Vol. 73
J. REX GOATES,ARTHURG. COLEAND EARLL. GRAY
3596
[CONTRIBUTION FROM THE DEPARTMENT O F CHEMISTRY O F BRIGHMIYOUNG UNIVERSITY1
Free Energy of Formation and Solubility Product Constant of Mercuric Sulfide BY J. REX GOATES,ARTHURG. COLEAND EARLL. GRAY
'1
I 1
+
HzS
1 (o.l
1
i
HCl molal) (o,l molal) Hz* Pt and Hg, HgS S' normal calomel, values of the standard free energy change of the reactions Hg(1) HS(g) (1 atm.) HgS(s) Hp(g) and Hg(1) S'(aq) & HgS(s) 2e have been determined. From these values the standard free energy of formation and solubility product constant of HgS (black) at 25' are calculated to be -10.22 kcal./mole and 9 X lo-", respectively. By means of electromotive force measurements on cells of the types Hg, HgS (1
+
+
+
The two most generally accepted values for the ard free energy change of the half cell reaction calcusolubility product constant of the black form of HgS lated from the relationship AFO = -nSE?, using are 3 X and 3 X The former was re- the value of 23,063 cal. abs. v.-l g. equiv.-l for the ported by Kolthoff, who had recalculated electro- faraday is -2.33 kcal. This value together with ~ in - 10.22 chemical data reported by Knox2 (1906); the lat- the value of -7.8926for A F ~ " Hresults ter was calculated by L a t h e r 3 (1938) from heat of kcal. for AFfoRgsa t 25". formation and entropy data. The discrepancy of Cell type II was these values, which represent the most reasonable Hg, HgS IS"I/normal calomel data from the very meager information on the soluthe sulfide half cell reaction for which is bility product constant of mercuric sulfide, made further investigation of this subject desirable. Hg(0 S'(aq) HgS(s) 2e The method used in the study reported in this This cell will not give results as accurate-as the paper was to measure the standard free energy of formation of HgS (AFfoH,s) and calculate the solu- cell previously described because of the uncertainty bility product constant from the free energy data. of the assumption of complete elimination of liquid Values of AFj'"*s were obtained from electromo- junction potential by a saturated KC1 salt bridge. tive force measurements on two types of cells which However, within the limits of the accuracy of this had proved successful in a similar study with AgzS. assumption, the results obtained with this cell can act as a check on the results of cell type I. The Cell type I was study of Bjerrum and Unmack,6 shows that the error involved in the above assumption may be as high as 1-2 millivolts. A 2 millivolt error in the the over-all reaction for which is value of E results in slightly less than a 1% error in the value of AFfoH,s. HzS(g) HgS(s) Hdg) The liquid junctions with the KC1 solution were The Nernst equation for the cell reaction is formed inside a glass tube 4 mm. in diameter, The reproducibility of the junctions as determined by E = Eo - ( R T / n S )In [ ( e H g S ~ H n ) / ( a H g . f H n S ) l measuring the electromotive force of each Hg, Calculations of the fugacity of H2 and H a gases at HgS, S- half cell against two different calomel half one atmosphere pressure by means of the Berthelot cells was good to within 0.3 millivolt. equation of state show the value of h(fHl/fH&) to The free energy of formation of HgS was obbe negligible. Since the other substances involved tained from measurements of the electromotive in the reaction are in their standard states, the force of cell type I1 through the relationship measured electromotive force was taken as the A F ~ O H ~=S AF~OHS- - n3E RTln (uas-.&~-/K,) (1) standard electromotive force. Experimental.-The Hg, HgS electrodes were very simply in which E refers to the electromotive force of the prepared by making gas outlet holes one cm. from the bot- Hg, HgS, S" half cell, UHS- and UOH- refer to the tom of 1.6 X 13 cm. glass tubes sealed at the lower end. activities of the HS- and OH- ions in the solution The one cm. of the tubes below the holes was filled with mercury and the tubes immersed in the electrolyte of the of Na2S used as the electrolyte of the half cell, and cell. H2S gas was led into the cell through side arms in the K, is the ion product of water, 1.008 X electrode tubes and bubbled gently over the surface of the This equation is derived from the following reaHg, which formed a black coating within a few minutes soning: The standard free energy change of the after contact with the gas. The mercury used was triply distilled reagent grade. The remainder of the experimeiital Hg, HgS, S' half cell reaction is
+
+
+
+
+
details is the same as was used in the study of AgzS
Results.--The arithmetical mean of the standard electromotive force of a total of 12 cells at 2 acid concentrations (0.1 and 0.5 N HC1) was 0.0504 absolute volt, with average deviation from the mean of IO.0009 volt. The value of the stand(1) I. M. Kolthoff, J . Phys Chcm , 35, 2711 (1931). (2) J. Knoy, 2. Elckt~ochcnz, la, 366 (1906). (3) Fc'. M. Lsttmer, "Oxidation Potentials," Prentice-Hall Corp ,
New York, N Y , 1938. (4) J Rex Godtes, Arthur C> Cole, bat1 I. Gray and Neal D Faux, THISJOURNAL, 73, 707 (19Sli
AF" = AI?foirgg
-
A F f o ~ -= n i E o
(2)
The Nernst equation for tlie same reaction is E = I:"
-+- (Kl',/tt.s)In u.J-
(3)
Solving for Eo in ( 3 ) arid substituting into ( 2 ) gives .
A F f o ~ ~ s- A q " s - = -USE
+KT
111 US-
(4)
--_I___
( 5 ) F. D. Rossini, I).I). \Vagnian. \V, H. Evans, S. Levine and I. Jaffe, Nall. BUY.Stnizdardi C i r c . 300, U.S. Government Printing Office, Washington, 1950. (6) Bjerrum and Uiirrlack, K g l . Uanikc. Vid. Sclsk. Mat. P y s . M c d . , 9, 1 (1929).
Aug., 1951
FREEENERGY OF FORMATION AND SOLUBILITY CONSTANT OF MERCURIC SULFIDE 3597
value of 3.5 X for K i . This figure was calculated from the values of the standard free energy of formation of HS- ion (3.01 kcal.) and S- ion (20.0 kcal.) given in “Selected Values of Chemical Thermodynamic Properties.”6 The values of YHS- and YOH- used in equations (8) and (9) were calculated from Debye-Hiickel US- = U H s - * U o H - . K i / K w (5) cm. as the effective diametheory, using 3.5 X Substituting the value of as- in (5) into (4) gives ter of the ions. The ionic strength did not exceed A F f o ~ ~-s AFJob- = -nFE RT In ( U E ~ - * U O H - , K ~ / K0.02 , ) in any of the solutions. Results.-The arithmetical mean of the value (6) Ki refers to the reaction HS- F? H + S-, the of the standard free energy of formation of HgS calculated from electromotive force measurements standard free energy change for which is made on a total of 6 cells at 3 concentrations of AFfOs- - AFJOHS- = -RT In Ki (7) NazS (0.005 - 0.01 molal) was -10.5 kcal., the average deviation from the mean being f0.07 kcal. Substitution of (7) into (6) gives (1). The activities of the HS- and OH- ions were obDiscussion tained from the following relationships, in which parentheses denote molal concentrations. Measurements of the free energy of formation of mercuric sulfide from the two types of cells are in UHS- = ( H S - ) Y H B - = [(A) - (S-)]YHS(8) fair agreement (-10.22 and -10.5 kcal.) EstiUOH(0H-1~0~ =- [(B) - (HS-) 2(S’)l’YOH- (9) mates of accuracy based chiefly upon reproducibilThe symbol (A) represents the concentration of to- ity of electromotive force readings, analytical data, tal sulfides (HSS-), which was determined accuracy of the thermodynamic constants used in volumetrically by oxidation with calcium hypochlo- the calculations, and estimates of error from liquid rite.’ The symbol (B) is the hydroxyl ion concen- junctions are indicated by the number of signifitration produced by complete hydrolysis of the cant figures reported. NazS solution, and was determined by back-titratSolubility Product Constant.-The solubility ing an aliquot of the solution that had been treated product constant of HgS may be calculated from with an excess of acid and heated to drive off all the AFO of the reaction H2S. HgS H g + + f S‘ The molality of the S- ion, which is required in equations (1) and (2), was calculated from the re- by means of the relationship In K = - AP/RT. lationship Using the value of -10.22 kcal. for the standard [ [ Y ~ - ’ K ~ / Y H S - . Y O Hf- ] (B)I(S’) - (s-)* = (A)(B) - (A)* free energy of formation of HgS, and 39.385 and (10) 20.05kcal. for the standard free energy of formation This equation results from substituting the expres- of the Hg++ and S- ions, respectively, we calcusions given for QHS- and U O H - in equations (8) and lated the solubility product constant of HgS at 25’ (9) into to be 9 X If the value reported by Kolthoffl is corrected for the latest values of the free Us- = U o H - * U H s - / K h The value of Kh was taken as 0.029, which was ob- energy of formation of Hg++ and Sp ions,5 it bewhich is in fair agreement with tained from the relationship Kh = K,/Ki, using the comes 8 X the value obtained in this investigation.
The activity of the sulfide ion may be expressed in terms of UHS -, UOH -, and the hydrolysis constant ( K w / K j ) of the S- ion. Only the first hydrolysis to the HS- ion needs be considered, the effects of the second step of the hydrolysis being negligible in solutions of NazS; hence,
+
+
-
=i:
+
(7) I. M . Kolthoff and E. B. Sandell, “Textbook of Quantitative Inorganic Analysis,” The Macmillan Co., New York, N. Y., 1937.
PROVO, UTAH
RECEIVED JANUARY 29, 1951
