Determining Rate Laws and the Order of Reaction

1. Preparing H₂O₂ Dilutions

1. Stock 3% hydrogen peroxide has a concentration of 0.882 M. Prepare 5 dilutions ranging from 0.882 M to 0.176 M (Table 1). Prepare these solutions volumetrically, but prepare them additively since the solute is very dilute and volumes of water are additive.
2. Place the solutions in a constant temperature water bath or leave them on the bench top to equilibrate at room temperature. A temperature range of 20–25 °C (293–298 K) is good for this reaction.

Table 1. H₂O₂ solutions used.

2. Preparing the Reaction Vessel

1. To determine the volume of the reaction vessel, fill a large test tube to the top with water and insert a 1-hole rubber stopper into the test tube until tight and water pushes out the sides and through the top.
2. Remove the stopper and pour the water into a graduated cylinder to determine the exact volume of the water. This is the total volume of the reaction vessel (test tube).

3. Measuring Oxygen Evolution

1. Replace the water with 50 mL of the first hydrogen peroxide solution and place it back into the water bath. Once equilibrated, add the platinum-coated reaction disc and seal the system with a stopper connected to a gas pressure sensor. These discs are commonly used in contact lens cleaning systems.
2. Once the pressure sensor is setup to acquire data at 2 points/s, run the experiment for 120 s. The Vernier gas pressure sensor, GPS-BTA, is recommended for this experiment.
3. Bubbles should be observed as the peroxide is decomposed to oxygen gas and water. Release the pressure, dispose of the solution, rinse, and replace the solution with the next hydrogen peroxide solution. Repeat the gas pressure measurement until all solutions are tested.

4. Data Analysis

1. Transfer all data files of pressure versus time to a spreadsheet program.
2. Determining initial rates -assume that the concentration of hydrogen peroxide has not changed much during the short timeframe of the experiment. The data represent the initial linear region of the kinetics experiment.
   1. Determine slope by plotting pressure versus time and using a slope formula or linear regression. Plot the pressure in any common unit.
   2. The slope is the initial rate in units of pressure_O2/s.
3. Determining Reaction Order
   1. Because pressure of evolved O₂ is directly proportional to the moles of decomposed H₂O₂, plotting the ln(initial rate) vs. ln[H₂O₂]₀ yields a slope equivalent to the order of the reaction. The initial concentration of hydrogen peroxide, [H₂O₂]₀, is what was used in each of the trials.
      1. The equation for the rate law is . Taking the natural logarithm (ln) of the equation produces a linear equation , where m, the slope, is the order of the reaction.

4. Determining the Rate Constant, k
   1. For each trial, convert the rate, P_O2/s, into units of atm/s if the rate is in a different unit such as torr/s.
   2. Because bubbles were evolved in aqueous solution, subtract the vapor pressure of water from the system pressure for each trial. The new rate reflects only the pressure due to oxygen evolution.
   3. Apply the Ideal Gas law to convert the rate from atm/s into moles/s in each trial.
      1. Rearrange PV = nRT to n = PV/RT. The s^-1 unit remains unchanged. The volume is equivalent to the test tube volume minus the solution volume (50 mL).
   4. Use the balanced chemical reaction to convert from moles of oxygen produced to moles of hydrogen peroxide decomposed in each trial.
   5. Divide the moles of H₂O₂ by the volume of the solution, 0.050 L, to yield the molarity of H₂O₂ decomposed per second, [H₂O₂]/s.
   6. Because this experiment follows first-order kinetics, divide the rate, [H₂O₂]/s, by the original solution concentration for each trial, [H₂O₂]₀, to yield a rate constant, k. This solution for the rate constant would vary slightly based on the order of the reaction previously determined.
   7. Average the rate constants for each trial together since the temperature is constant.