Akira Matsubara' and Kazuo Nomura College of General Education Kyushu University 01 Ropponmatsu, Fukuoka 810 Japan
I
I
Coupled Phenomena in Chemistry Understanding of chemistry through Gibbs energy utilization
Various biological phenomena have been understood by the principle of coupled reactions, where an energetically unfavorable reaction can he proceeded by coupling it with other reactions liberating a larger amount of Gihhs An example of a coupled reaction is glucose + H3PO&= glucose-&phosphate + Hz0 ?A ?
= +12.6 kJ
(1)
where AGO is the standard Gihhs energy change a t pH = 7. Since the above reaction has a positive A p , it would not he expected to occur by itself. The reaction (1)can he driven by coupling it with hydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP), ATP + HzO = ADP + H3P04 AGO = -33.9 kJ (2) The coupling of the reaction (1) with (2) gives the reaction (3) having a large negative value of AGO. glucose + ATP = glucose-6-phosphate + ADP A g o = -21.3 kJ (3) Further, the Gihhs energy liberated from the reaction (2) can he utilized not only for promoting other chemical reactions hut also for causing muscle contraction or active mass transport. In this way, various phenomena in modern biology have been understood through Gihhs energy utilization. This must he due to the fact that the energetics of modern biology has been developed under the benevolent influence of thermodynamics. Well, how about chemistry? We chemists can also find a number of coupled phenomena in chemistry. However, the field of physical chemistry had been cultivated by great scientists such as van't Hoff, Ostwald, Arrhenius and so on, well before the establishment of thermodynamics. Therefore, we usually interpret such phenomena in terms of equilibrium constant, pH, electrode potential, solubility product, etc. As a result, the vivid image of Gihhs energy utilization has been veiled, although these terms were related to thermodynamics later. Let's consider some common phenomena in chemistry through Gihhs energy utilization. For the sake of simplicity, ideal systems are assumed throughout the text. Utlllzatlon of Gibbs Energy Liberated from Chemical Reaction ~eutralization
Acetic acid which is a weak acid is only slightly dissociated in an aqueous solution,
where AGO is the standard Gihhs energy change. However, the acid is almost completely dissociated in a hasic solution. We usually use the following expression for interpreting this phenomenon; "In order to dissociate acetic acid, we have to make a solution basic or to increase the pH of asolution." We To whom correspondence should he addressed. Lehninger, Albert L., "Bioenergetics," 2nd Ed., W. A. Benjamin, Inc., Menlo Park, California, 1971, p. 45. 3 Dickerson, Richard E., "Molecular Thermodynamics," W. A. Benjamin, h e . , New York, 1969, p. 394. 1
718 / Journal of Chemical Education
cannot perceive any hint of energy from these expressions. The phenomenon can he interpreted as follows. The reaction (4) can he driven by coupling it with the avaricious proton-eating reaction (5)
+
OH- H30t = 2H20 AGO = -79.89 kJ (5) The coupling of the reaction (4) with (5) gives the reaction (6) having a large negative value of AGO. In these coupled reactions, proton is a common intermediate. CHCOOH + OH-
= CHEOO-
+ Hz0
AGO = -52.74 kJ (6)
Hydrolysis
Hydrolysis is a reverse reaction of neutralization. Sodium acetate, which is a strong electrolyte, is almost completely dissociated in an aqueous solution. However, only a small fraction of acetate ion reacts with water to give undissociated acetic acid and hydroxide ion, so the solution becomes basic. We usually use the expression-"Since a conjugate hase of a weak acid is a strong hase, acetate ion accepts proton from water to give undissociated acetic acid and hydroxide ion2'for interpreting this phenomenon. The phenomenon can he interpreted as follows. Since acetate ion is a strong hase, it reacts with the proton vigorously, CH3COO- + H30f = CH3COOH + H20 AGO = -27.15 kJ (7) However, this reaction is forced back by the reaction, 2Hz0 = H30C+ OHAGO = +79.89 kJ (8) The coupling of the reaction (7) with (8) gives the hydrolysis reaction (9) having a large positive value of A G O , from which the hydrolysis constant, Kh = 5.78 X 10-lo a t 25 "C, is obtained. AGO = +52.74 kJ (9) CH&OO- + Hz0 = CH3COOH+ OHThanks to the coupling, in spite of poor dissociation of acetic acid, its salt is a strong electrolyte. Oxidation and Reduction
Oxidation and reduction reactions are usually interpreted in terms of electrode potential, but they can be alternatively interpreted as follows: AGO = +84.9 kJ (10) Fe2+(;iq)+ Ze(rneta1) + Fe(s) AGO = -147.2 kJ (11) Zn(s) = Zn2+(aq)+ Ze(rneta1) The reaction (10) can be driven by coupling it with the reaction (11). AGQ= -62.3 kJ (12) Zn(s) + Fe2+(aq)= ZnZ+(aq)+ Fe(4 where electron is a common intermediate for the coupling. Simultaneous Dissociation Equilibrium of Two Weak Acids
This phenomenon is usually interpreted in terms of dissociation constant hut it can be alternatively interpreted as follows. Suppose we have a solution that is simultaneously a M H N 0 2 and b M CH3COOH. HNOdaq) = H+(aq)+ NO;(aq) CH&OOH(aq) = Ht(aq) + CHsCOO-(aq)
AG4
= +19.12 kJ
(13)
AGZ = t27.15 kJ (14)
The reactions (13) and (14) are coupled in this solution. However, the mode of the coupling is different from that described in the previous sections. They are not coupled stoichiometricallv but are mutuallv interlinked throuah - their contributions to proton concentration (a(:tivityJ. 11' the ronrentrations of suecies dissociated from HNOn and CH3COOH are x M and M, respectively, the foll&ng equations must hold
y
AGY = -RTln-
+Y)'
(I-X
= +l9.l2 kJ
(15)
of which the pressure dependence a t constant temperature is usually explained by the equation
G
-
(25) where a! is the degree of dissociation and K,, equilibrium constant. According to eqn. (25), a! is increased by lowering pressure. Interpretation of the phenomenon is as follows. The chemical equilihrium (24) is attained a t pressure PI and temperature To. AGO = - R T O I ~ ( P ( N O ~ ) ~ / P ( N ~ O ~ )
By solving the simultaneous eqns. (15) and (16). we obtain x and y. Each of x and y is smaller than the corresponding value for the separate dissociation equilibrium (13) or (14), respectively. The proton is a common intermediate for the coupling. Common Ion Effect on Solubility
= -RToln{~(N02)~lx(N203) - RTolnP, (26) where P(N2O4)and P(N02)are partial pressures of NzO4 and N02, respectively, and x denotes mole fraction. By changing pressure from PI to Pz at constant temperature To, the system [the reaction (24)] derives a supply of Gihbs energy from the surrounding and eqn. (26) becomes
The common ion effect on the soluhility of sparingly soluble salts is usually interpreted in terms of solubility product. The interpretation for this phenomenon is essentially the same as that described in the preceding section. Suppose the solubility equilihrium for AgCl is established in a M NaC1.
where
AGP = +55.664 kJ (17) AgCl(s) = Ag+(aq)+ C1-(aq) NaCKaq) = Na+(aq)+ CI-(aq) AGB = ? (18) The reactions (17) and (18) are coupled through their contributions to concentration of C1-. If the concentrations of species dissociated from AgCl and NaCl are x and y, respectively, we have
AV = zV(N02) - V(NzO4) (28) where V(Nz04) and V(N02) are partial molar volumes of N204 and NO2 a t pressure P and temperature TO,respectively. In order to equalize both sides of eqn. (27), the ratio, X ( N O ~ ) ~ / X ( N Zmust O ~ )change , to a new value, x1(N0~)2/x'(NZO,). AGO = -RTolnI~'(NO2)~lx'(N20a)l - RTolnP, -
Unfortunately, AGZ is unknown, but we can obtain the value of x from eqn. (19) hy assuming y = a. AGP = -RTlnK., = -RTln
x(*.
+ a ) = +55.664 kJ
(21)
where the solubility product, K.,, is 1.75 X 10-lo a t 25 OC. Chloride ion is a common intermediate for the coupling. The same interpretation is applicable to the pH of buffer solutions. Utilization of Gibbs Energy Supplied by the Surrounding There are various phenomena utilizing the Gibbs enerw supplied hy the iurrc>unding.An exampleis electrorhemi&l equilihrium. For certain concentrations of %n2' and Fez+,the Gihhs energy change of the reaction (12) is written as [Z"2+] AG = AGO RTln [Fe2C1 (22)
+
If the system is allowed to stand, the ratio, [ZnZ+]/[Fez+],must change until AG becomes zero. However, by utilizing electrical energy supplied by the surrounding (for example, battery), the electrochemicalequilibrium can be established a t a certain value of [Zn2+]/[Fe2+], [Znz+] -zFE = AGO + RTln (23) IFe2+1 where z is charge number, F, Faraday constant, and E, electromotive force. Another example is osmotic equilihrium where a solution is equilibrated with its solvent across a semipermeable memhrane by utilizing osmotic energy supplied by the surr~unding.~ Now we consider Le Chatelier's principle through Gihbs energy utilization.
AV~P (29)
The chemical equilihrium with a positive AV is shifted to the right by lowering pressure. For ideal gas mixtures, partial molar volume>are equal to the_molar volume of ideal gas, V, and hence AV = 2V(N02) - V(Nz0.t) = V. Equation (29) becomes
-RToln{~'(N0~)~1x'(N~O~)lRTolnP, - RToln (PSIPI) = -RTolnl~'(NOz)~/x'(N201)) - RTolln PZ (30) Eqns. (26) and (30) can be reduced to eqn. (25) at pressure PI and Pz, respectively. By comparing eqn. (29) with eqn. (26), we see that the chemical reaction with AV = 0 cannot couple with the surrounding. AG'
=
Temperature Dependence of Chemical Equilibrium
We consider the following chemical equilibrium, Idg) = 2Ik) (31) of which the temperature dependence a t constant pressure is usually explained by the equation
. ~ .
Pressure Dependence of Chemical Equilibrium
where Kp(T1) and K,(Tz) are the equilibrium constants a t temoerature T I and Tq. resoectivelv, and AHo. the standard heaiof reaction. The e&ilidrium c o & n t of thd reaction with a positive AH is increased bv raisine.. tem~erature. . Interpretation of rhe phenomenon is as follows. The chemical equilibrium r.31) is estahlished at TI and Po. AGQ(T1)= -RTlln- P(U2- -RTllnK,(T1) (33) P(Id By changing temperature from TI to Tp a t constant pressure
We consider the following chemical equilibrium, 'Reference 3, p. 316.
Volume 56, Number 11, November 1979 1 719
Po, the system [the reaction (31)] derives a supply of Gihhs energy from the surrounding and eqn. (33) becomes
ACD(T2)= ACa(Tl) -
KAS'~T=
-RTdnKp(Td
(38)
By comparing eqn. (34) with eqn. (33), we see that the chemical reaction with A S = 0 cannot couple with the surrounding. Since ASo is not very sensitive to temperature? eqn. (38) can he written as
where AS = ZS(1) - S(Iz)
- Rlnz(1))- (S(I2) -Rlnx(Idl = 2(S0(I)- RlnPo - Rlnx(I)l - (SD(12)- RlnPo - Rlnx(Iz)l = ASD- Rln Po' = ASo - R h K J T ) (35) P(I7) = 2(S(I)
where S(I2) and S(1) are molar entropies of 1% and I at pressure Poand temperature T , respectively, S and Sodenote molar entropies a t pressure Po and 1atm, respectively, and A S o = 2So(I) - So(12). By substituting eqn. (35) into eqn. (34), we have
-
-.
If K p ( T ) is assumed to he kept constant at Kp(T1), eqn. (36) becomes
- ., Actually, the chemical equilibriumis shifted to equalize both sides of eqn. (37) and hence Kp(T1) must change to a new value, Kp(T2).
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AG'(T1) - (1 - $)AsO T2
= -RlnK,(Td
(41)
By subtracting eqn. (40) from eqn. (41), we have
~ by average valSince AHo(T1) and A S O ( T ~ ) ' Cbe~ replaced ues, AHoand ASo, over the moderate temperature interval? respectively, eqn. (42) reduces to eqn. (32). Although eqn. (32) is expressed in terms of AHo, hS is originally responsible for the equilibrium shift with temperature. In this way, various phenomena in chemistry as well as in biology can he understood through Gihhs energy utilization. Pirnentel, George C., and Spratley, Richard D., "Understanding Chemistry," Holden-Day, Ine., San Fransisco, 1971, p. 388.
