JOURNAL OF CHEMICAL EDUCATION
LECTURE DEMONSTRATIONS1 1.
Flotation
2. Derivation of the Equilibrium Constant W. H. SLABAUGH State College of Washington, Pullman, Washington
FLOTATION
The process of flotation may he demonstrated in a simple but effective manner by the use of.large glass test tubes. Galena, ground in a mortar and pestle to approximately 60 mesh, and a white sand of similar particle size are mixed together to give a synthetic 10% galena ore. A water slurry of this ore containing 25% solids by weight is placed in three 38- X 300-mm. test tubes. Kothing is added to the first tube. To the second and third tube is added 0.1 g. of potassium pentasol xanthate. To the third tube, in addition to the collecting agent, is added one-half drop of pine oil as a frothing agent. I n commercial practice approximately 0.25 Ih. of collector per ton of ore, and 0.06 to 0.1 lb. of frothing agent per ton of ore areqused. The quantities used for a small-scale operation must be altered. The tubes are stoppered and shaken vigorously. They are then placed in a rack, whereupon the effect of the flotation agents may be observed, as noted in the illustration. Only a relatively small amount of the black galena remains suspended in the first and second. tubes, while in the third tube there may be up to 90% of the galena appearing in the froth. I t is best to grind the galena immediately before use on account of its tendency to oxidize and become more or less difficult to separate by flotation. If distilled water is used to make the slurry, it may be necessary to make the system slightly alkaline in order to facilitate the action of the frothing agent. Presented a t the Symposium on Lecture Demonstrations before the Division of Chemical Education at the 115th meeting of The American Chemical Society in San Francisco, March 27April 1, 1949.
Samples of the collector agent are obtainable from the American Cyanamid Company. Other detergent type materials may be substituted for the pine oil. DERIVATION OF THE EQUILIBRIUM CONSTANT BY THE USE OF BLOCKS
On the premise that visualization is a valuable aid in the learning process this demonstration of the derivation of the equilibrium conitant is offered. The basis of the demonstration lies in the conception of the lettered blocks as molecules. These blocks are used in such a manner that the derivation of the equilibrium constant and several of its applications may be made. The argument is based primarily upon the number of opportunities for- chemical reaction which occur when the required molecules collide with each other. The requisite materials include two dozen square blocks of suitable size which are lettered as follows: one half of the blocks are lettered "A" on one face and "C" on the opposite face, the other half are lettered "B" on one face and "D" on the opposite face. Two rectangular blocks of comparable size are inscribed as follows: an arrow is placed on one of the faces of one block and a set of equilibrium arrows is placed on the opposite face. Inscriptions which indicate exothermic and endothermic effects are placed on opposite faces of the other rectangular block. In a simple chemical reaction which requires the collision between two different molecules, blocks are displayed which describe the reaction (Only the forward reaction is considered a t this point.)
AUGUST, 1949
When one "A" block and one "B" block are shown, there is but one possible collision which might produce a chemical reaction. If two "A" blocks are shown, two possible collisions may occur. If two "B" blocks are then shown there may be four possible collisions. Any number of combinations may be shown here which will further verify the conclusion that the number of possible collisions will be the product of the number of "A" blocks and "B" blocks. Thus, in Figure 2 there are six possible collisions. This illustrates the principle of the classical law of mass action.
Since the velocity of the reaction will be proportional to the number of possible collisions, the expression for the speed of the forward reaction is derived: SL= k, X [A]X [Bl By manipulation of the blocks, the value of kl may be shown to consist of several factors such as temperature (kinetic properties of the molecules), molecular orientation (particularly in the case of organic molecules wherein the active centers of the molecules must be involved in the collision), and catalysis (role of the surface in bringing about molecular orientation). When a collision between "A" and "B" blocks results in a chemical reaction, the blocks are moved to the right and their reverse faces shown, thus illustrating the reaction: A+B-C+D
If the reaction is reversible C and D molecules may collide to produce A and B again. 'This leads into the relationship : SX = k? X [C] X
[Dl
At first the number of opportunities for C and D collisions is small, but as more blocks are moved from left to right there will be more possible collisions. Eventually, the number of C and D molecules which react in a given time will become equal to the number of A and B molecules which react in the same time. A typical system in equilibrium is shown in Figure 3. Since Sl equals Sa a t equilibrium, the equilibrium constant for the reversible reaction may be derived:
These blocks may be used to explain the appearance of exponents in the equilibrium constant expression for those reactions which require the effective collision of two or more molecules of one substance with each other or with one or more molecules of another substance. In a simple case of this nature a reaction which requires two molecules of A and one of B is considered: "A" blocks and "B" blocks are displayed which represent this reaction. With one' "B" block, two "A" blocks are required in order to provide one possible collision. If three "A" blocks are present there are
Figure 3
The numerical value of the eauilibrium constant may now three possible combinations by which two "A" and one "B" block may collide. Four "A" be calculated for the systemas it appears in ~ i ~ u r blocks e 3. Thus, blocks and a "B" block offer six possible collisions. Using more and more blocks, each time observing the number of possible combinations, it is finally concluded
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that the number of possible collisions can be related by the exmession:
a
temperatwe of the system is increased the effectis that of adding heat. This increases the quantity of heat rig"re4 which can apparently combine with C and D to produce A and B, and the equilibrium point is shifted toward the left. In a similar fashion the blocks can be used to show the number of blocks becomes large, as do the number the effect of temperature changes upon an endothermic of molecules involved in a chemical reaction, it can be reaction, shown that [A] X [*'ll approaches [A]'. Thus, the The blocks are also useful in showing the effect of speed of the reaction is shown to be proportional to the pressuR on a gaseous reaction. A number of number of collisions: "A" blocks and "B" blocks are placed in a prescribed area on the lecture table. Assuming the reaction to be ,S, = kl x [A]' x [Bl of the nature A B -t , the number of possible colliIn a similar manner, the appearance of higher ex- sions is noted, Then by reducing the area it is obponents in the equilibrium constant expression can be served that the blocks will collide with each other more verified. Thus, when three molecules of one substance frequently, so that in a given timethere will be a greater are required for a as in 3A + --*, number of possible collisions than previously, resulting the number of possible collisions is found to be: in an increase in the speed of the reaction. The blocks may also be used to illustrate the shift in [A1 X [A - 11 X [A - 21 31 the eauilibrium mint when the concentrations of reUpon increasing the number of blocks it is seen that this actanis and/or Goducts are varied. Thus, if a certain number approaches [AI3/3!and the speed of this reac- product is a precipitate or a gas, it becomes removed from the seat of the reaction. The number of possible t,ion becomes: collisions becomes reduced, thereby decreasing the SL= k, X [AIa X [B] speed of the reverse reaction. Illustration of the solubility product constant, the The exothermic and endothermic blocks are used to illustrate the LeChatelier principle. In an exothermic ionization constant, the distribution coefficient, and energy of activation-may also be made with the blocks. reaction, In the general field of chemical equilibrium the use of these blocks is limited only by the imagination of the the heat is considered as a "product" (Figure 5). If the instructor. lz?l
+
