0
THE SOLUBILITY PRODUCT: A PROPORTIONALITY CONSTANT JOHN A. BISHOP Newark College of Engineering, Newark, New Jersey
Tm solubility product constant, K,,,
is usually developed in the textbooks on introductory qualitative analysis from the standpoint of equilibrium. Most teachers then run into the fact that students get rather b a e d by the ignoring of the concentration of the solid phase. This disregard for the total amount of solid is always explained properly as being due to the building up of crystals in which the reactive part of the solid is only a t the surface. The author's experience has been that too great a proportion of students still try t o work in the solid phase concentration. For several years the author has tried t o develop the solubility relationships from the graphical approach, since his classes conslst entirely of engineers, who can use this approach later in treatment of data. Starting with AgCl (graph 1in the figure), i t is shown that there will be a certain concentration of Ag in any solution of AgN03 (point A ) . It is then pointed out that the addition of C1- will not result in formation of a precipitate until point B is reached. Repeating the process, starting with a solution of AgN08 half the original concentration, a point C i s obtained which represents a CI- concentration which is not necessarily double the CI- concentration found in the first case. Continuing this process, the curve of graph 1 is obtained. The attention of the class is now called to the fact that the curve is apparently one of the type (xy = constant). If, therefore, [Ag+] is plotted against l/[Cl-1, a straight line should result, as in graph 2 in the figure. Since a straight line has been produced by such a plot, it must he that the correct equation relating the concentration of Ag+ to C1- is
in the formula. From the mathematical standpoint, however, we realize that a doubling of the C1- concentration will only shift the curve to one side, and not straighten it. Raising to a power will be a way of straightening the curve, so a new plot of [Pb++] against l/[Cl-l2 is made and results in the straight line B of graph 3. The equivalence point is the only plare a t whirh [Pb++]is half the [Cl-1. Similar graphical methods are carried out by the student to determine values of K,, for more complex compounds. This leads to the problem of an unknown A.B, to determine values of x and y and K. The students now find out about log-log plots and about log-log paper, about both of which they seem to be ignorant, in spite of being sophomores. From his previous work it now has become apparent to the student that the form of the ion product is set up by simply taking the formula, putting in brackets t o represent concentrations in moles per liter, and "moving the subscripts upstairs." So the correct form of the ion product expression for AXBYbecomes [A+ulr [B-=lu = K Taking logarithms zlogA+u
+ y l ~ g B -=~l o g K
When log A'Y is plotted against log B-* the slope is -y/x. The result of such a plot is shown in graph 4. Since x and y must be small whole numbers for the solubility product expression to apply, it is fairly simple to figure out their values once the ratio is determined. Once this is done, K can easily he determined. Graph 4 is for the compound Sb2S3. [Ag+] [CI-] = 6 The effect of pH on solubility can also be illustrated K is the slope of the line produced in graph 2 , and graphically, as in graph 5, which is for ZnS. Error due can be used t o calculate how much of either of these to low pH can be observed from the graph. ions can exist in the presence of a given amount of the The log-log plot returns with graph 6, when the effect other if the solution is saturated with AgC1. The "if" of varying more than one component shows up. For in the last sentence returns us to graph 1. A saturated engineers such a graph can be used as an important solution of AgCl is represented by the curve of graph 1. precursor to work to be done in later courses. The author has tried to illustrate a slightly different Below the curve there is unsaturation. Above the curve there is supersaturation. Only a t point D (the approach to the presentation of solubilities in salt solutions and the calculations involved in them. He equivalence point) is [Ag+] equal to [Cl-1. If the same procedure is carried out with PbCL, a believes that for engineers this approach has certain adcurve similar in appearance to that of graph 1 is pro- vantages over the traditional one and avoids the traps duced, hut on plotting [Pb++] against l/[Cl-], it is set up by doubling concentrations when the initial found that a straight line does not result (graph 3, approach is from pure salt solutions. Since there are curve A). We now return to.the difference between students who get confused by either method and it is the formulas AgCl and PbC12. From the ionic stand- impossible to remove previous knowledge and start point the difference is in the number of C1- per cation over, teachers cannot be quite sure which is better. 51'4
NOVEMBER. 1954
Graphical Pr-ntation
of the R e k t l o ~ h i p sbetwan A n i o and ~ ation.
1. Variation of silver ion concentration with chloride ion mncentrntion 2. Variation of silver ion eoneentration with the reciprocal of t h e chloride ion concentration 3. Variation of lead ion concentration with the reciprocal of t h e chloride ion concentration 4. Variation of antimony ion Concentration with ~ulfideion conccotr&on using a Log-log graph 5 . Variation of zinc ion concentration with p H in t h e presence of sulfide ion. Semilag graph 6. Interrelationships between [Mgt*1, [POd-aI, and IN&+], log-log scale
