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GEORGE L. GILBERT Denison University Granville, Ohio 43023
A Demonstration of the Relationship between Rate Constants and Equilibrium Constants Submitted by:
Checked by:
Felicia Smoot, Shirley Ragan, a n d Allan R. Burkett Dillard University, New Orleans, Louisiana Kenneth H. Lothrop Marshfield High School Marshfield, Massachusetts 02050
This demonstration is designed to point out the relationships and distinctions between rate constants, rate expressions and equilibrium constants. Consider the following equilibrium:
AAB hz
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where the equilibrium expression is K., = [B]/[A]. Further assume that the conversion of A B is a first-order process, ratel = kl[A], and the conversion of B to A is also first-order, ratez = kz[B]. The overall rate expression is given by rate = kl[A] - kz[B]. This situation is a convenient one to demonstrate and is analogous to a variety of actual chemical systems, for example the cis-trans isomerization of styryl cyanide (C,jH&H=CHCN). Procedure
The actual demonstration involves two 2-1 beakers labeled A and B, a 250-ml beaker anda 50-ml beaker labeled ratel and rate2, respectively. That the smaller beakers represent reaction rates and NOT rate constants should be made clear. The beaker labeled A is filled with 1.600 1of water and represents the initial concentration of reactant A. A few drops of food coloring added to the water will improve visibility, particularly for large classrooms. The beaker marked B is left emDtv . . and represents the fact that no reaction products are available a t zero time. Two members of the audience are asked to be volunteers; one is given the beaker labeled ratel and placed be-
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790 1 Journal of Chemical Education
side beaker A, the other is given beaker labeled rate2 and placed beside beaker B. A t a signal from the instructor both students simultaneously transfer as much water as possible from their respective beakers to the other vessel. Obviously a t time zero, B = 0 and no transfer can be made from B to A. Each transfer represents a unit of time which can be arhitrarily assigned as one minute. An equilibrium mixture is established within a12 cycles in a manner similar to that described by Martin in a previous demonstration? Two members of the audience are asked to keep track of the reaction rates by noting the volume transferred by the two volunteers during each cycle. At equilibrium ratel = rate2. The rest of the audience monitors the Drogress of the reaction by recordind the total volume in a c h \.esseI until equilihri&n is rs~ahlished.The equilihrium constant, K,,,, is computed assuming that the um1 wlume in beakers A and B reflect actual concentrations. uolurne in beaker B Kw = ualume in beaker A The procedure is then repeated surtlng with 1.6(K)I oiaater in vessel B and none in A. The same value for K,,, will, narllrally, be obtained. Remarks
The rate expression for the overall reaction starting with [A] = 1.600 and [B] = 0 is given by Rote = hl[A]
0 1 - kz[B] = dt
During the initial stages of reaction where kl[A] >> kz[B] the rate expression can be approximated by -- - hl[A] = ratel
dt
This equation is exact for the first transfer ([B] = 0) and kl can he evaluated directly uolume transfered in beaker ratel h, = 1.600
where 1.600is representative of the concentration of A at zero time. Analogous arguments are utilized for evaluation of kn uolume transfered in beaker raten hp = 1.fin0 where 1.600 reoresents the concentration of B when IAl . .= 0 and t = 0. At eauilibrium the overall rate of reaction is zero. Substitution &to equation (1)and rearranging gives hlIA1 = hzP1 or
Calculation of the equilibrium constants from the rate constants thus evaluated will aeree within a few Dercent of the pre\.iously determined \.due of K,, Small differences between to difficulties in arrumu.ly the values of I
