
52 T H E BALANCE
for the weighing of pycnometers and all other operations where precision weighing is required. It should have a capacity of at least 160 grammes and a sensitivity reciprocal of 0.1 rnilligramme per scale division or less. The great majority of balances of this class utilise the two knife edge, constant load principle, employing built in weights, critical damping of the swing of the beam and an optical projection system for reading the beam deflection. A modern balance of this type is shown in Fig. 30 while the diagrammatic representation in Fig. 31 shows the components.
Fig. 31—Diagrammatic representation of a single pan constant load balance (Sartorius).
The sensitivity of a balance is defined as the deflection produced by the addition of unit mass to the pan and is usually expressed in divisions per milligramme. The more useful term sensitivity reciprocal, S.R., is the mass which must be added to the pan to change the reading by one scale division.
The value of the sensitivity depends on the position of the centre of gravity of the moving system in relation to the axis of rotation of the beam. For stability, the centre of gravity of the beam must lie below the axis but the smaller the separation the more sensitive the balance becomes. In a three knife edge equal arm balance the sensitivity varies with the load being weighed unless the three knife edges are accurately co-planar. The two knife edge balances, in which weighing is made by substitution, operate at constant load and the sensitivity remains constant irrespective of the value of the load being weighed.
A small weight moving on a vertical screw fixed to the beam is provided to vary the vertical distance of the centre of gravity from the main knife and hence the sensitivity of the balance. A constant load balance having a sensitivity reciprocal of 0.1 mg per division should be adjusted so that the error in reading at the full deflection of the beam is less than 0.2 mg. A three knife edge balance should be adjusted, with half full load in each pan, to the same order of accuracy.
1 Compensating stirrup 2 Front knife edge 3 Pan brake 4 Weight carriage 5 Built-in weights 6 Pan
7 Weight control mechanism 8 Recording disc 9 Projecting scale 10 Micrometer mirror 11 Weight shaft 12 Arrestment shaft 14 Bulb 15 Arrestment 16 Objective regulator 17 Scale and objective 19 Damping 19 Sensitivity adjustment 20 Zero adjustment 21 Beam 22 Center bearing plate 23 Center knife edge
T H E BALANCE 53 In all balances provision is made for poising the beam and adjusting
the zero reading by means of poising nuts carried on horizontal screwed rods parallel with the beam. In all balances with optical projection reading, fine adjustment of the zero is made by moving the reading index of the balance.
All precision balances are equipped with an arresting mechanism which supports the pans, stirrups and beam of the balance, so protecting the knife edges and bearings from damage when the pan or pans are loaded and un- loaded. When loading has been completed and the case closed the balance is released and the pan, stirrup and beam are released, preferably in t h a t order.
W e i g h t s : The majority of modern balances have the weights built in to the balance, the weights being applied and removed by the manipulation of controls external to the case. Balances of the older type require to be used in conjunction with a set of standard weights.
Irrespective of which type of weights is used they must conform with certain basic requirements. To ensure both long and short term stability the weight must be constructed in one piece from a hard inoxidisable material, the surface must be smooth and free from sharp edges and the material must be non-magnetic. These requirements are met by well made weights of non- magnetic stainless steel containing approximately 2 5 % chromium, 20%
nickel, which has a density between 7.8 and 8.0 g c m- 3a t 20°C. Weights of this material are far superior to those of brass, either plain or with a protective plating of gold, chromium or any other material.
It is customary for precision weights to be adjusted to their nominal value on the assumption that they are all of uniform density—8.0 g cm- 3. That is, the weights are adjusted to balance a standard weight of true nominal mass and of density 8.0 g c m- 3 when in air of density 0.0012 g cm- 3. This practice is followed by N.S.L. Australia, and by most national standard- izing laboratories.
It follows from this that in weighing of the highest precision, where air buoyancy corrections must be applied, they should be calculated on the basis that the density of the weights is 8.0g cm~3 and using the actual value of the density of the air in the balance case.
Weights must never under any circumstances be touched with the fingers. They should be manipulated only with plastic-tipped or chamois covered forceps.
Setting up the Balance: In the case of a new balance it is most desirable if possible to have the balance set up and adjusted by the maker's re- presentative.
The balance must be set up on a firm bench, free from vibration and in a room in which the temperature is reasonably constant or varies only slowly during the day. A good criterion for an acceptable level of vibration is the appearance of the image of the optical scale. This should, of course, be focus- sed until the lines appear quite sharp, and the balance then released. The appearance of the lines is closely observed and any slight blurring is a good indication of the presence of excessive vibration. If this occurs, steps should be taken to isolate the balance from the bench by means of anti-vibration mountings.
The balance should be placed on the bench and the inside of the case thoroughly cleaned. The case should be levelled using the circular level bubble or plumb bob provided and the rest point adjusted to zero. The sensitivity should be adjusted to its nominal value by placing on the pans a weight which should give full scale deflection of the reading index.
54 T H E BALANCE
After these adjustments have been made the balance case should be closed and (he balance left to stand for at least one hour to settle down.
After this period the zero reading and sensitivity should be re-checked and any further minor adjustments made if required.
General Precautions in Weighing
Objects should never be weighed until they have attained the temper- ature of the balance case. Hot bodies should never be placed on the balance case but should be allowed to cool, preferably in a desiccator, until they are approximately at ambient temperature. The time taken by a body to cool to room temperature depends on its initial temperature, its size, and the material from which it is made.
Hygroscopic materials can only be weighed when contained in an air- tight vessel. Under no circumstances should any chemical come into contact with the scale pan. All material to be weighed should be placed in a clean dry tared container of suitable material such as platinum, glass, aluminium etc. In the case of non-hygroscopic crystals a piece of clean dry paper may be used.
Method of Weighing: The operator must first make sure that the pan and the interior of the weighing compartment are clean.
The operation of weighing with a direct reading balance with weight loading facility is very simple. With the weight selector dials set to zero, release the balance, and when the image comes to rest adjust the balance to read zero. Arrest the balance. Place the object to be weighed on the balance pan, and close the balance case. Select a weight which is judged to be close in value to the mass of the object being weighed. Release the balance and note whether the object is heavier or lighter than the weight selected. Arrest the balance and select the appropriate greater or smaller weight and read again. Repeat the process until a reading on the scale is obtained. Allow the beam to come completely to rest and read the weight of the body.
Some balances of this type have a partially released position of the beam in which it is possible to change the dial settings and watch the change in scale reading without having to arrest the beam between settings.
In making weighings with an equal arm three knife edge balance the following procedure is observed. The pans are wiped with a small camel-hair brush, the case is closed, and the beam is carefully released. The pointer will now swing slowiy over the scale, and when the amplitude has fallen to about five scale divisions, the readings of the extremities of the swing are taken for five successive swings. Care should be taken to avoid parallax in the readings.
It is best to number the scale continuously from left to right rather than to call the centre division O and those to the right positive and to the left negative. Suppose the central point to be numbered 10, and that the following numbers represent observations: —
THE BALANCE
The beam is then arrested, taking care that this is done when the pointer is at the centre of the scale, so as to avoid damaging the knife-edges.
The object to be weighed should be removed from a desiccator in which it has been placed in order that it may be free from moisture, and at the same temperature as the balance. The object is placed on the left-hand pan. A large weight should then be put on the right-hand pan, and the beam released just sufficiently to determine the direction in which the beam will move. The beam is again arrested and a larger or smaller weight applied as required. Each weight is tried in turn until equilibrium has been obtained as closely as possible. The balance case is then closed, and the further adjustments made by means of the rider.
It is not necessary to adjust the weight so that the resting point is identical with that initially found, provided the precise sensitivity of the balance is known. Suppose the following turning-points were determined with a mass of 21.682 g on the right hand pan:—
Right
Mean 9.53 12.05
The weight is, therefore, insufficient and should be increased by an amount which would change the resting point by 10.79-10.03 or 0.76 division. If, from a previous determination, it has been found that the sensitivity at 20 g load is 4.0 scale divisions per mg the correction to be added is:—-
It will be observed that the average of the last left-hand and the last right-hand swing of the balance gives a result which would be indistinguish- able on the scale from the true resting point. A skilled operator makes use of this fact to determine when the correct mass is on the scale pan. By a careful release of the mechanism he may confine the first deflection to one or two divisions and observe if the next two are at equal distances from the centre of the scale.
Testing a Precision Balance
The essential attributes of any precision balance are:—
(1) The reading of the balance must be consistent for any given condition of loading.
(2) The balance must give weighings which are closely reproducible.
In the case of balances fitted with optical projection reading and inbuilt weights the following are additional requirements.
(3) The sensitivity must be close to its nominal value and must be constant over the full range of the scale.
56 T H E BALANCE
(4) T h e e r r o r i n a n y w e i g h t o r c o m b i n a t i o n o f w e i g h t s s h o u l d n o t e x c e e d t h e c o r r e s p o n d i n g Class A t o l e r a n c e specified b y t h e N a t i o n a l S t a n d a r d L a b o r a t o r y .
(5) I n t h e c a s e o f t w o p a n t h r e e k n i f e e d g e b a l a n c e s t h e effective l e n g t h s o f t h e b a l a n c e a r m s s h o u l d b e e q u a l t o w i t h i n 1 0 p a r t s i n a m i l l i o n . Methods of Test: (1) T h e g e n e r a l c o n d i t i o n of a b a l a n c e c a n n o t be c h e c k e d q u a n t i t a t i v e l y b u t a n i n s p e c t i o n s h o u l d s e r v e t o c h e c k t h e f o l l o w i n g p o i n t s . T h e b a l a n c e s h o u l d b e c l e a n a n d all p a r t s s h o u l d b e free f r o m c o r r o s i o n . T h e a r r e s t m e n t s h o u l d o p e r a t e s m o o t h l y a n d s h o u l d n o t c a u s e a n y u n - w a n t e d m o t i o n o f t h e p o i n t e r o r p a n s .
M a n i p u l a t i o n o f t h e b u i l t i n w e i g h t s s h o u l d n o t c a u s e a n y s i g n i f i c a n t j o l t i n g o r s w i n g o f t h e p a n .
(2) R e p r o d u c i b i l i t y o f r e a d i n g s . T h i s i s c h e c k e d b y t a k i n g t w e n t y c o n - s e c u t i v e r e s t p o i n t r e a d i n g s , t h e b a l a n c e c a s e b e i n g k e p t closed a n d t h e b a l a n c e a r r e s t e d b e t w e e n e a c h r e a d i n g .
T w o c r i t e r i a of s t a b i l i t y a r e u s e d :
(a) T h e m a x i m u m difference b e t w e e n a n y t w o c o n s e c u t i v e r e s t p o i n t s a n d (b) T h e s t a n d a r d d e v i a t i o n o f t h e r e s t p o i n t s .
(a) i s a m e a s u r e o f e r r a t i c v a r i a t i o n i n t h e r e s t p o i n t a n d (b) g i v e s a m e a s u r e of d r i f t or slow c h a n g e in t h e r e s t p o i n t . I f S i s t h e a c c u r a c y o f e s t i m a t i o n o f t h e r e a d i n g e i t h e r b y v e r n i e r o r b y v i s u a l e s t i m a t i o n , b o t h c r i t e r i a (a) a n d (b) s h o u l d be less t h a n 2 8 for a g o o d b a l a n c e .
(3) T h e s e n s i t i v i t y o f t h e b a l a n c e i s m e a s u r e d b y s e t t i n g t h e o p t i c a l scale t o z e r o a n d t h e n a d d i n g t o t h e p a n a w e i g h t e q u i v a l e n t t o t h e m a x i m u m deflection of t h e scale. T h e d e p a r t u r e of t h e full s c a l e deflection f r o m i t s n o m i n a l v a l u e s h o u l d n o t e x c e e d 2 S in t h e c a s e of a c o n s t a n t l o a d b a l a n c e a n d 1 0 8 i n t h e c a s e o f t h r e e knife e d g e b a l a n c e s w i t h o p t i c a l p r o j e c t i o n .
(4) T h e l i n e a r i t y o f r e s p o n s e o f t h e b a l a n c e i s t e s t e d b y u s i n g s u c c e s s i v e
r a n g e of t h e scale.
(5) T h e t e s t i n g of t h e a c c u r a c y of t h e i n d i v i d u a l w e i g h t s is a m o s t i n - v o l v e d p r o c e s s b u t a n i n d i c a t i o n o f t h e p r e s e n c e o f a n y g r o s s e r r o r s c a n b e o b t a i n e d b y c h e c k i n g t h e s u m o f v a r i o u s g r o u p s o f w e i g h t s a g a i n s t a p p r o p - r i a t e s t a n d a r d s . F o r e x a m p l e i f a b a l a n c e h a s a n o p t i c a l r a n g e o f 0 . 1 0 0 g r a m m e a n d g r o u p s o f w e i g h t s
0, 0 . 1 - 0 . 9 g 0, 1 - 9 g 0, 1 0 - 9 0 g c h e c k 0.9 + scale a g a i n s t 1 g
9.9 + scale a g a i n s t 10 g 99.9 + scale a g a i n s t 100 g
A m e t h o d of c a l i b r a t i o n of i n b u i l t w e i g h t s , u s i n g all a v a i l a b l e d a t a , h a s b e e n d e s c r i b e d ( H u m p h r i e s , 1961), w h i c h y i e l d s self c o n s i s t e n t r e s u l t s o f a n a c c u r a c y c o m p a r a b l e w i t h t h e d i s c r i m i n a t i o n o f t h e b a l a n c e .
T H E BALANCE 57 Balance for Coarse Weighing
For general approximate work at heavier loads a speedier balance of more robust construction is used. A balance having a maximum load of 3 or 4 kilogrammes and a discrimination of 0.1 gramme is suitable for this purpose.
Single pan balances with optical scale and taring facility are available and they are very suitable for this purpose.
Although these balances are robust they should nevertheless be kept clean and their accuracy periodically checked with known weights.
REFERENCE
H u m p h r i e s , J. W. (1961). The calibration of the weights built into a balance.
Aust. Jour, of Ap. Sci. 2, 3, 360
CHAPTER IV
By reference to tables showing the density of water at various tempera- tures it is possible to derive a factor for the conversion of specific gravities based on water at 4 °C to values based on water at some other selected temperature, e.g., s.g. 20 °C.
The relationship between two masses is correctly expressed by the ratio of their weights in vacuo. When a weighing operation is conducted under normal laboratory conditions, the buoyant effect of the atmosphere is exerted on both the sample and the weights, and as these usually differ in volume, the resultant force creates a difference between the weight of the sample in air and its weight in vacuo. A weight "in air, with brass weights" is con-
*This follows from the old definition of the millilitre, i.e., the volume occupied by 1 g of water at the temperature of its maximum density.
DENSIMETRIC METHODS OF ANALYSIS
The quantity of mass in unit volume of a substance is known as the density of that substance, and is expressed in such units as grammes per milli- litre, or pounds per cubic foot. Mathematically where d is the dens- ity, m the mass and v the volume of the substance. The volume of a given mass may, and almost invariably does, vary with temperature and pressure.
For liquids and solids the change of volume with temperature is quite significant, but the effect of variation in pressure is usually negligible, so t h a t it suffices to specify the temperature to which any statement of density is related.
At any given place the mass of any body is proportional to its weight in vacuo. The ratio of the masses (weights in vacuo) of equal volumes of a substance and some standard material is known as the relative density of the substance. Customarily, when the standard material is water, the ratio is known as specific gravity, so that specific gravity (s.g.) may be defined as a number which indicates how much heavier or lighter a material is than water.
The derivation of specific gravity involves two densities each of which must be qualified by a temperature and so the ratio
are numerically the same.
ts in g per ml and its specific gravity
Since one ml of pure water at 4 °C (the temperature at which the density of water is a maximum) weighs one gramme in vacuo* and thus has a density of 1 g per ml, the temperature of 4 °C is frequently adopted as a basis for expression of specific gravities. It follows that the density of a substance at
are usually quoted as s.g
For convenience it is customary to adopt a standard temperature for which the density of the test material is specified. In the Queensland sugar industry the accepted standard temperature is 20 °C and specific gravities
DENSIMETRIC METHODS OF ANALYSIS
vertible to the weight in vacuo if the density of the test sample is known.
Hence, densities and specific gravities may be expressed in terms of weight in air with brass weights, and as most weighings are conducted under these conditions, tables of density on this basis have great practical value. Great care should be taken to avoid confusion between density figures based on weight in vacuo and those based on weight in air with brass weights.
The determination of specific gravity is one of considerable importance in sugar analyses. This is due to the interesting fact that solutions of different sugars of equal concentrations have almost identical specific gravities. The following values for 10 per cent solutions of nine distinct sugars illustrate this fact:—
Further, the mean value for all sugars approximates closely to that for sucrose. It is possible, therefore, to determine very closely the percentage of dissolved substance in any solution of sugar or mixture of sugars simply by determining its specific gravity.
While the application of specific gravity tables established for sucrose may be applied with reasonable accuracy for the estimation of dissolved substance in a solution of mixed sugars, this is not the case where other dissolved substances are present. The errors resulting from this cause are at times very great as, for example, with final molasses. The influence of the salts present in such a solution may be gauged from the following data showing the concentration of solutions of sodium-potassium tartrate and potassium carbonate in comparison with sucrose solutions of equal specific gravity.
When the specific gravity of such solutions is determined after dilution with water, the error is still further intensified, owing to the difference in contraction between sugar and dissolved impurities in aqueous solution, as is seen from the above table. Concentrations determined by this method for other than pure sugar solutions must, therefore, be regarded as rough estimates only.
60 DENSIMETRIC METHODS OF ANALYSIS The Pycnometer
A highly accurate instrument for the determination of specific gravity is the pycnometer or specific gravity bottle (Fig. 32).
Fig. 32—Illustrating the types of pycnometer in use in Queensland.
It is simply a glass vessel which is designed to contain an accurately reproducible volume of liquid at any particular temperature. The best pycnometers are vacuum jacketed for thermal insulation, and are fitted with a thermometer. By weighing the bottle filled first with water and then the given solution at constant tempeiature the weights of equal volumes of the two fluids may be determined, and hence the specific gravity of the test solution.
The pycnometer is mainly used in the sugar mill laboratory for the determination of the Brix of dilute sugar solutions extracted in the analysis of cane or bagasse.
To Determine the Volume of the Pycnometer at a Standard Temperature.—This determination has little practical use, but serves to describe the technique and develop the theory. The bottle is thoroughly cleansed, using in turn glass cleaning solution, water and alcohol. It is then dried in a stream of dry air and weighed. It is next filled with distilled water which has recently been boiled to expel dissolved air and cooled to 2 to 3 °C above ambient temperature. The stopper is inserted*, care being taken to prevent the introduction of air bubbles, and the excess water is carefully removed by means of a filter paper (from the stopper and also from the capillary in the side-arm type).
*The temperature of the water must be determined at the instant the stopper is fully inserted. Where a thermometer is incorporated in the stopper, the stopper is lightly set in place and the thermometer allowed to come to reading; where a stopper only is provided, a thermometer is inserted first, read and withdrawn. The stopper is inserted immediately.