determination of the rate equation for a reaction

THE DETERMINATION OF THE RATE EQUATION FOR A REACTION

The purpose of this exercise is to illustrate the calculations you will be doing when you study the reaction of Hydrogen Peroxide and Iodide ion in the lab. In this exercise, the reaction under consideration is between ammonium cation and nitrite anion as indicated in the following equation reaction equation:

NH41+(aq) + NO2

1-(aq) → N2(g) + 2 H2O(l) Eqn. 1.

For purposes of this exercise, it is assumed that the rate law for the reaction above has the form:

Rate = k [NH41+]a[NO2

1-]b

A set of eight experiments was undertaken to determine:

a. the numerical value of the exponents a. and b. in the reaction equation (in other words the order of the rate law, and

b. the numerical value of the rate constant, k.

In these experiments, the initial concentrations of ammonium cation and nitrite anion were varied in a systematic fashion and the initial rate of the reaction was determined. The data obtained from those experiments, taken from Chemistry: The Central Science by Brown, LeMay and Bursten, Eighth Edition, is displayed in the follow table.

Rate for Date the Reaction of Ammonium cation and Nitrite anion in water at 25°C

Experiment Number Initial NH41+

Concentration (M) Initial NO2

1- Concentration (M)

Observed Initial Rate (M/sec)

1 0.0100 0.200 5.4 x 10-7 2 0.0200 0.200 10.8 x 10-7

3 0.0400 0.200 21.5 x 10-7

4 0.0600 0.200 32.3 x 10-7

5 0.200 0.0202 10.8 x 10-7

6 0.200 0.0404 21.6 x 10-7

7 0.200 0.0606 32.4 x 10-7

8 0.200 0.0808 43.3 x 10-7

The important thing to note about the data in the table is that it can be divided into two subsets of data. In reactions 1 – 4, the concentration of nitrite anion is being held constant and only the concentration of ammonium cation is being changed. That means that the dependence of the rate of reaction on ammonium cation can be determined by analyzing the data for reactions 1 - 4. Similarly, in reactions 5 – 8, the concentration of ammonium cation is being held constant and only the concentration of nitrite anion is being changed. That means that the dependence of the rate of reaction on nitrite anion can be determined by analyzing the data for reactions 5 - 8.

Principles of Chemistry II Kinetics Pre-Laboratory Exercise

CALCULATIONS

Note1: Use Excel to complete all the calculations. All plots should be printed and submitted as part of the pre-lab exercise. The template containing the calculations should be saved under the name PRE_PEROX. Excel functions should be used to determine the slope and the intercept of all linear plots.

Note2: The calculations can also be completed using a TI-graphing calculator. You should also do the calculations using your calculator for two reasons. First, it is good practice for using the calculator. Second, it is a good way to check the Excel calculations.

1. Construct a table of your results with the following headings: Reaction Number Initial [NH4

1+] Initial [NO21-] Rate of Reaction

2. Construct another table of results by taking the log of the above quantities:

Reaction Number Log Initial [NH41+] Log Initial [NO2

1-] Log Rate of Reaction

3. Using Excel to plot Log Rate along the y-axis against Log [NH41+] along the x-axis*. Use

Excel functions to calculate the slope and the intercept of this line. The slope of this line is equal to the value of exponent "a" in the rate equation. Round the slope to the nearest integer. The intercept is equal to Log K′app. Using the relationships derived on the next page, calculate a value for the rate constant k from Log K′app. Use the data from reactions 1, 2, 3 and 4 for this plot. Starting from a general statement of the rate law for this reaction: Rate = k [NH4

1+]a[NO21-]b

For solutions 1, 2, 3 and 4, [NO2

1-] is constant Therefore: Let K′app = k [NO2

1-]b After substituting: Rate = K′app [NH4

1+]a Take the logarithm of the equation: log Rate = log K′app [NH4

1+]a

Separate the terms being multiplied: log Rate = log K′app + log [NH4

1+]a Remove the exponentiation: log Rate = a log [NH4

1+] + log K′app The general equation for a straight line is: y = mx + B


Defining: y = log Rate

m = a (slope) x = log [NH4

1+] B = log K′app (intercept)

Thus "a" and B can be determined by plotting log [NH4

1+] on the x-axis vs. log Rate on the y-axis for solutions 1, 2, 3, and 4. and drawing the best possible straight line through the data. The exponent "a" is equal to the slope of the line, and log K′app is the intercept. The rate constant k can be calculated from K′app by recalling the definition of that variable.

4. Generate the same graph and complete the same linear regression calculations as in questions 3 above using your graphing calculator. a. Enter the data from experiments 1 -4 for the initial concentration of ammonium cation

([NH41+]) into L1 and the data for the initial rate into L2.

b. Take the log of contents of the L1 data vector and store it L3, and take the log of the contents of the L2 data vector and store it in L4.

c. Generate a graph of the data with L3 on the x-axis and L4 on the y-axis. Make sure that a graph of the data vectors is turned on (STAT PLOT). Use STAT EDIT to view the minimum and maximum values in the two data vectors. Use WINDOW to set the minimum values to be graphed. Remember this graph is in the third quadrant, so it might look a little strange!

d. Use STAT CALC lin reg to calculate the slope and intercept of the best fit line through this data.

5. Using Excel plot Log Rate along the y-axis vs Log [NO2

1-] along the x-axis*. Use Excel functions to calculate the slope and the intercept of this line. The slope of this line is equal to the value of "b" in the rate equation. Round the slope to the nearest integer. The intercept is equal to Log K″app. Using relationships for Log K″app similar to those derived above for Log K′app, calculate a value for the rate constant k from Log K″app. Use the data from reactions 5, 6, 7, and 8 for this plot.

A derivation similar to that done above may be performed for the determination of the exponent "b". You should derive the relationships between k, K″app and "b" for yourself.


6. Generate the same graph and complete the same linear regression calculations as in questions 3 above using your graphing calculator. a. Enter the data from experiments 5 -8 for the initial concentration of nitrite anion

([NO21-]) into L1 and the data for the initial rate into L2.

b. Take the log of contents of the L1 data vector and store it L3, and take the log of the contents of the L2 data vector and store it in L4.

c. Generate a graph of the data with L3 on the x-axis and L4 on the y-axis. Make sure that a graph of the data vectors is turned on (STAT PLOT). Use STAT EDIT to view the minimum and maximum values in the two data vectors. Use WINDOW to set the minimum values to be graphed. Remember this graph is in the third quadrant, so it might look a little strange!

d. Use STAT CALC lin reg to calculate the slope and intercept of the best fit line through this data.

7. Using the values of "a" and "b" obtained above, the rate expression on the first page of the

experiment and your data from the table in step 1 above, calculate a value for the rate constant k for each solution.

8. Using the results of step 7, above calculate an average value for the rate constant k and compare this value of k to the value of k obtained from the plots in steps 9 and 10 above.

9. Write a completed expression for the rate of reaction for this reaction. For a value for k use

the average of the three determinations.

* In these two graphs, the x-axis must start at zero; the y-axis does not need to start at zero.


REPORT FORM

Rate of Reaction

1. Table I:

Reaction Number Initial [NH41+] Initial [NO2

1-] Rate of Reaction 1 2 3 4 5 6 7 8

2. Table II:

Reaction Number Log Initial [NH41+] Log Initial [NO2

1-] Log Rate of Reaction 1 2 3 4 5 6 7 8

3. What is the slope of the line plotted in calculation steps 3 and 4. Round off to the nearest integer. This is the value of exponent "a" in the rate equation.

4. What is the slope of the line plotted in calculation steps 5 and 6. Round off to the nearest integer. This is the value of exponent "b" in the rate equation,

5. Calculate the value of the specific rate constant k from the y-intercept of the line plotted in calculation steps 3 and 4. The value of the y-intercept equals Log K′app. The relationship between K′app and k was derived earlier.

6. Calculate the value of the specific rate constant k from the y-intercept of the line plotted in calculation steps 5 and 6. The value of the y-intercept equals Log K″app. The relationship between K″app and k was derived earlier.


7. Calculate an average value for the specific rate constant k from the 8 different values calculated in calculation step 12.

8. Calculate an average value of the specific rate constant k using the values calculated in

steps 5, 6, and 7 of this report. 9. Write the complete rate of reaction expression for this reaction.

determination of the rate equation for a reaction

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