John P. Chesick and A. Patterson, Jr.
Yale University New Haven, Connecticut
I
Determination of Reaction Rates with
1
an A.C. Conductivity Bridge
1
A student experiment
In this paper we describe a quantitative experiment in chemical kinetics which is suitable for advanced freshmen or for a physical chemistry course. It involves a study of the solvolysis of tertiary hutyl chloride (hereafter called TBC) by means of condnctance measurements. In all freshman c,hemistry courses a t Yale, certain fundamental ideas concerning rates of reaction are taught. The law of mass action is presented in terms of simple collision theory, and the concept of reaction order in a chemical rate equation is explored. The .4rrhenius equation for the effect of temperature on a reaction rate constant is discussed in terms of the distribution of molecular energies, and the idea is presented that only collisions hetween molecules having energies in excess of some minimum energy, the activation energy, will be successful in terms of chemical reaction. We thought that it would be worthwhile to introduce an experiment to illustrate these ideas into the accompanying quantitative laboratory course. After examination of available experiments, we came to the conclusion that none of these was of sufficient precision for our purposes. We wanted an experiment which would be cheap enough to permit performance by a number of groups of students, yet accurate and complex enough to he challenging to the students. We were not averse to a measurement of an indirect sort which would involve some manipulation of the data t,o arrive at the desired constants. The following experiment mas developed and has been successfully tried by students in our freshman honors course. The experiment should also be suitable for a physical chemistry laboratory course since it yields results of good quantitative precision and exemplifies all the points of interest usually covered in chemical kinetics. The resistance measurements used to follow the reaction are performed with a 1-kc transistorized AC bridge which we designed and built for the purpose. The oscillator, bridge, and detector were assembled for parts expenditure of $8.50 per set exclusive of batteries. The philosophy of design and construction is similar to that for the potentiometer we have previously described.'
' CHESICK,J. P., A N D PATTERSON, A., JR., J. CREM.EDUC., 36,496 (1959).
242
/
Journol of Chemical Education
The Reaction
TBC reacts with water according to the over-all equation
+ 2HpO-
(CHa)dXI
(CH8)&OH
+ HsO+ + C1-
(1)
Of the reactants and products, only hydrochloric acid contributes significantly to the electrical conductivity of the solution, so a measurement of conductance can be used to follow the progress of the over-all reaction. The reaction has been shown to be first order in [TBC]; it is believed that the rate determining step is the formation of a carbonium ion, followed by afast reaction with a hydroxylic solvent such as water or ethanol.* This mechanism may be represented as follows: (CHa)dXI (CH&CC
Hz0
slaw
+ CL(CH&COR + ROHli
(CH,),Ct
+ 2 ROH fast
Here R is either H or C2H6.
(3)
For this mechanism
-d[TBC]/dl = d[HCl]/dl
=
k[TBCI
(4)
where k is the first order rate constant for (2). Since IHCII = [TBCIo - [TBC]
(5)
where [TBCIois the initial concentration of the reacting chloride, the rate equation (4) may he written d[HCLl/dt
=
k([TBC]o - [HCI])
(6)
This may be integrated to give [HCI] = [TBCIo(1 -
(7)'
e-kl)
The conductance of the solution is identical to 1/R, where R is the measured resistance, and l/R = K,[HCl]
+ KzIX]
(8)
In this equation KI and K2 include the cell constant and mobilities of the ions, and [XI is the concentration of any impurity ions in solution. It is a t this point that a Guggenheim analysis3 is performed to extract k from the data without having to evaluate the cell constants, [TBCIO, [XI, or the ionic mobilities. It is pointed out to the student that this is typical of ~
a
STREITWIESER, A,, Chem. Rev., 56, 571 (1956). ROBERTSON, R. E., Canadian J . Cbm., 33, 1536 (1955).
the juggling an experimeutal scientist will do when he ran avoid unnecessary work. Solve (8) for [HCI] and substitute into (7).
Row evaluate (9) for R = Rl+s a t the time t+6, and for R = R t a t time t, where 6 is a constant increment of time. Subtract the second evaluation of (9) from the first and multiply the resulting expressioil by I
