T.
HE teaching of heat effects accompanying solution is generally confined to a very short time during the first c o m e in physical chemistry. As a result students generally do not obtain a feeling for the principles involved nor do they see any connection with the usual ideas associated with the heats of chemical reaction. I n an effort to give the matter greater clarity, the following approach has bten used.hy the author. He believes the method to be novel, although i t is implied in some discussions of the material. It might well he, since correct discussions must have a common basis in the fundamental law of Hess. A concept necessary to this approach is that of the "mol-unit of solution." This quantity is defined as that amount of solution containing one mol of the active or significant ingredient. Thus when one mol of sulfuric acid is mixed with 20 mols of water, the resulting quantity of solution is a mol-unit of that particular solution. If, however, the same concentration is prepared by mixing one-half mol of the acid with ten mols of water, the resulting quantity is one-half of a mol-unit of the same kind of solution. A further designation is necessary in order to identify completely the solution, since the term "mol-unit" defines quantity but not concentration. Mol-fraction or some other designation might be used without difficulty. The advantage of adopting this concept lies in that the integral heat of solution1 may then he used i n a manner similar to that using heats of formation. The integral heat of solution may in fact then be considered the heat of formation of the solution with respect to the pure components. For the formation of one mol-unit of a solution containing two mols of water per rnol of sulfuric acid, we may write an equation, H&Oa
+ 2H.O
-
+ 2HaO);
(H2S04
-
+ 4Hn0
2(H2S04
WILLIAM S . HORTON Indiana University, Bloomington, Indiana
In this example the convenience of the subscript notation on the AH'S becomes evident as well as the analogy to the use of the more usual heats of formation. The heat of a reaction is equal to the sum of heats of formation for the products minus that sum for the reactants. Integral heats of solution may now be substituted for heats of reaction when the "reaction" is of the type here considered, and AH = AH4 - AH, AH = -12.300 - (-9400) = -2900 cal.
Note that the two mols of water on the left of the arrow have no heat of solution in this regard since they represent one of the pure components, corresponding to elements in standard states for the analogous case of heats of formation. That the equation written for the AH of the reaction is correct can be seen by application of the law of Hess. Thus,
whence, by subtraction is obtained.
AH* = -9400 cal
where the parentheses enclose the components of the solution formed. The subscript on the A H refers to the fact that the heat change quoted is the integral heat of solution for a mol-unit containing two+mols of water. The convenience of this notation will become evident in the examples to be given. Wben the idea herein explained is once grasped, a good many dilution, solution, and mixing heats may he computed with ease. A few examples are offered below. 1 . The heat effect of dissolving two mols of sulfuric acid in four mols of water. 2H801
On Heats of Solution
+ 2&0) ; AH = 2 AH* =
- 18,800cal.
Notice that this is just the formation of two mol-units of the same solution as used in the introductory example. As such, the heat effect must be twice that of theformer. 2. The heat effect of mixing two mols of water with a solution containing one mol of sulfuric acid and two mols of water. LEWIS.G . N., AND M. RANDALL, "Themdynamics," Mc-
Graw-Hill Book Company, Inc., New York, 1923, p. 89.
-
3. The heat effect of mixing two different solutions. (Ha01
+ 2H20) + (HISOI + 4H10)
AH = 2AH3 - AH4 - AH2 AH.=2(-11,700)
+
~ ( H ~ S O I 3H20)
- (-12,300) - (-9400)
= -700 cal.
In this kind of problem the analogy to heats of formation is quite obvious. 4. Heat effect due to solution when a chemical reaction is being considered. (HdOl
+ 6H.O) + 2(NaOH + 6 g 0 )
+
(Na&O,
+ 20AHHnO); = ?
The heat effect here can he computed in two parts, that for the reaction and that for solution. The heat effect for the reaction is computed from the usual heats of formation of the pure compounds,i. e., for HnSOl
+ 2NaOH
-
NadO' f 2H20; AH1
the beat effect involving solution can be computed as AH,, = AH, (NarSOS
-
AHdHnSO,)
- 2~HdNa0H)
where now parentheses have been used to enclose the formula of the compound whose integral heat of solution is being - indicated. The heat effect of the original reaction is now 393
A H = AH1
+ AHu
A similar method is used if water is one of the reactants rather than one of the products. This latter type of example may be checked by recourse to the law of Hess as previously indicated for a simpler example.
It is believed that this method, when mastered, leads to greater facility in computing heat effects in solution. Introduction to the method should not prove too dicult if i t is undertaken immediately after treating the usual heats of formation.
