Fourth order reaction rate law

Reaction Order and Rate Laws Hands-On Labs, Inc. Version 42-0195-00-02

Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will need and set aside a safe work space in which to complete the exercise.

Experiment Summary:

You will determine how chemical concentration affects the rate of a reaction, calculate the order of the reactants, and define the rate law for a reaction between hydrochloric acid (HCl) and sodium thiosulfate (Na2S2O3). Additionally, you will define zero, first, and second order reactions.

EXPERIMENT

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Learning Objectives Upon completion of this laboratory, you will be able to:

● Define chemical kinetics and reaction rates, and discuss why they are important for understanding chemical reactions.

● Differentiate between independent and dependent reaction rates and how they are graphically represented.

● Define a rate law and how it can be used to determine reaction orders.

● Examine the effects of varying reactant concentrations in a chemical reaction.

● Analyze data to determine the order of a reaction rate.

● Summarize the rate law for an observed reaction.

Time Allocation: 1.5 hours

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Experiment Reaction Order and Rate Laws

Materials Student Supplied Materials

Quantity Item Description 1 Bottle of distilled water 1 Dish soap 1 Sheet of white paper 1 Source of tap water 1 Timer, clock, or watch with second hand

HOL Supplied Materials

Quantity Item Description 1 Pair of gloves 1 Pair of safety goggles 1 Permanent marker 1 Test tube cleaning brush 1 Well plate - 24 1 Experiment Bag: Reaction Order and Rate Laws

1 - Dropper bottle, empty 15 mL 1 - Hydrochloric acid, 1 M, 15 mL in dropper bottle 2 - Short, thin-stem pipets 1 - Sodium thiosulfate, 0.3 M, 15 mL in dropper bottle

Note: To fully and accurately complete all lab exercises, you will need access to:

1. A computer to upload digital camera images.

2. Basic photo editing software, such as Microsoft Word® or PowerPoint®, to add labels, leader lines, or text to digital photos.

3. Subject-specific textbook or appropriate reference resources from lecture content or other suggested resources.

Note: The packaging and/or materials in this LabPaq kit may differ slightly from that which is listed above. For an exact listing of materials, refer to the Contents List included in your LabPaq kit.

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Experiment Reaction Order and Rate Laws

Background Chemical Kinetics

Chemical kinetics is the study of how quickly chemical reactions occur, and the factors that affect this speed. The speed of a chemical reaction is called the reaction rate. The reaction rate is a measure of the change in reactant concentration per unit of time.

Reaction rates may be almost instantaneous, such as the chemical reaction that occurs when our eyes adjust for night vision. In order for our eyes to see in dark conditions or at night, a chemical called rhodopsin absorbs a photon and isomerizes, then breaks down into metarhodopsin II and sends a signal to the brain in less than a second. Alternatively, reaction rates may be billions of years long, such as in the formation of diamonds. Determining the reaction rate of a chemical reaction is useful to scientists in many ways, including the development of drugs and the manufacturing of chemicals. See Figure 1.

Figure 1. An almost-instantaneous reaction rate of hydrogen and oxygen causes an explosion which gives the space shuttle enough energy to propel into the outer orbit of Earth. © Jose

Antonio Perez

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Experiment Reaction Order and Rate Laws

Reaction Rates may be Independent or Dependent of the Concentration of Reactant

Reaction rates may be constant with the changing concentration of the reactants, or they may be dependent on the reactant concentration. If the reaction rate is independent of the concentration, then the relationship between the amount of reactant consumed and time is linear. If the reaction rate is dependent on the concentration of the reactant, then the relationship is curvilinear, as it is dependent on the changing amount of reactant. See Figures 2A and 2B. In Figure 2B, the reaction rate is changing (getting slower) as the amount of reactant is consumed.

Figure 2. Reaction rate examples. A. A hypothetical example of the reaction rate that is independent of the reactant concentration. In this hypothetical example, the amount of

reactant is used at a rate of 0.2M every 50 seconds. B. A hypothetical example of the reaction rate that is dependent on the reactant concentration. The amount of reactant used per time is

constantly changing with concentration.

When chemists process food, they use knowledge of

chemical kinetics to understand how foods decompose and what increases or decreases the rate

of decomposition.

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Experiment Reaction Order and Rate Laws

The dependence of the reaction rate upon reactant concentrations is expressed in the “Rate Law” equation.

Rate Law Equation

Where k is the rate constant, [A] and [B] are the concentrations of reactants; m and n are exponents that reflect how the rate depends on the reactant concentrations. The exponents m and n give the “order of the reaction.” Thus, A is said to be of mth order and B to be of the nth order. For example, if m is two, chemical A would be a second order reactant, and if n was four, B would be a fourth order reactant. The rate constant and the exponents m and n cannot be determined merely by looking at the balanced chemical equation; rather, they must be determined experimentally.

The sum of m plus n is the overall reaction order. The exponents m and n are usually positive whole numbers, but they may be fractions or may even be negative numbers. In the example given previously, if m was two and n was four in the rate law equation, then the overall reaction order would be six.

Orders of Reactants

The order of the reactant gives the following information about how the concentration of the reactant changes the rate:

● Zero Order: If a reactant has an order of zero, the rate is independent of the reactant’s concentration and that reactant does not appear in the rate law (because anything raised to the zero power is one). Refer to Figure 2; view the graph that shows when the reaction rate is independent of the concentration rate. For example, consider “Reaction Example 1” as shown below. The order of CO is zero and therefore [CO] does not appear in the rate law.

Reaction Example 1:

● First Order: When a reactant is first order the reactant will have an exponent of 1. For example, consider “Reaction Example 2,” in which both F2 and ClO2 have an order of 1. Increasing the concentration of F2 or ClO2 increases the rate and decreasing the concentration of F2 or ClO2 decreases the rate. For instance, if the concentration of F2 is doubled, the rate will also double. If the concentration of F2 is halved, the rate will also be cut in half. Therefore, the rate is directly proportional to any reactant that is first order. Refer to Figure 2; view the graph that shows when the reaction rate is dependent of the concentration rate.

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Experiment Reaction Order and Rate Laws

Reaction Example 2:

● Second Order: Reactants that are second order will appear in the rate law as the concentration of the reactant squared. For example, in the previous example, “Reaction Example 1,” [NO2] appears in the rate law and is squared. Therefore, NO2 has an order of 2. As a result, if the concentration of NO2 is doubled, this will cause the rate to increase by a factor of 4.

● Orders above Second Order: Any order above second order will increase the rate to the power as indicated by the exponent. For example, an order of 3 would increase the rate to the 3rd power. If a chemical was third order and if it were doubled, the rate would increase by 23, or 8.

Experimentally Determining a Rate Law

Use the following reaction as an example of how a rate law can be determined from experimental data:

From the following sample data set, determine the rate law:

Initial Concentration Initial Concentration [NO] [O2] Initial Rate

Experiment 1 0.010 M 0.020 M 0.025 M/s Experiment 2 0.020 M 0.020 M 0.105 M/s Experiment 3 0.010 M 0.040 M 0.050 M/s

Notice that when the concentration of one chemical is changed, the other chemical’s concentration is held constant. When testing for the order of [NO], [O2] is held constant. When testing for [O2], [NO] is held constant. In doing so, the variable can be computed by using a ratio to determine the variables m and n since we have isolated the effect of the concentrations of one of the reactants on the outcome.

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Experiment Reaction Order and Rate Laws

Using a ratio, you can isolate the variable m:

Step 1: Determine the initial rate of two experiments in which the concentration of NO ([NO]) varied (from Table 1), but the concentration of O2 ([O2]) stayed the same.

Step 2: Use known values to compute unknown values. Since you have at least two experiments in which the chemicals are the same but the concentrations are different, use a ratio of the two experiments to determine the unknown variables.

Step 3: In order to find the value of the exponential variable, take the natural log (ln) of both sides of the equation.

Step 4: Determine the initial rate of two experiments in which the concentration of O2 ([O2]) varied (from Table 1), but the concentration of NO ([NO]) stayed the same.

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Experiment Reaction Order and Rate Laws

Step 5: Use known values to compute unknown values. Since you have at least two experiments in which the chemicals are the same but the concentrations are different, use a ratio of the two experiments to determine the unknown variables.

Step 6: In order to find the value of the exponential variable, take the natural log (ln) of both sides of the equation.

Therefore, from this data set, we see that the rate law is:

The reaction is first order in O2, second order in NO, and third order overall.

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Experiment Reaction Order and Rate Laws

Step 7: In order to find “k,” plug in all known numbers using experimental data. The following is data from Table 1, Experiment 1.

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Experiment Reaction Order and Rate Laws

Exercise 1: Determining the Rate Laws In this exercise, you will be determining the rate law for the reaction between HCl and Na2S2O3. Reaction rate data will be generated and used to determine the rate law for the reaction between hydrochloric acid, HCI, and sodium thiosulfate, Na2S2O3.

From the general form for a rate law given above the general rate law for the reaction between HCl and Na2S2O3 is written as:

By determining how the reaction rate varies as the concentration of the reactant is varied in the orders m and n, you can determine the rate law.

Note: Completely read all instructions and assemble all equipment and supplies before beginning work on this experiment.

Procedure

Part 1: Varying the Concentration of 1.0 M HCl

1. Gather the materials needed for this laboratory found in the materials list. Wear gloves and safety goggles throughout this experiment.

2. Draw a black “X” on the white sheet of paper with the permanent marker. Make the X just large enough to show under one well of the 24-well plate. See Figure 3.

Figure 3. Draw a black “X” on the white sheet of paper just large enough to show under one well of the 24-well plate.

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Experiment Reaction Order and Rate Laws

3. Pour distilled water into the empty dropper bottle labeled “For Distilled Water.” Push the tip of the dropper bottle into the bottle so that it snaps.

4. From the distilled water dropper bottle, carefully add:

● 6 drops of distilled water to wells C2 and D2.

● 8 drops of distilled water to wells C3 and D3.

Note: No water will be added to wells C1 and D1.

5. From the HCl dropper bottle, carefully add:

● 12 drops of the HCl to wells C1 and D1.

● 6 drops of the HCl to wells C2 and D2.

● 4 drops of the HCl to well C3 and D3.

6. Carefully add 8 drops of Na2S2O3, sodium thiosulfate, into each of the following wells of the 24-well plate: A1, A2, A3, B1, B2, and B3. See Figure 4 for setup.

Figure 4. Setup in the 24-well plate. For this portion of the experiment, you will be using columns 1, 2, and 3 of the well plate.

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Experiment Reaction Order and Rate Laws

7. Use the permanent marker to label the bulb of an empty short-stem pipet “Na2S2O3.”

8. Slide the well plate so that well C1 is over the “X” on the sheet of white paper.

9. Slightly tip the 24-well plate forward so that the drops of the wells containing Na2S2O3 puddle together along the bottom rim. Suck all of the contents of one of these wells into the Na2S2O3 pipet. See Figure 5.

Figure 5. Slightly tip the 24-well plate forward so that the drops of the wells containing Na2S2O3 puddle together along the bottom rim and then suck all of the Na2S2O3 from one well into the

empty pipet.

10. When you set the well plate back on the paper (with well C1 over the “X”), lightly shake the plate back and forth so the liquid covers the entire bottom of the wells again.

11. Zero the timer and hold it in one hand, ready to begin timing.

12. Take the pipet of Na2S2O3 in your other hand. Squeeze all of the contents from the bulb into well C1 and immediately begin timing.

13. Carefully observe the reaction in Well C1. The moment that the “X” is no longer visible stop the timer. Record the exact time in seconds under the “Reaction Time (sec): Trial 1” column in the Data Table 1 in your Lab Report Assistant in the row entitled “C1, D1.”

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Experiment Reaction Order and Rate Laws

14. Repeat steps 8 through 13 for well D1 and record the reaction time data under the “Trial 2” column in the Data Table 1 in the row entitled “C1, D1.”

15. Repeat steps 8 through 14 for wells C2 and D2 and then for wells C3 and D3.

16. Determine the reaction concentrations of HCl and Na2S2O3, using the following equations.

For Example:

Note: Because you are reaching the same amount of moles of the product (the solid that blocks the view of the ”X”), the same amount of moles of the reactants are being used for each trial (M). Therefore, this number should be the same for each trial. Since you are using a ratio to determine the exponents m and n, when you divide one rate by the other, that number of moles will cancel. This is why you only have the rate in sec-1 instead of in the units of M sec-1.

17. Calculate the average reaction time of trials 1 and 2. Record this value in Data Table 1 in the column labeled “Reaction Time: Average.”

18. Calculate the reaction rate for each row in Data Table 1 by taking the inverse of the average reaction time (1 divided by the average reaction time). Record this number in Data Table 1 in the column labeled “Reaction Rate (sec-1).”

Part 2: Varying the Concentration of 0.30 M Na2S2O3 19. Use the same sheet of white paper with an “X”on it as you used in Part I.

20. From the distilled water dropper bottle, carefully add:

● 6 drops of distilled water to wells C5 and D5.

● 8 drops of distilled water to wells C6 and D6.

Note: No water will be added to wells C3 and D3.

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Experiment Reaction Order and Rate Laws

21. From the Na2S2O3 dropper bottle carefully add:

● 12 drops of the Na2S2O3 to wells C4 and D4.

● 6 drops of the Na2S2O3 to wells C5 and D5.

● 4 drops of the Na2S2O3 to wells C6 and D6.

22. Carefully add 8 drops of HCl, hydrochloric acid, into each of the following wells of the 24-well plate: A4, A5, A6, B4, B5, and B6. See Figure 6 for setup.

Figure 6. Setup in the 24-well plate. For this portion of the experiment, you will be using columns 4, 5, and 6 of the well plate.

23. Use the permanent marker to label the bulb of an empty short-stem pipet “HCl.”

24. Put well C4 over the “X” on the sheet of white paper.

25. Slightly tip the 24-well plate forward so that the drops of the wells containing HCl puddle together along the bottom rim and you can suck all of the contents of one of these wells into the “HCl” pipet. Refer to Figure 5.

26. When you set the well plate back on the paper, lightly shake the plate back and forth so the liquid covers the entire bottom of the wells again.

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Experiment Reaction Order and Rate Laws

27. Reset the timer.

28. Squeeze the contents of the HCl pipet into well C4 and immediately begin timing the reaction.

29. Carefully observe the reaction in well C4. The moment that the “X” is no longer visible stop the timer. Record the exact time in seconds under the “Reaction Time (sec): Trial 1” column in the Data Table 2 in your Lab Report Assistant in the row entitled “C4, D4.”

30. Repeat steps 24 through 29 for well D4 and record your data under the “Trial 2” column in the Data Table 2 in the row entitled “C4, D4.”

31. Repeat steps 24 through 29 for wells C5 and D5 and then for wells C6 and D6.

32. Determine the reaction concentrations of HCl and Na2S2O3. Refer to Part I, step 16.

33. Calculate the average reaction time for the 2 trials. Record this value in Data Table 2 in the column labeled “Reaction Time: Average.”

34. Calculate the reaction rate for each row in Data Table 2 by taking the inverse of the average reaction time (1 divided by the average reaction time). Record this number in Data Table 2 in the column labeled “Reaction Rate (sec-1).”

Note: Because you are reaching the same amount of moles of the product (the solid that blocks the view of the ”X”), the same amount of moles of the reactants are being used for each trial (M). Therefore, this number should be the same for each trial. Since you are using a ratio to determine the exponents m and n, when you divide one rate by the other, that number of moles will cancel. This is why you only have the rate in sec-1 instead of in the units of M sec-1.

Cleanup:

35. Properly dispose of used chemicals.

36. Clean the equipment with soap and water and allow to thoroughly dry.

37. Return cleaned equipment to the lab it for future use.

Questions A. Determine the reaction order for HCl using calculations described in the Background section.

Show your work. Note that your answer will probably not be an even whole number as it is in the examples, so round to the nearest whole number.

B. Determine the reaction order for Na2S2O3 using calculations described in the Background section. Show your work. Note that your answer will probably not be an even whole number as it is in the examples.

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Experiment Reaction Order and Rate Laws

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Experiment Reaction Order and Rate Laws

C. Write the rate law for the reaction between HCl and Na2S2O3.

D. Using the following rate law, and the experimental values given, calculate k:

Experiment [F2] (M) [ClO2] (M) Initial rate (M/s) 1 0.5 0.5 0.300 M/s 2 0.8 0.8 0.768 M/s 3 0.5 0.8 0.480 M/s

E. Describe sources of error in this experiment.