Here k is the rate constant and alpha and beta are the orders of the iodide and persulfate respectively.
The iodine formed in the reaction will combine with the iodide according to the following equilibrium reaction to form the triiodide ion
The equilibrium constant for this reaction at 298 Kelvin is 697. Consequently, at the beginning of the reaction described in equation 1, we will assume that all of the iodine will be in the triiodide ion form. You can then use the uv absorption of triiodide ion at 288 nm or 352 nm to follow the appearance of the iodine using equation 4. Here epsilon = 34,500 at 290nm (23,500 at 350nm), l = 1 cm and Ab is the absorbance of the triiodide ion. Equation 2 can then be rearranged to give equation 5 that can be used with experimental data to evaluate the rate law.
Mathematically it is convenient to evaluate the orders (alpha and beta) using a logarithmic form of equation 6.
This is accomplished experimentally by holding the initial concentration of one of the reactants constant and varying the concentration of the other and then reversing the process for the other reactant.
A linear regression can then done on each set of data to evaluate the value for the respective order.
For example, alpha can be evaluated by measuring the initial rates of reaction where the persulfate ion is kept constant and the iodide ion is changed by finding the slope of a linear regression analysis using equation 7.
An alternative method for finding alpha ( or beta with the appropriate set of data) is to use equation 8 with the same data as would be used for equation 7. Note that you must solve for alpha using all possible pairs (i.e. 1 and 2, 1 and 3, .. 1 and n,....(n1) and n) of data in order to properly determine the standard deviation of alpha.
Once alpha and beta have been determined, k can be evaluated using all of the measured rates and equation 2.
This reaction rate constant is dependent upon ionic strength and it will be necessary to keep the ionic strength constant by using appropriate sodium chloride solutions to maintain the constant ionic strength. The equation for calculating ionic strength is shown in equation 9. Here M_{i }refers to the Molarity of the ionic species(i) and z_{i} refers to the charge on the ionic species(i).
Discussion of the dependence of the rate constant upon ionic strength is not found in Barrow, but is found in other physical chemistry texts which discuss the effect of ionic strength on rate constants (e.g., Laidler). Note that a in equation 10 is not the same as a in the previous equations. At 298 Kelvin the alpha in equation 10 is 1.179. You will be expected to find the rate constant at zero ionic strength by plotting the ln k vs the square root of the ionic strength. Compare the slope of that line to 2 a z_{A }z_{B} .and discuss the results.
In addition, comment in the post
laboratory
report on the obvious curvature in the data plotted in
figure
151 of Barrow that has been ignored in the discussion of this reaction
as well as following the reaction at 414 nm, see Example 151.
Representative
Table of Concentrations
KI 
NaCl 
K_{2}S_{2}O_{8} 
NaCl 


alpha


















beta 

















Ionic strength 
















2. Make a stock solution of 0.05 M potassium iodide and one 0.05 M sodium chloride. This sodium chloride solution will be used to maintain a constant ionic strength when the amount of potassium iodide is varied.
3. Make a stock solution of 0.025 M potassium persulfate and make a 0.075 M sodium chloride solution that will be used to maintain a constant ionic solution when the amount of potassium persulfate is varied.
4. Follow the spectrometer operating
instructions
that are linked to the lab's home page (following the link for this
experiment).