hugust, 1960
THERMODYNAMIC FLXCTIONS FOR CALCIUM HYDROXIDE IS WATEK
1057
THE THERllODYSAJIIC FUSCTIOSS FOR THE SOLUTIOS OF CALCIUJI HYDROXIDE IS n',lTER BY S. il. GIZEESBERG ASD L. E. COPELAXI) Portland Cement Assorialion, Skokie, Ill. Hrcszr ed
lfarcii 19, 1960
The solihilit;v-products for calciilm hydroxide ww evaliiated from the, so1ul)ility as :i fiiiictioii of ionic strcJngth, pH MI(I temprrature. From thesc dat,a thc standard thermodynamic fiinctioiw tvcw derived: AF" = - 17.67/27' In 7' -4- 0.078, R T 2 89.0/27', AH0 = 17.67X1' - 0.078/21'*, and LIS" = l7.6iIZ 111 7' - O.l.jGK7' - i1.8K. The lattice cliicrgy of calcium hydroxide is -56% Bcal./mole when calculated by means of thc Born expression. A Horn-Halw r y c l ~g a v ~a value of i 7 kcal./mole for t,he electron affinity of the hydroxyl ion and a heat of hydration of 98 kcal./mole for the ymeous hydroxyl ion. At 25' the solubility product K,, is 9.10 x 10-6.
+
Introduction Alt'hough the chemist,ry of calcium hydroxide is involved in many indust,rial processes aiid is especially important, for an understanding of the nature of fresh concrete, relatively lit8ttlequant8itat8ive information on this subject is available. In this survey a n attempt is made t,o use the literat'ure solubilit,y data to obtain the solubilit'y products. With these data t,he thermodynamic: fuiictioiis for solut,ion were derived. The lnttice energy of the solid cdciuin hydroxide was evaluated from theoretical considl:rnt#ions. Discussion Lattice Energy. - - T i ~ o methods are availahle for calculating the lattice energy Cy(,. Oiie 1' from experimental data niid the ~ e c o n dfrom theoreticd conhideration5 a i developed by Born, Haber aiid lladelung. The lattice eiicrgy of - 562 Icc~ul. mole J\ a i fouiid I\ ith the theoretical Borii expres.iion.?
Cs(r)
S
I
+ Ca(gj + Ca+-(g)
where t,he sublimation eiiergy S is 4T.3 ked.' m ~ l e ~ t'he , ~ ; ionization energy I is 41'2.9 kcal.,' m o w 9 ; aiid the heat' of formatioii of t,wo C>Hradicals is 20.12 kcal. :mole.'" The value for the elect'ron affinity F for OH groups has been estimated t o be between -48 a,nd -88 kcal.:mole.ll.l? For t h e equation Ca(fi)
+ O ? ( g ) + H,(y) = Cti(OH),(r)
(2)
the heat of reaction Q is -235.8 kcal. !mole according to t'he Sational Bureau of Standards value for the heat of format,ion of calcium hydroxide. l o The relat,ionship bet\\-een the terms in the Borii-Haber cycle is (J = S + I + AH1 - 3F + Iii (3I
When it, is assumed that, I T o is -562 aiid 8 ,I niitl AHf have the values given abo\.e, t>heiiF is i'ouiid to be 77 kcal./mole, which is reasonably close t,o thc 88 f 1 value est,iniated by Lederlell and the iti value originally set by Goubeau.'? It was later rewhere S is A\Togudro's number, 6.0228 X ported by Goubeau and RlemmI3 t,o be 48. . l a is t,he Lladeluiig constaiit, 0.2l4,";6 is the cube It is interesting t,o calculate the Ca-OH dist,ance root of t'he molecular volume (i4.10~'2.24I)'':i: e is in calcium hydroxide. The rat'io of t,he -4, Madet8hecharge, 4.802 X 10-lo e.s.u.; and n is the Born lung const8aiitto the equilibrium catioii-anion disconstant' which is 8 for calcium hydroxide according tanre r is equal3 t,o the ratio of t,he A 6 t o 6. Siiiw t,o t,he l'auliiig a p p r o x i m a t i o ~ i . ~In . ~ this cdcula- A, is 4 . i l for the cadmium iodide strucaturr', \\-hic:h tioii second-order effecmt s such as t8hei ~ deri 1V::ials cdvium hydroxide reseiiihlrs. thciio r is 2.4{ A. at,t,rltct'iveforce> aiid the zero-point ei!ergy ai'c iieg- Thi.s is reusoiiably (*loseto the 2.87 A. ('a~-C)iiitcrlect'ed. ,Justification for this pro(*edure hi(,>heeu at,omica distanc*e i i i c A i u m hydroxidc a; rcpurtcd discussed by Shc?rniaii3who dcmoiist,rated that, the hy Husiiig :tiid Levy. I I error involved in most' w s c ~ is iiot, morc t.li:tii t IYO or Thermodynamic Solubility Products I
