INDUSTRIAL A N D ENGINEERING CHEMISTRY
408
Vol. 38, No. 4
phatic hydrocarbons, n-heptane and n-undecane. ‘Il-hile athat tht: jxiraffiii Couriti by Schorgt-r iri t h i l sugar pine ol(vrcwin pinene is the most common terpene of pines, the presence of 15-as n-undecane. J,ater, n-undecane T T ~ Sloillid in turpentine+ of phellandrene in pine oleoresin is not, very common. Schorger P . mxelsa and P . nionticola (3, 1 2 ) . (10, page 756) reported it in turpentine of lodgepole pine (Pinits So far, n-undecanr hiis h e m found in four pine s p c i w , in(*Iu(liiig r o n b t a murrayann). I n both Coulter and lodgepole pine it is :i Coultvr pinc: n-heptaiit,, in tiso species. Thus, n t prcsc,nt thc: levorotntory form of p-phellandrene. Heptane has been found oleoresins of a t least six pines contain paraffins. Prohihly t’urthtlr bcforc in oleoresins of P. jeffreyi and P. sabiniuna (10, pages 739 irivestigations in this direction will ri 11thc prcwnw i)f lx+rxffitl tirid yt?2). I n both species the voiatile oil consists of 9;c: hcphydroc;rrhris in othc~i.pinc~*. tniie, the remaining 57; being st raight-chain aldchytlcs ( 1 , 3, LITEKA’TUKE CITEI) 1 3 ) . Heptane was found also in a natural hybrid betxeen Jeffrey F’oore, P. A , . .1. Am. Phurm. Assoc., 18,350-3 (1929). and ponderosa pines ( 4 , 8 ) . In this hybrid about l5C; of the volaFoote, P: A, a n d Mirov, N. T., Ibid., 22, 828-34 (193:j). tile oil consisted of n-heptane a,rid 8.5% consisted of terperiw. Gordon, S. M., A m . J . Ph,urm., 100, 156-61 (1928). Coulter pine is the only pine species (not hybrid) SO lar knowii Harvley, L. F., arid Beglinger, E., u n p u h . rept., Forest, ~’rlJdllc6S L a b o r a t o r y , Madison, \Tis., 1929. in whose olcorcsiI: heptane is found as an admixture, t o the terHeusler, F., t r . by F . J. P o n d , “Chemistry of Terpenes”. 1RO2. penes. The presence 01 normal undecanc i n Coultvr pine turpcvH o d g m a n , C . D.. H a n d b o o k of Chemistry and I’liy~im, tine is of extraordinary interest. Originiiil) thiq l!~-tlrr~c.;irl~ot~ 27th e d . . p. 808, No. 4426, CleT-eland, Cbeni. Riihher T’iib. rvas isolated from Pennsylvania petroleum ( 7 , . CO.. 1943-44. Mabery, C . F.. Proc. Am. Acad. A r t s Sei., 32, 121-76 (1897). Schorger (10, page 753) found an oil th:it ma>-h:ivc, :i parMirov, N. T., J . FoTe.strY, 27, li6-87 (1929). affin hydrocarbon in P. lumbeitiana turpcritilics. The liydrocarIbid., 40, 953-4 (1912). h n , purified by repeated shaking with sulfuric acid, boiled heSchorger, 9.W., Trans.Wiu. Acad. Sei., 19, Pi. 2 , 728-66 (19191. Scliorger, A. IT., U. S. D e p t . Agr., Forest Seraice KwU. 119 tween 194’ and 200’ C. a t 742.7 nim.; the specific gravity l m s (1913). 0.7549 and thc indrx of refraction 1.4249. Schorger attributed Simonsen, J. L., and Kau, 11. G.. I n d i r m Forest Records, 9, I -12 the p r e v n w of thi hydrocarbon to the coiitaminat ion of the (1922). oIror(:siii n-ith kt~rorrnt~: aftc>rlattsr findings thew can lw n o doubt 1-111. A . IT,,. I . A m . Phnrm. _issoc..24, 380-2 (~RRS‘I t i c L c , i i
CORRELATING EQUILIBRIUM CONSTANTS Chemical Reactions and Heats of Reaction D O N i L D F. OTHMER mi) M W H U K H. LL‘LEY Polytechnic I n s t i t c t i e of B r o o k l y n , IT. Y-.
NooL
iyhich ‘has been iounti usc.ful in correlating inan!. properties of gases, of liquids, aiid of solutions is a grapli on which soiiie property is plotted on logarithmic papor against the vapor pressure of a referencc substance a t the same trinperature. Sucli a graph was first, I w t l t o correlatv vapor prcss~~rc. data ( 7 ) . The vapor pressures of soine staiidard substaiicc arc’ indicateti on the horizontal scale of an ordinary sheet of log paper, and tho corresponding points of t emperaturc are indicated. OrdinateP for these points are erected, and on these temperature ordinate.; are plotted values of the m p o r pressures of thc desired snbstanccLs to give straight liner;. The slopes of these lines are the ratios of the molar latent lieat of the substance to the molar latent hrat of the reference at every temperature. Besides vapor pressurc, many other propert,ira of gases and solutions have been found to givr straight lines on the same type of plot, such as gas soluhilities and partial pressure (12), the pressure of adsorbed materials from adsorbents ( 1 0 ) ,vapor composit,iorisand related propotc. crtics of solutions (U), viscositics (8), REiCTION CO\STAh’T
This method ot correlation, giving straight lines, allows the ready checking of experimental data and the possibility, by extrapolation or interpolation f r o m a relatively few experimentai
points, of obtaining data tliroughout a coniplet,e range. k‘igitrc I shows the plot of t,he recent data of Kelley ( 5 ) on the Ilissociation pressures as a function of temperature for various reartions (curves 1, 3, 4, 6, 7) and the equilibrium constants against the same tempera,turc functions for ot,her reactions (oiirws 2, 5, 8). The latter three straight liiios were obtained by extt’iitiitig tlict field of application of the mct.hod of plotting; the thcmiod?.riarrii[, background will be indicattvl lattbr. Reaction rate coiista.nt,s, ionization constants, eqiiilil)riuiii const’ants, and solubility product constants may all bo im-related by the use of E’igurc I . In rach case the slopes of tho resulting straight lines are the ratios of the heats of reaction for the particular system to thc latent heat of the reference substance.. All of these plots ma,y be construct,ed in the same way as thc previous correlations on log paper. The Y axis is calibrated i n units for the appropriate rate or equilibrium constant; tile X axis is calibrated, first in units for the vapor pressure of a suitablc reference substance, and then in corresponding temperat,ures, as indicated above. On the vapor pressure scale of the X axis tho temperature lines are erect,ed a t the eorrespoiiding vapor prcssure values, and then the rate or equilibrium constants are plottorl on t,hese temperature ordinates. For equilibrium constant,s (Figures 2, 3), reaction rate constants (Figures 4, 5 , B), and solubility product constants (Figure 8),
April, 1946
409
INDUSTRIAL AND ENGINEERING CHEMISTRY Temperature " G .
Reaction rate constants, equilibrium constants, solubility product constants, and ionization constants give straight line plots on logarithmic paper against the vapor pressure of a reference substance at the same temperature, using the method of plotting developed for vapor pressures (7) and many other physical properties of gases and liquids. The slopes of the lines give the heats involved in the reactions. This method may be conveniently used to correlate the limited amount of experimental data available upon the change of the iarinys types of equilibrium constants with temperature. A minimum of two experimental values is needed to fix the straight tine obtained over a wide temperature range. In addition, the slope of the line may be used to obtain the heat of reaction a t any temperature for any particular system. The heat evolved in the change in the polymetric structure of water, as indicated by the break in the ionization constant lines, is the same quantity of heat obtained for a similar break in the correlation for viscosity (8).
itraight lines are obtained by the use of this method of plotting. For ionization constants (Figure 7) straight lines with breaks a t about 25" C. are obtained. The abrupt break is probably due to a change in the molecular jtructure of the solvent water, as noted i n plotting other physical properties (8, 11). 111 the first three cases only two values of the constant or one value and the value of the heat of reaction are needed to obtain the entire straight-line plot. For the case where the line breaks, two values of the constant are needed for each straight section of the plot. EQUlLIBRIUM CONSTANT
Figure 1. Log Plot of Dissociation Pressure US. Vapor Pressure of Water a t Same Temperature The corresponding temperatures are indioated by the ordinates and the scale a t the t o 1. Mg&z 6RzO --t MgClz 4Hz0 2Hz0 3. MgCh 4Hz0 --t MgCIz 2Hn0 2Hz0 4. MgClz 2Hz0-+ MgCIz HzO Hz0 6. MgClz Hz0 -+ MgOHCl HC1 7. MgCIz. Hz0 -+ MgClz HzO
++ + ++
Log plot of equilibrium constant io1 following reactions on same coordinates 2.
5. 8.
++
+ + + +
MgClz Hz0 -+ MgOHCl HC1 MgClz $ 0 2 -+ MgO Clz MgClz 2H20+ MgOHCt "21 Hz0
The van't Hoff isochore is: d In KP
dT
- 4.-
RT2
where the relation between the two different equilibrium constants (1)
The Clausius-Clapeyron equation may be written for some wference material:
dT or -1 d In P = -
RTz
L
(3)
Combining Equations 1and 3 and integrating: I n K , = hL l n P + C
(4)
The equilibrium constant may also be expressed in terms of concentration as well as partial pressure; for such a case Equation 4 becomes AE lnK,=-lnP+C
L
(5)
is:
Kp
=
KO(RT)*n
(6)
I t can be seen that K , is equal to K Owhen an is zero. Another demonstration of the correctness of Equatlons I and 5 follow from the similar equation.deve1oped for activities (9). Since the log of the equilibrium constant is equal to the difference of the sums of the logs of the activities of the reactants and of the products, these equations for the activities and the respective heat terms may be combined to give Equations 4 and 5. Figure 2 shows the result of a plot ot K , against the vapor pressure of mercury for several reactions. The slopes of the lines are the ratios of the heat of reaction to the latent heat of mercury a t the same temperature. A positive slope to these lines indicates an endothermic reaction; a negative slope indicates an exothermic reaction. For the reaction between hydrogen and oxygen to form water, the heat of formation a t 0" C., as given in the literature from calometric determinations, is -68,310 calories per mole, and that calculated from the slope extrapolated down to 0" C. is - 68,600 calories per mole.
410 Recently, Rossini and eo-workers compiled equilibrium ronstants over a ~ i d e range of temperature (16) for reactions involving oxygen, hydrogen, water, methane, and carbon oxides. This includes an extension over a nider temperature range of the data plotted in Figure 2 on the reaction betn ern hydrogen and oxygen to give water. This and other reactions are shown in Figure 3. Because of the extremely large range of temperatures and equilibrium constants covered bv these data. the Y axis is calibrated in terms of the tabulated values of loga-
INDUSTRIAL AND ENGINEERING CHEMISTRY 30 0
0
50 70 100
30
Vol. 38, No. 4 Tern
200 300 500 700
Vopor Pressure O f M e r c u r y
(atm.)
Figure 2. Log Plot of Equilibrium Colistant us. Vapor Pressure of Mercury a t Same Temperature Line No. 1 2 3 4
Ten
Reaction
$Os* SOa ++?Oz@ HpS + HzO COz + H n G CO + Hz0 SO1 H 2
H2
'rature
K p , Multiply Vertical Scale bl 10-1 10' 105 10-1
O K .
19 18 17
16
I5 14
Figure 4. Log Plot of Reaction Rate Constant vs. Vapor Pressure of RIercur) a t Same Temperature
13 12
Line KG.
Heiictirm
k, 3Iultipl> Vertical Scale h >
Constmt Plotted
IO
9 8 f-
7
6
5 4
Figure 3. Plot of Logarithm of Equilibrium Constant z's. Vapor Pressure of 3Iercury a t Same Temperature Arrows indicate whether left- or right-hand scale is t o be used f o r log of equilibrium constant. Because of the aide range of values of K encountered (over 1040 times) i t is necessars- t o add the indicated nurnbel t o t h e respective wale veaclini: t n g i v ~l o g K , Line
3 2 I O V a p o r P r e s s u r e M e r c u r y (rnm.)
KO.
1 2 3 4
Keactiori
.\(Id t o
Vertical Scale +10, left 5 , left
--
+
5,riglir
5
-io,'ieft
i9
- 3 , right - 16, riaht
:
10 11
12
.
...
- 3 > , left
-30, left - 1, right
-1.5, right
INDUSTRIAL AND ENGINEERING CHEMISTRY
April, 1946
Temaeroture OC.
41 1
of Dushman (2) who compiled the best work of other experimenters. Cohelation of the plotted line with the crosses is good. This type of plot is independent of the order of a chemical reaction, since first-, second-, and third-order reactions give straight lines (Figure 5). Figure 6 is ZL plot of reaction rate constants for the alkaline hydrolysis of several different esters. The slopes of these lines are nearly the same, and indicate that the activation energies and, hence, the heats of esterification are about constant for these several different alcohols when esterified with acetic acid. IONIZATION CONSTANT
Figure 5. Log Plot of Reaction Rate Constant for Reactions of Different Orders us. Vapor Pressure of Water a t Same Temperature Line NO.
1 2 3
Order of Reaction First Third Second
Reaction NzOs+ Nz04 302 02 2NO -+ 2NOn HZ 1 2 4 2HI
+
++
10-* 10-6 10-1
REACTION RATE CONSTANT
Equilibrium constants for a reaction are actually a combination of two reaction rate constants. By definition, =
(7)
h/kz
constants
Equation
4
may
A Ei lnKi=-lnP+C
k,.Multiply Vertical Scale by
rithms of equilibrium constants, Values plotted are against the temperatures corresponding to the vapor pressure of mercury but do not go below the temperature where the vapor pressure of mercury is I mm. Figure 3 shows the excellent correlation obtained in this simple method of plotting even over this tremendous range.
Kc
For ionization written :
(10)
L
Figure 7 is a plot of ionization constants for several weak electrolytes. As mentioned before, these lines break a t about 25' C. The heat change shown by this break may be calculated by determining the slope of the straight line just below and just above the break. By subtraction, the heat change a t the break'is determined. These values are given in Table I. Since all of the ionization constants were calculated from the concentrations of the ions in gram moles per liter of solution, the heats of ionization obtained from the slopes are expressed in calories per mole. ,Table I indicates that the change in the heat of ionization shown by the breaks in the lines is aRproximately the same for all cases represented. This seems to show that the change was not due to the electrolyte but rather to the solvent, which was water in all cases. There is probably some change in
Tolman (16) showed that the reaction rate constants may be expressed, according to the van't Hoff equation, as follows:
Temperature
OC.
7 5
This may be combined with the Clausius-Clapeyron equation to give :
E
Ink = Z l n P
3
+C
(9)
2
Figure 4 shows the plot of reaction rate constant kl for the decomposition of hydrogen iodide, reaction rate constant LZ for the formation of hydrogen iodide from hydrogen and iodine, and equilibrium constant calculated from the ratio of kl and kl. Line 3 was obtained by dividing kl by kz and plotting the values so obtained. The points for the plotting are not shown since this line is derived from the other two; crosses indicate the values
I .7
.5 .3
TABLEI. HEATCHANQEAT BREAKIN CURVESOF FIQURE 7 Weak Electrolyte water
&-%%robenzoic, acid &-%%robenzoic Methyl cyanonitroacetate Bmmonium hydroxide Toluic acid m-Hydroxybenzoic acid
Heat of Ionization, Calories/Mole Change due Below break Above break t o break 12,600 1000 13,600 1220 3,010 4,230 -91 823 732 1040 1,110 2,150 928 1,660 732 1280 -648 732 Average 1060
-
-
be
20 30
5070
Figure 6. Log Plot of Reaction Rate Constant for Alkaline Hydrolysis of Esters us. Vapor Pressure of Water a t Same Temperature 1 Prop 1 acetate Butyracetate 3. Isobutyl acetate Arrows indicate whether the leftbe used for k. 2:
4.
Isobutyl acetate
5. aec-Butyl acetate 6. tevt-Butyl acetate
or right-hand scale is to
INDUSTRIAL AND ENGINEERING CHEMISTRY
412
Vol. 38. No. 4
Figure 8. Log Plot of Solubilitj product Constant t’s. Vapor Pressure of Water at %me Tein pera t lire
Figure 7 . Log Plot of Ionization Constant for Weak Electrolytes us. Vapor Pressure of Water at Same Temperature Line NO. 1 2 3 4
5 6
L1ne No. 1
r
Ki,Multiply
R
Weak Electrolyte Vertical Scale h y Water 10 -1 m-Nitrobenzoic acid 10-5 Methyl cyanonitrosoacetate lo-; Ammonium hydroxide 10 10.h Toluic acid m-Hydroxybensoii, ai% 10-5
4 5
Salt Lead iodate Lead fluoride Silver chloride Barium sulfate Calcium oxylate
K a p . Multiply
L eitical Scale h \
10-14 lo-* 10-11 10-11 10-Q
VO Yl EN C L 4TUIt F:
C = toristan1 ot iiitcgratioii -
statr of’ the water at the poinr wlierr the CUI version from one polymeric state to another which occurs for pure water not far from this temprrnt,ure ( I ) is the most likely explanation for the breaks. A similar break in t’hestraight 1iiit:s \\-asobtained in correlat ions for viscosity (8) and sbrface trnxiori (1‘1). For the viscosity curvc of water, the break in the line is equivalent to the same change in heat (1090 calories per mole) as was obtaincd for the brcak in the ionization curve. For the break in the surface tension correlation, the slope has not hren defined in usahlr heat valuw,
= 2 3 =
AEi = AH = kl
=
k? =
K, = Ki =
K,, = K q p=
L = An = P =
P,
= 1 =
energy of activation increase in t,otRl internal c>iieryy heat of ionization change in heat content, for tcactioii specific rat’e constant of f o r ~ a i drwction specific rate constant cquilibrium constant ionization constant equilibrium constant. solubilit,y product const.ant, latent heat of referonce sut)st,aiic(* change in number of mol( vapor pressure of roferenc yasconstant temperaturtx
SOLUBILITY PRODUCT COYSTAh r
F ui ionizable materials that are very slightly soluhlt, iii 13 atel the product of the ion concentrations 17 a constant Thii: rnnstant may he used in F:quation 4 to pivc” 111
K,,
In P
=
+c
Figure 8 shons a plot of solubility product constantq as of straight lines for several slightly soluble salts
(11) H
group
OTHER REFERENCE SCALE
In all the plots presented, the vapor pressures of some liquid was used as the reference scale. If, however, t F o van’t IIoff isochores are combined rather than one isochore with the Clapeyron equation, the reference scale may be that of the equilibrium constant of the reference substance; the slope of the linp will be the ratio of heats of reaction: 111
K,
AE AE
= -,In
K,‘
+C
(12)
Any of the four types of equilibrium constants may be used as the reference scale, but in the usual case the method using vapor pressures will be found to be the simpler.
nInLIoC;fi.wtiY
Uorsey, N. E., “Properties of Ordinary Water Substance“, Ken. York, Reinhold Pub. Corp., 1940. ( 2 ) Dushman, S., J . Am. Chem. SOC.,43, 397 (1941). (:3) Giasstone, S., “Text-Book of Physical Chemistry”, New Y o r k . D. Van Nostrand Co., 1940. (4) International Critical Tables, Kew York, McGraw-Hill Book Co., 1928. is) Kelley, K. K., U. S.Bur. Mines, Tech. Poper 676 (1945). (A) Lange, N. A . , Handbook of Chemistry, 3rd ed., Sandnsky, Ohio, Handbook Publishers, 1939. (7) Othmer, D. F., IND. ENG.CHEM.,32, 841 (1940). ( 8 ) Othmer, D. F., arid Conwell, J. ST., I b i d . , 37, 1112 (1946). (9) Othmer, D. F., and Gilmont, H . , I b i d . , 36, 8.58 (1944). (10) Othmer, D. F., and Sawyer, F. G., Ibid., 35, 1269 (1943,. ( 1 1) Othmer, D. F., and Schmutrler, A. F., unpublished data. (12) Othmer, D. F., and White, R. E., Ibid., 34, 952 (1942). (13) Perry, J. H., Chemical Engineers’ Handbook, 2nd ed., S e w York, McGraw-Hill Book Co., 1941. t, 14) Seidell, A,, “Solubility of Inorganic and Metallic’Orga.niv C‘OIIIpounds”, 3rd ed., D. Van Nostrand Co., 1940. ( 15) Tolman, R. C., J . Am. Chem. Soc., 47, 1533 (1925). !le) Wagman, D. D., Kilpatrick. J. E., Taylor, W.J., Pitser, J. S.. and Rossini. F. D.. ,T. Research S a t [ . Bur. Standards, 34, 143 (1)
.
I
(1945). PRESENTED on t h e program of the Division of Industrial and Engineerinc Chemistry of the 1945 Meeting-in-Print. AXERICANCHEVICAI, SOCIETY..
