Kinetics of a First-Order Reaction

Introduction

Using sodium hydroxide and bromthymol blue indicator, the hydrolysis reaction of tert-butyl chloride is confirmed to be a first order reaction in this student participation demonstration.

Concepts

• Hydrolysis reaction
• First-order reaction
• Kinetics

Materials

Safety Precautions

Acetone is a flammable liquid and a dangerous fire risk. It is mildly toxic by inhalation. tert-Butyl chloride is a flammable liquid and is slightly toxic by ingestion, inhalation and skin absorption. Sodium hydroxide solution is a skin and eye irritant. Avoid contact of all chemicals with skin and eyes. Wear chemical splash goggles, chemical-resistant gloves and a chemical-resistant apron. Please review current Safety Data Sheets for additional safety, handling and disposal information.

Disposal

Please consult your current Flinn Scientific Catalog/Reference Manual for general guidelines and specific procedures, and review all federal, state and local regulations that may apply, before proceeding. The reaction solution may be disposed of according to Flinn Suggested Disposal Method #26b. Unused tert-butyl chloride may be disposed of according to Flinn Suggested Disposal Method #27j. The unused sodium hydroxide solution may be disposed of according to Flinn Suggested Disposal Method #10.

Prelab Preparation

1. Make copies of the worksheet and graph paper masters. Pass out a worksheet and graph paper to each student before beginning the demonstration.
2. Using a Beral-type pipet, add 1 mL of tert-butyl chloride to a 10-mL graduated cylinder.
3. Add acetone to the graduated cylinder up to the 10-mL mark. Stir the solution with a glass stirring rod.
4. Obtain a clean 10-mL graduated cylinder. Mix the solution by pouring it back and forth between the graduated cylinders.
5. Add 1.5 mL of this solution to a clean 10-mL graduated cylinder.
6. Add acetone to the 10-mL mark. With another clean 10-mL graduated cylinder, mix the solution as in step 4.
7. Add about 30 mL of 0.1 M NaOH solution to a 50-mL beaker.
8. Fill the 20-mL syringe to the 20-mL mark with 0.1 M NaOH solution.

Procedure

1. Using a 500-mL graduated cylinder, add 400 mL of distilled or deionized water to a 600-mL beaker.
2. Place the 600-mL beaker on the magnetic stirrer. Add a stir bar to the beaker and start the stirrer.
3. With the second Beral-type pipet, add 10–20 drops of the bromthymol blue indicator solution to the distilled water in the 400-mL beaker. The solution color should be green.
4. Using the syringe, add 1.0 mL of the 0.1 M NaOH to the solution in the 600-mL beaker. The solution will turn blue (basic).
5. Add all of the tert-butyl chloride/acetone solution to the beaker. Start the stopwatch or timer.
6. Have students record the time elapsed when the solution turns yellow. Record this time in the data table. Note: The total volume of 0.1 M NaOH added at this point is 1.0 mL.
7. Add another 1.0 mL of 0.1 M NaOH solution to the beaker.
8. Have students record the time elapsed when the solutions turns yellow again. Record the time in the data table. Total volume of 0.1 M NaOH added is 2.0 mL.
9. Repeat steps 7 and 8 for eight or more cycles (2–4 minutes).
10. Allow the reaction to proceed for an additional 5 or 6 minutes.
11. The solution color should now be yellow. Measure the volume of 0.1 M NaOH solution that must be added to the solution to neutralize all of the acid by titrating the yellow solution to a green endpoint. Use a drop-by-drop technique as the endpoint nears.
12. Have students record the total volume of 0.1 M NaOH solution added in the data table for the time equal to ∞. Note: The total volume is the amount added in step 11 plus the amounts added in steps 4–9.
13. Have students perform the calculations outlined on the demonstration worksheet and discuss the results.

Student Worksheet PDF

13947_Student1.pdf

Teacher Tips

• Enough materials are provided in this kit to perform the demonstration as written seven times.
• The addition of sodium hydroxide does not have to be precisely at the moment of color change. Determine the reaction times as close to the actual color changes as possible. All reaction times are total elapsed times.
• This is an excellent opportunity for students to learn to use graphing calculators or computer spreadsheets in solving for the slope of a line.
• Make a transparency of graph paper and plot the values of ln [(CH₃)₃CCl] (natural log of tert-butyl chloride concentration) versus time.
• The starting concentration of tert-butyl chloride calculated using the “infinity volume” measurement is about 70–80% of the actual amount added. Whether through evaporation, low solubility, or a combination of both, the calculated concentration of tert-butyl chloride is less than the amount added. This reaction, however, still follows first order kinetics and the data yield a reasonably accurate rate constant.
• If the 1 mL aliquots of 0.1 M NaOH are consumed too rapidly at first, the reaction can be slowed down by reducing the temperature. Place the distilled or deionized water in an ice bath until a temperature of 20–22 °C is achieved.

Sample Data

Perform calculations on a separate sheet of paper.

rate constant, k __1.6 x 10^–2___ sec^–1 [(CH₃)₃CCl]₀ __2.7 x 10^–3___ moles/L

Answers to Questions

1. The concentration of tert-butyl chloride at each time a color change occurs can be calculated from the values of total volume of sodium hydroxide added at each time, Vol_total and the total volume of sodium hydroxide added at time = ∞, Vol_inf.
   {13947_Answers_Equation_11}
   1. Calculate (Vol_inf – Vol_total) for each time recorded. Enter these values in the data table.

      At time = 38 seconds,

      Vol_inf – Vol_total = 11.1 mL – 5.0 mL = ___6.1 mL___

   2. Calculate [(CH₃)₃CCl]_t for each time recorded. Enter these values in the data table. Enter [(CH₃)₃CCl]₀ on the line below the data table.

      At time = 38 seconds,

      [(CH₃)₃CCl]_t = (Vol_inf – Vol_total) × (0.1 M)/400 mL = 6.1 mL × 0.1 M/400 mL = 1.5 × 10^–3 M

   3. Calculate ln[(CH₃)₃CCl]_t for each time recorded. Enter these values in the data table.

      At time = 38 seconds,

      ln[(CH₃)₃CCl]₃₈ = ln(1.5 × 10^–3) = ___–6.51___

2. Have students plot ln[(CH₃)₃CCl]_t versus time, in seconds, on their graph paper. From the graph, have students determine the rate constant k (– slope). Enter this value on the line below the data table. Did the reaction follow first-order kinetics?

   From the graph, the rate constant k was determined to be 0.016 sec^–1.

   {13947_Answers_Figure_1}

   Yes. The graph of ln[(CH₃)₃CCl]_t versus time yields a straight line.

3. The half-life of a reaction (t_½) is the time it takes for one-half the reactants to be consumed.

   For a first-order reaction

   {13947_Answers_Equation_12}

   Calculate the half-life for the reaction.

   The rate constant, k, is determined from the slope of the line from the graph of the data.

   {13947_Answers_Equation_13}

Discussion

The hydrolysis of tert-butyl chloride is a convenient reaction for demonstrating first-order reaction kinetics. The reaction takes about ten minutes to complete at room temperature. The rate of reaction can be determined by measuring the time needed for the HCl generated in the reaction to neutralize premeasured amounts of a standard base added to the reaction solution.

The hydrolysis of tert-butyl chloride is a first-order reaction. Studies point to a three-step reaction mechanism, called S_Nl, for this reaction to occur

Since step 1 is the slowest step of the three, it is the rate determining step. The overall rate can therefore be expressed as: The integrated rate law for this first-order reaction is: where [(CH₃)₃CCl]₀ is the concentration of tert-butyl chloride at time t = 0 and [(CH₃)₃CCl]_t is the concentration at any time t during the reaction. This equation can be rearranged to: If the ln([(CH₃)₃CCl]_t) is plotted versus time, a straight line with slope –k should result.

Because step 1 is the slowest reaction in the three-step mechanism, hydronium ions, H₃O⁺(aq), are essentially produced as fast as tert-butyl chloride molecules are reacting. If the concentration of hydronium ions produced can be measured at a specific time of the reaction, the concentration of tert-butyl chloride consumed at that time will be the same.

An acid–base indicator solution is added to a fixed volume of distilled or deionized water, followed by 1 mL of 0.1 M NaOH solution. The hydroxide ion, OH^–(aq), concentration exceeds the amount of hydronium ions, H₃O⁺(aq), in solution and the solution color is blue—the color of bromthymol blue in a basic solution. The reaction starts when tert-butyl chloride is added to this solution.

The amount in millimoles (mmoles) of hydroxide ions added is: As hydronium ions are produced in step 3 of the hydrolysis reaction, they are immediately neutralized by the hydroxide ions in solution (Equation 9). The solution remains blue until the mmoles of hydronium ions produced by the hydrolysis just exceeds the mmoles of hydroxide ions added. At this point, the solution becomes acidic and the indicator color changes to yellow. The time needed for the indicator to change color is equal to the time required for 0.1 mmoles of tert-butyl chloride to react. For each successive aliquot of 0.1 M NaOH added, the time it takes for the indicator to change color increases, since the rate of the reaction decreases as the concentration of tert-butyl chloride decreases.

The time required for the indicator to change color is recorded for eight or more additions of base. The solution is then allowed to react undisturbed for about five minutes until the reaction is essentially complete. The solution is then titrated with the 0.1 M NaOH solution to a green endpoint. The total volume added is recorded as volume at time equal to infinity, or V_inf.

Multiplying V_inf by the molarity of the sodium hydroxide solution gives the total number of moles of hydronium ions produced in the reaction. This is also equal to the initial moles of tert-butyl chloride. At any time t, the amount of tert-butyl chloride in solution is equal to 0.1 M times the volume at time equal to infinity, V_inf, minus the total volume of 0.1 M sodium hydroxide solution added at time t (Equation 10).

The concentration of tert-butyl chloride at any time t is equal to: where 400 mL is the volume of the solution. (To simplify the calculations, the volumes of acetone and sodium hydroxide are ignored.)

References

Special thanks to Lew Brubacher, Department of Chemistry, University of Waterloo, Waterloo, ON, for providing Flinn with the idea and procedure for this demonstration.