LIMITATIONS OF THE MASS LAW
BY WILDER D. BAXCROFT
Nernstl and Luther” have shown that the dissociation of a compound in solution can be deduced from the dissociation in the vapor provided Henry’s law holds for the compound and its dissociation products. If we have a compound AB dissociating into A and B, let cr, c, and c3 be the concentrations of AB, A and B in the vapor phase and let c,’, c2’, c3’ be the corresponding concentrations i n the solution phase, the solvent being one in wliich no polymerization occurs. If the solubility relations of AB, A and R are given by the equations
(11
c, = k,c,’,
c, = k2Czr,
c, = k&;,
and if the equation for equilibrium in the vapor phase is (2)
Kc, = CJ,,
the equation for equilibrium in the solution phase will be (3)
This would seem to show that a solvent has no effect on the form of the equilibrium equation so long as it does not change the molecular weights of the reacticg substnnces and does not form compounds with them. There is one assumption, made explicitly by Nernst and by Luther, which does not hold in all cases. They have assumed Dalton’s law : that each substance in the vapor phase is absorbed proportionally to its partiai pressure and independently of the nature of the other absorbed substances. In many cases this is not true. T h e presence of benzene i n alcohol or acetone decreases the absorption of water and vice versa. Salicylic acid precipitates water from aqueous acetone at 0’. In other words, the solubility coefficient varies Zeit. phys. Chem. 6,36 (1896) ; 8, I I O (1897) ; Ibid. 26, 317 (1898).
28,
457 (1901).
Limitations of the Mass Law
191
with the nature and concentration of the other substances present. We will therefore take up the case where the relations c, = k2c2’ and c3 -- k 3 c3 hold for A and B by theniselves but not for A and B together. Ignoring any disturbing effect 011 the conipound we shall have
‘
(4)
c1 =R,c,‘,
c,=K,c,%(c,’),
c3 = k,c,%(c,’).
T h e equation for equilibrium in the solution phasd becoities
In a case of this sort, the equilibrium would not be represented by the usual equation and the experimental data might be more accurately reproduced by an equation with fractional exponents. Chloral hydrate is a case where the dissociation products, chloral and water, are only partially miscible and the change of the dissociation with the concentration in acetone solution, for instance, must be different from that of the dissociation of aniline acetate. We are not limited to a case where the dissociation products precipitate one another. Take the case of chloral hydrate in chloroform solution. Since water is very sparingly soluble in chloroform, the partial pressure of water vapor will vary with the amount of undissociated chloral hydrate present and this will introduce a special complication, We see therefore that even i n cases where the molecular weight of each reacting substance is constant and where Henry’s law holds absolutely for each reacting substance taken singly, the orthodox mass law equation will not apply in the solution if any one of the reacting substances influences the partial pressure of any of the other reacting substances either’ positively or negatively. In the cases where Dalton’s law may be assumed to hold, the effect dne to the nature of the solvent will be seen in the change of the equilibrium constant, the more soluble system increasing at the expense of the othef. This seems at first sight to be contradicted by the fact that a reaction runs practically to an end in the other direction when one of the reacting substances
192
Limitatiom of the Mass Law
is practically insoluble. This apparent discrepancy is due to the introduction of a new phase. Let the equation for the dissociation of the compound AB in a given solvent be (6) Kc,‘ = c5)c6)) and then let us change to a solvent in which the solubilities of A and B are unchanged, but it] which AB is I/D times as soluble. We shall then have,. if the solution remains unsaturated, (7)
KDc,” = c5)’cc.
If we let y be the amount of AB which has changed over into the dissociation products, we may write the last equation
+
+
KWc,’ - r>=; (c5) r)(c6) Y). If the solution in the first solvent had been saturated with respect to AB, we should have written equations 7 and 8 as follows : (8)
KC,‘ = c,’c,’
(9)
=H
KDc,’’ == ~5)’c;’ = H,
(10)
where H is a constant. If we let x be the amount of AB which has precipitated and y , as before, the amount which has changed into the dissociation products, equation (IO) becomes (11)
K D ( c , ’ - ~ - - y ) = ( ~ j ’ $ ~ ) ( ~ g l $ y )= H .
A comparison of equations g and 11 shows that they can hold simultaneously only when y is zero. In other words, there will be increased formation of the dissociation products when the solution is first unsaturated and no increase when it is saturated with respect to the compound. T h e tendency to form the more soluble system is therefore consistent with Berthollet’s law. Cornell Universily
