KINETICS OF CHEMICAL REACTIONS I:
				IODIZATION OF ACETONE

A) Theoretical

	The purpose of this laboratory measurement is to determine the rate coefficient of the reaction of acetone and iodine. This problem belongs to the field of reaction kinetics.
	The subject of reaction kinetics is measuring rates of chemical reactions and interpreting their dependence on different parameters. The first step of such an investigation is establishing the stoichiometric equation as that expresses the conservation of both mass and electric charge, it must be valid both in equilibrium and  during a process:

										1)

There are N components in the reaction, Mi is the molecular formula and i.the stoichiometric coefficient of the i'th component. Stoichiometric coefficients are negative for reactants and positive for products.
	The customary definition of reaction rate  utilises the time derivative of  the concentration of any component in the reaction:

										2)

Generally, reaction rate can not be immediately measured, only concentrations (in most cases: some of the concentrations) are measurable as time proceeds.
	Reaction rate depends on concetration of its reactants according to the mass-action law:

										3)

		i is the order of the i'th reactant,
		i is the order of the reaction,
		k is the rate coefficient (with a usual loose term: rate constant),
		L is the number of reactants. Eq. 3) may have reactants absent from the 			stoichiometric equation, catalysers, for instance, and some of the 			reactants in the soichiometric equation may be absent from the			 rate equation 3).
	The reactions whose reactants both in the stoichiometric and in the rate equation are the same and, in addition, i= -i, for each reactant are called elementary reactions. Their mechanism is completely given by stoichiometry.
	The mechanism of a reaction is its decomposition to a network of simpler, possibly elementary, reactions. Generally, a component in such a network , both as reactant and as product, takes part in many reactions. Clearly, the time derivative of a component is the sum of contributions of the reactions it takes part in:

									4)
		i,j is stoichiometric coefficient of the i'th component in the j'th reaction,
		R is the number of reactions.
In most cases, not every component is independent that is its mass balance of type Eq. 4) can be constructed as a linear combination of mass balances of some other components. 	The mechanism can be declared to be one of the possible mechanisms of the reaction if the concentration vs. time curves got by  integration of differential equations of the independent components and by solution of the algebraic equations of the dependent components agree with the measured ones.
	It happens frequently with consecutive (serially connected) reactions that one reaction in the serial has much smaller rate coefficient than the others. In this case the rate of the total reaction can not surpass the rate of this slow process, that's why it is called rate limiting step. Of course, only the rate law of the rate limiting step can be determined experimentally in such a system.
	The rate of chemical reactions depends seriously on temperature. With thermal activation and for elementary or, at least, not too complicated reactions this dependence is described by Arrhenius equation:

										5)

		Ea is the activation energy of the reaction.

	Iodization of acetone is catalysed by both acids and bases. We are going to work with acid catalysis. The stoichiometric equation of the reaction:

						6)

It is very unlikely that this reaction would be elementary. Reaction kinetic measurements show that iodine is absent as reactant in the rate law and, in addition, bromination of acetone follows the same experimental rate law:

									7)

These experimental findings make likely and some spectroscopical measurements with NMR make sure that the rate limiting step of the reaction is formation of enol from acetone. The mechanism is as follows:

					      R1-R-1)
					R2)

	The rate laws for the previous reactions:

									R1)
									R-1)
									R2)

	There are six components in the mechanism: acetone (more precisely: its oxo-form), proton, enol-form of acetone, iodine, iodide anion and iodo-acetone. One can write the following differential equations of type Eq. 4) for the concentrations of the components:

									8a)
							8b)
									8c)
										8d)
										8e)
										8f)

It is obvious at first sight that time derivatives of concentrations of iodoacetone, iodide, iodine and proton are not independent of each other:

							9a)

One can reveal that the time derivatives of  acetone, enol and proton are connected to each other:
								9b)

Integrated forms of Eq. 9a) and 9b) clearly show that they are entirely mass balances:

							10a)
							10b)

Superscript 0 marks initial concentrations.
	Both equations 9) and 10) provide us four equalities, consequently the number of independent components is 6-4=2. This is further decreased to 1 by taking into account that there is a rate limiting step () as that creates a new mass balance:

						11)

, or, in integrated form
:
								12)

We have to measure the concentration of merely one component versus time.
	R1 remains rate limiting until concentration of iodine becomes too small. From that point R2 limits the rate, despite of its large rate coefficient, and the experimental rate law must contain the concentration of iodine, too.
	As Eq. 6) shows, catalyst proton is a product of the overall reaction, consequently, iodization of acetone is an autocatalytic reaction. The expextable selfaccelerating character will be manifested only while the concentration of H+ is smaller than that of acetone. Eq. 12) reveals that the sum of their concentration is constant in time , consequently the product of their concentrations reaches a maximum at the point of their equality.

B) Equipment
	We use a galvanic cell composed of two redox electrodes whose redox system is

			2I-   I2 + 2e-							13)

The belonging Nernst equation reads
								14)

				628mV is the standard potential of the electrode, 29.6mV/decade is  				its slope. The latter is ln10RT/zF at room temperature, for z=2.
A by-reaction has to be taken into account:
			 I2 + I-    I3-	,	=641dm3/mol		15)

	Luckily enough, the equilibrium of this process settles fast, however, concentrations needed in Nernst equation will be less than the gross concentrations. In order to avoid complex sub- and superscripts, let us use the following symbols:
		c1:	gross concentration of Br-
		c2:	gross concentration of Br2
		x:	concentration of I3- in the reference half cell
		xM:	concentration of I3- in the measuring half cell
		y:	concentration of iodoacetone in the measuring cell
Now, the equilibrium constant of by-process (Eq. 15)) can be expressed both in the reference:
									16)

and in the measuring half cells:
							17)

. The Nernst equations are

							18)

and 
						19)

, respectively. The electromotive force (E) of the galvanic cell is the difference of electrode potentials of the half cells:

				20)

	Eq. 16) can be solved for x separately and the pair of Equations 17) and 20) can be solved for xM-and y. The latter problem needs a suitable numerical treatment that can be found in the laboratory. A program calculates concentration of iodine in the measuring half cell () for each triad E, c2 and c1.
	The galvanic cell is thermostated and the liquids are stirred by magnetic stirrers.

C) Experimental
	Our goal is to determine the rate constant for R1 and check the order of iodine in R2.
	1. Start the thermostat.
	2. Assemble 98cm3 solution from a KI-containing I2 solution (nominal gross concentrations: c1=0.03mol/dm3, c2=0.01mol/dm3), from a HCl solution of concentration 0.5mol/dm3 and from distilled water. The real concentration of iodine can be determined by titration with sodium thiosulfate:

							21)

Indicator is a freshly made solution of starch.
	3. Divide the solution into equal volumes and pour them into the thermostated vessels. Start the magnetic stirrers. Immerse a flat platinum electrode into each vessel and connect the half cells by a salt-bridge filled up with 2.5M KNO3 solution.
	4. Connect the electrodes to the input sockets of a precision pH-meter working in mV mode. (You can not read polarity from some meters, however, you can decide it, if you want, with the aid of a Weston normal cell.) Electromotive force should be zero but it is usually not. Note the value.
	5. Pipette 1cm3 acetone (=0,789g/cm3) into the measuring and 1cm3 distilled water into the reference half cell at the same time. Mix the solutions with a glass-rode and read electromotive force in intervals of one minute.
	6. Calculate concentration of iodine for each point you measured.
	7. Plot the graph ciodine vs. time. Read reaction rate of R1 and calculate the rate coefficient. As both acetone and the acid have 20-100 times larger quantities than iodine, you may regard their concentrations to be constants.
	8. Plot the ln ciodine vs. time. If the order of  iodine is really one you can observe a straight line in the region where R2 is rate limiting. Mark this region on your plot.