Spectrophotometric determination of an equilibrium constant

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Experiment 18:

Spectrophotometric Study
of an Equilibrium Reaction

 

 

 

Fe3+ and SCN- ions react with each other to spectrophotometric determination of an equilibrium constant form an orange-red colored product. This is a reaction which reaches an equilibrium: although you might mix Fe3+ and SCN- in the correct stoichiometric ratio for reaction, the reactants are never completely converted to the colored product. Rather, as the concentration of product builds up, product molecules convert back into Fe3+ and SCN-, until a steady-state is reached (the concentrations of reactants and products no longer change with time).

 

In this experiment you prepared several mixtures of different amounts of the reactants, and measured with a spectrophotometer the amount of product that formed in each case. From your data, you are to determine which of the following reaction stoichiometries is correct:

 

1.

2.

3.

 

 

The method used to determine which stoichiometry is correct involves using the three potential equilibrium constant expressions for the three possible reactions. Since only one equilibrium of the stoichiometric ratios can be correct, it follows that only one of the possible equilibrium constant expressions can be correct. By filling in the data for your several experiments into each of the possible equilibrium constant expressions, only one equilibrium constant expression should lead to a value which is effectively "constant" over all the experiments. The equilibrium constant expressions corresponding to the three possible stoichiometries being considered are given on Page 139 of the lab manual.

Calculations 

 

Because of the complexity of the calculations in this experiment, we won't be able to provide you with a totally complete sample lab report. We will illustrate, however, all the important points.

 

The only data recorded in the lab for this experiment are the transmittances of your five Fe/SCN mixtures. Realize, however, that some data is implied in the Procedure part of the experiment. For example, the concentrations of the stock solutions, as well as the volumes of the stock solutions used for the various mixtures, are found as part of the procedure. Also note that the data necessary to plot the required calibration curve for the colored product is provided in the Calculations section of the experiment.

 

Page 181, Part II

 

A sample calculation is to be done for Solution #3 of the procedure.

 

Let's assume that Solution #3 had a %Transmittance of 45.1% T when measured with the spectrophotometer.

 

A. Absorbance

 

 
A = 2 - log (%T) = 2 - log (45.1) = 2 - 1.654 = 0.346
 

 

 

B. Concentration of Product (from Beer's Law Plot)

 

Data for plotting a Beer's Law calibration curve for the colored product of this reaction is found on Page 142. You should review Experiment 15 for how to plot this graph and how to use it to determine concentration.

 

Using the graph I prepared from the data on Page 142, the absorbance I calculated in Part IIA above (0.346) corresponds to a concentration of 6.961 X 10-5M for the colored product in my Mixture #3.

 

C. [Fe3+]init in Solution #3

 

The concentration we calculated in Part IIB above was for the colored product of the reaction. Now, in this part and the next, we have to calculate the initial concentrations of the reactants that were taken, which led to the production of this amount of product. The two stock solutions-Fe3+ and SCN---were both at a concentration of 0.00200 M (2.00 X 10-3M), but we used different amounts of these two stock solutions (plus some water) in each of the mixtures. It is important to use the correct composition when calculating each of your solutions.

 

Solution #3 had the following composition:

 

  • 5.00 mL of 0.00200 M Fe3+ solution
     
  • 1.50 mL of water
     
  • 3.50 mL of 0.00200 M SCN- solution

 

This is a total volume of 10.00 mL for Solution #3. So the initial concentration of Fe3+ in Solution #3 is

 

 

 

 

 

D. [SCN-]init for Solution #3

 

The composition of Solution #3 is indicated in Part C above. The concentration of SCN- in Solution #3 is

 

 

 

 


E. [Fe3+]eq in Solution #3

In Part IIC above, we calculated that the initial concentration of Fe3+ was 0.00100 M (1.00 X 10-3M )when we first mixed the Fe3+, SCN-, and water together. Then the reaction occurred. In Part IIB, we determined from our graph that the concentration of product produced by the reaction was 6.961 X 10-5M. Note that production of the product uses up some of the Fe3+ taken initially.

Since we are assuming that all the possible reactions stoichiometrically only involve one Fe3+ reacting to form each product molecule, the concentration of Fe3+ remaining unreacted at equilibrium must be

 

 

 

 

F. Calculations Based On Trial Reaction 1

In the next three portions of the calculations (Parts IIF, G, and G), we are going to calculate values for the equilibrium constant based on Solution #3, using each of the possible stoichiometries and each of the possible trial equilibrium constant expressions. Each of the trial reactions involves a different stoichiometric coefficient for SCN- in the reaction.

1. [SCN-]eq in Solution #3 Based on Reaction 1

In this section, we are going to calculate [SCN-]eq and a value for Keq using the first possible stoichiometry:

 

 

               

 

 

The initial mixture taken to make up Solution #3 contained SCN- ion at a concentration of 0.000700 M (7.00 X 10-4M). We found from our graph, that the concentration of colored product was 6.961 X 10-5 M.

Since in Reaction 1 we are assuming that each product molecule results from the reaction of only one SCN- molecule, the concentration of SCN- remaining unreacted at equilibrium is just

 

 

 

 

2. Keq for Solution #3 using Reaction 1

For Reaction 1,

 

 

               

 

 

the equilibrium constant expression would have the form

 

 

 

 

Using the values we have calculated in Parts IIB, IIE, and IIF1 for the concentrations of the three species, we can calculate Keq as

 

 

 

 

 

Note that although we have preserved an extra digit in some of the intermediate calculations, the final answer for Keq should be rounded off to three significant figures. Each of the reagent concentrations was only known to three significant figures, and the spectrophotometer scale could only be read to a maximum of three significant figures.

 

G. Calculations Based on Trial Reaction #2

In this part of the calculations, we are going to test the second possible trial reaction stoichiometry

 

 

               

 

 

In this trial reaction, a stoichiometric factor of two has been introduced for SCN- (one Fe3+ reacts with two SCN-). This factor of two will enter into our calculations of the amount of SCN- remaining at equilibrium. This factor of two (as an exponent) will also affect the trial equilibrium constant for this reaction (which we'll be calculating below).

1. [SCN-]eq in Solution #3 using Reaction 2

The initial mixture taken to make up Solution #3 contained SCN- ion at a concentration of 0.000700 M (7.00 X 10-4M). We found from our graph, that the concentration of colored product was 6.961 X 10-5M. Each molecule of product, in this trial reaction, requires two SCN- to react. So if we have measured that 6.961 X 10-5M has formed, then twice this number of SCN- must have reacted. So the amount of unreacted SCN- present at equilibrium is

 

 

 

 

2. Keq for Solution #3 Using Reaction 2

For Reaction 2, we consider that one Fe3+ reacts with two SCN-

 

 

               

 

 

This factor of two not only enters the stoichiometric calculations (See IIG1 above), but also enters (as an exponent) into the expression for the equilibrium constant for the reaction. For the reaction above, the equilibrium constant expression would be

 

 

 

 

The concentration of SCN- is squared in this equilibrium constant expression, reflecting the stoichiometric factor of two.

In Part IIE, we calculated that the equilibrium concentration of Fe3+ was 9.30 X 10-4M. In Part IIG1 above, we calculated that the equilibrium concentration of SCN- was 5.61 X 10-4M. And in Part IIB, from our graph, we determined that the concentration of product at equilibrium was 6.961 X 10-5M. Filling all this into the expression for the equilibrium constant for Reaction 2 gives

 

 

 

 

 

 

Note that we got a completely different (much larger value) for Keq using the different stoichiometry and different expression for Keq.

 

H. Calculations Based On Trial Reaction 3

In this part of the calculations, we are going to test the third possible trial reaction stoichiometry

 

 

               

 

 

In this trial reaction, a stoichiometric factor of four has been introduced for SCN- (one Fe3+ reacts with four SCN-). This factor of four will enter into our calculations of the amount of SCN- remaining at equilibrium. This factor of four (as an exponent) will also affect the trial equilibrium constant for this reaction (which we'll be calculating below).

1. [SCN-]eq in Solution #3 Using Reaction 3

The initial mixture taken to make up Solution #3 contained SCN- ion at a concentration of 0.000700 M (7.00 X 10-4M). We found from our graph, that the concentration of colored product was 6.961 X 10-5M. Each molecule of product, in this trial reaction, requires four SCN- to react. So if we have measured that 6.961 X 10-5M has formed, then four times this number of SCN- must have reacted. So the amount of unreacted SCN- present at equilibrium is

 

 

 

 

 

2. Keq for Solution #3 Using Reaction 3

For Reaction 3, we consider that one Fe3+ reacts with four SCN-

Fe3+ + 4SCN- = [Fe(SCN)4]-

 

This factor of four not only enters the stoichiometric calculations (See above), but also enters (as an exponent) into the expression for the equilibrium constant for the reaction. For the reaction above, the equilibrium constant expression would be

 

 

 

 

The concentration of SCN- is raised to the fourth power in this equilibrium constant expression, reflecting the stoichiometric factor of four.

In Part IIE, we calculated that the equilibrium concentration of Fe3+ was 9.30 X 10-4M. In Part IIH1 above, we calculated that the equilibrium concentration of SCN- was 4.22 X 10-4M. And in Part IIB, from our graph, we determined that the concentration of product at equilibrium was 6.961 X 10-5M. Filling all this into the expression for the equilibrium constant for Reaction 2 gives

 

 

 

 

 

 

Page 184, Parts III A, B, and C

The tables on Page 147 may seem overwhelming at first glance, but when you analyze them, it turns out that they're not too bad!

 

First of all, after completing Part II (see above), you have already done all the calculations for Solution 3. So fill this information into the table.

Then realize that some of the data repeats in Parts A, B, and C. The first six columns in each Part (A,B, C) are the same for the three trial reactions. It is only the [SCN-]eq and Keq that vary. The data vary for each solution (1,2,3,4,5) within a Part, however.

Page 184, Parts III D and E

 

D. Which Reaction Occurs?

Looking at your tables on Page 147, you should notice that the five values for Keq calculated should be effectively the same (within experimental error) for one of the sections of data (A, B, or C). There may be a slight variation in values (in the third significant figure) for the correct choice, but you will notice a major variation (by factors of 10, 100, or even 1000) in the other choices.

E. Average Value

Come on, you know how to do this!! Add up the five values for Keq and divide by 5!

 

Page 185, Part IV

Question:

What do you think? We'll accept any answer that is well thought out and well presented!





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