Chemistry 150

Please have the following pages ready before class on Thursday, March 7. As usual, please write an abstract and paper-clip it to the front of your individual writeup. The abstract and the carbon-copy pages of the write-up is due in class on Thursday, March 14.

Lab 5: Determination of the rate law of a reaction using visible wavelength spectrophotometry

As noted in class, in order to determine a rate law in the form of:

rate = k [A]^m[B]ⁿ

where k is the rate constant and A and B are chemical species in the reaction, you need to measure the concentrations of A and B. Due to Beer’s Law (the absorbance of a solution is proportional to the concentration of a light-absorbing substance in the solution), you can use a spectrophotometer and colored substances to watch either the colored reactant disappear or the colored product appear.

The reaction for which you will determine the rate law is:

Cr³⁺ (aq) + EDTA (aq) ® Cr³⁺-EDTA complex (aq)

The chromium (III) ion is green and the complex is purple, so using the spectrophotometer should allow us to monitor the extent of the reaction. The graph of the absorbance of both the complex and the chromium (III) ion is given below:

EDTA stands for “ethylene diamine tetraacetic acid” and looks like:

which is why its name is abbreviated.

The rate law for the reaction has the form:

rate = k [Cr³⁺]^m [H⁺]ⁿ [EDTA]^p

Because EDTA has many hydrogen atoms that can dissociate and thus become many different anions, [EDTA] is going to be kept constant throughout the reaction. What you will determine is m, n and k.

Here is how you will determine those three numbers:

Consider the generic case of the reaction aA ® bB.

The rate of appearance of B is written as (D[B]/Dt), which is equal to the reaction rate:

rate = D[B]/Dt

but the rate is also found using the rate law:

rate = k [A]^w

so, combining the equations, you get:

D[B]/Dt = k [A]^w

Taking the base-10 logarithm of both sides (yes, I know in class we were using the natural logarithm, but there is a reason for this, I promise):

log (D[B]/Dt) = log (k [A]^w) and using the properties of logarithms:

log (D[B]/Dt) = w log [A] + log k

note the form: y = m x + b

So if you plot log [A] (x-axis) against log (D[B]/Dt) (y-axis), the slope of the resulting line should give you the order of the reaction in A.

You are going to do this to find m for [Cr³⁺], n for [H⁺] and k for both.

Part 1. Purpose

One sentence summarizing what you hope to accomplish in this lab (see title).

State the net ionic equation of the reaction to be studied.

Part 2. Materials and methods

Chemicals needed:

0.100 M disodium EDTA

0.100 M Cr(NO₃)₃

0.100 M NaOH

0.100 M HCl

distilled water

Equipment needed (sketch the setup):

Spectrophotometer

Stopwatch

A 10 mL EDTA dispenser

1000 and 5000 microliter pipetters (shared between all of those groups)

Five small beakers

Several test tubes for the spectrophotometer

Hot plate

pH meter

Part 3. Procedure

1. Turn on the spectrophotometer and set the wavelength to 545 nm.

2. Label 4 beakers and fill each according to the following recipe:

Beaker	0.100 M sodium EDTA (mL)	0.100 M NaOH (mL)	0.100 M HCl (mL)	distilled water
1	10.00	1.60	0	0
2	10.00	0.40	0	1.20
3	10.00	0	0	1.60
4	10.00	0	0.40	1.20

3. Initially, zero the spectrophotometer with nothing in the sample chamber. Fill one test tube with distilled water to use a 100%T reference for the spectrophotometer. Make sure this tube reads 100% transmittance on the spectrophotometer and leave on standby in absorbance mode (if you have a digital spectrophotometer)

4. As you start the timer, add 0.40 mL of the chromium (III) nitrate solution to beaker 1, and swirl for about 10 seconds to mix. Do not warm the beaker with your hands!

5. Pour enough of the contents of beaker 1 into the cuvette so that you will get a good reading (roughly two-thirds of the cuvette’s volume) on the spectrophotometer and place the cuvette into the spectrophotometer. Set the spectrophotometer on absorbance (A) mode.

6. Read and record the absorbance of the sample at 30-second intervals for 15 minutes.

7. Sometime at the beginning of the trial, measure and record the pH of the solution without interfering with the absorbance recording.

8. Measure and record the pH of the solution at the end of 15 minutes.

9. Repeat steps 4 through 7 with beakers 2, 3 and 4. Don’t forget to zero the spectrophotometer in between beakers!

10. When done, combine all of the solutions including what remains in each beaker into one beaker and place in a bath of boiling water for 10 minutes. Measure the absorbance of this solution and record as A(infinity).

11. Turn off the spectrophotometer and place all of the solutions in the chromium waste beaker in the hood.

Part 4. Original data and preliminary analysis

Set up four separate tables, one for each beaker’s conditions, that lists the time and absorbance. Make sure there is enough room for at least thirty-one measurements of time and absorbance.

Be sure to record the pH of the reaction solution at the beginning and the end of each trial.

Be sure that you record A(infinity).

Part 5. Calculated results

Note: while you can do the following calculations and plotting by hand, a spreadsheet and graphing program will make this part much easier.

For each trial, set up a table that has the following headings:

time (s)

A (trial 1)

log (A (trial 1)

A(infinity) – A (trial 1)

delta A/delta t

log (delta A/delta t)

Use the spreadsheet’s built-in mathematical functions to do all of these calculations. For the “log”, make sure you use the base-10 logarithm function.

First plot: Make a graph of time (x-axis) versus A(infinity) – A(trial x) (y-axis) for all of the beakers (all the trials) on the same graph (use different series). Be sure to use a different line pattern to distinguish the different beakers’ curves, and use the “series name” field to identify them by the pH of the solution

To calculate the fifth column, “delta A/delta t”, you might think you should drawn the tangent to the curve of the graph at this point and use the slope of the tangent, as shown below:

However, we are going to use the “triangle approximation”. Using this approximation, you are going to essentially “connect the dots” between the data points on the absorbance/time graph. Using the spreadsheet functions, and starting with the second row entry in the fifth column, define a function that will subtract the previous row’s absorbance from that row’s absorbance, then divide it by that row’s time minus the previous row’s time.

For instance, if your time information is in column A (starting with cell A1) on an Excel spreadsheet and your absorbance information is in column B (starting with cell B1), define column C as the “delta A/delta t” column. Start with cell C2 = (B2-B1)/(A2-A1), and then fill down the C column to the last entry.

Second plot: Plot the third column of all four trials on the x-axis against the sixth column of all four trials on the y-axis as overlays on the same graph. All four “curves” should have roughly the same slope. Be sure to use a different line pattern to distinguish the different beakers’ curves, and use the “series name” field to identify them by the pH of the solution.

Determine the order of the reaction with respect to the chromium (III) ion concentration from this plot.

Determine four values of the rate constant k from this plot, knowing that the [EDTA] = 0.085 M in the final solution. Give a mean and standard deviation for k.

Back on the first plot, find and draw a horizontal line across the plot so that the line intersects all four curves. Determine the time for each beaker where the curve crosses the horizontal line you have drawn. From the calculations in the table above, find the rate of reaction at these times. Calculate log(reaction rate).

Third plot: Graph log(reaction rate) against –pH (why? because –pH = log [H⁺] by definition).

Determine the order of the reaction with respect to the hydrogen ion concentration from this plot.

Attach these graphs to this writeup.

Part 6. Questions

1. Why didn’t I simply have you set the spectrophotometer on the maximum absorption for the chromium (III) ion, instead of the Cr-EDTA complex? I mean, it would have saved you the measurement of A(infinity) and the subtraction.

2. Why does the addition of OH^- to the solution change the [H⁺]?

3. Even without doing the experiment, would you think the error would be greater in determining the order of the reaction for [Cr³⁺] or the order of the reaction for [H⁺]? Explain your choice!

4. Did you introduce any error as a result of using the triangle approximation, rather than drawing the actual tangent to the curve in the determination of the slopes of the absorbance curves? Explain if this was a significant problem.

Part 8. Conclusion

State the order of this reaction with respect to the chromium ion and the hydrogen ion. State the value of k (both mean and standard deviation).

Use questions 3 and 4 to discuss if there were any significant systematic or random errors in this experiment. For instance, if you have an order for some substance of 0.345, you should explain why you might not have gotten an integral value.

Comment on the ease of use of the pH meter and the spectrophotometer. Suggest any changes to the procedure that would aid the next users of these devices.

Abstract

Summarize the main results. State any significant errors and their possible source.