CENG 343:
Chemical Engineering Lab I - Colorful Kinetics Experiment

Instructor:

Kyriacos Zygourakis
AL B217
Email: kyzy at rice.edu
Phone: 713-348-5208

 

Contents:

Chemical Reactions
Batch Reaction Model
Determining the Kinetic Constants
Laboratory Session
Report Preparation

Additional Files:

Entire Handout

Error Analysis Primer

Laboratory Procedures

 

 

A. Chemical Reactions

When phenolphthalein is added to an alkaline solution it first undergoes a rapid irreversible conversion to the quinoid form Ph^2- that has a pink color. The quinoid form reacts slowly and reversibly with hydroxyl ions to form the colorless (non-resonant) carbinol form PhOH^3-. Presumably, the reactions involved are:

	(R-1)
	(R-2)

Since reaction (R-1) is essentially instantaneous, the overall rate is determined by the rate of the reversible reaction (R-2) given by

(1)

where c₁ is the concentration of Ph^2- (in gmol/l), c₂ is the concentration of OH^- and c₃ is the concentration of PhOH^3-. The reaction rate is expressed as

and the rate constants k₁ and k₂ are assumed to depend only on the temperature T of the liquid.

B. Batch Reactor Model

Consider that these reactions are carried out in a stirred batch reactor. If the initial concentrations of OH^- is much larger than the concentration of Ph^2-, the hydroxyl concentration c₂ will remain almost constant over the course of reaction (R-2). A pseudo-rate constant can then be defined as

and the rate expression of equation (1) can be rewritten as

(2)

The transient behavior of a constant volume and isothermal batch reactor can now be described with the following differential equations:

(3)

(4)

By adding equations (3) and (4) we obtain

or

(5)

where the subscripts 0 and eq refer to the initial and equilibrium conditions respectively.
If c₃₀ = 0, then c₃ = c₁ - c₁₀ and we only need to solve the differential equation (3). The solution of this equation is given by:

(6)

By noting that the first term in equation (5) is equal to c_1,eq and that

(7)

equation (5) yields

	(8)

Suppose that we carry an experiment and measure c₁ as a function of time, c₁₀ (the initial concentration) and c_1,eq (the equilibrium concentration). Then if we plot the logarithm of

versus time, we should obtain a straight line with slope

(9)

In addition, the equilibrium constant K for reaction (R-2) is given by

(10)

where c₂ is the concentration of hydroxyl ions that is assumed to remain constant throughout the reaction.

The rate constants k₁ and k₂ at a temperature T can be obtained from equations (9) and (10) if c₁₀, c_1,eq and c₂ are known (or measured) and if the slope S is obtained from experimental data.

By repeating the experiment at several temperatures, the activation energies E₁ and E₂ for the forward and reverse reactions can also be obtained.

C. Determining the Kinetic Constants

You will study the kinetics of reaction (R-2) in a batch reactor by following the decolorization of the reaction mixture using a spectrophotometer. The reaction is initiated by rapidly mixing one or two drops of phenolphthalein into an aqueous KOH solution of known concentration. Its progress is followed by monitoring on the spectrophotometer the absorbance of the reacting mixture with time. To avoid removing liquid samples for analysis, a sample stream from the reaction mixture is continuously pumped through a flow cell in the spectrophotometer and recycled to the reactor. The temperature drop between the reactor and the flow-through cell may be considered negligible.

If we assume that the absorbance A(t) of the reaction liquid is proportional to the concentration c₁ of the quinoid form, equation (8) can be rewritten as

(11)

Equation (11) can now be used to determine the slope s by fitting a straight line through the experimental data.

D. Laboratory Session

The following is just an outline of the experimental procedures. A companion document provides the details.

• Charge the batch reactor with a known amount of KOH solution. Start the magnetic stirrer and the recirculation pump, and heat the reactor to about 30 deg.C. You should be extremely careful when adjusting the heater output, since even seemingly minor adjustments can result in large temperature excursions. REMEMBER that your objective is to keep the temperature constant during a run. Also, make sure there are no air bubbles in the recirculation lines as this will affect the absorbance of the solution.
  
  
• When the reactor temperature has stabilized, add one or two drops (NO MORE!) of phenolphthalein, start the timer and record the measured absorbance at time intervals that should not exceed 1 min. Continue taking measurements until the reaction reaches equilibrium. In addition, record the reactor temperature at the same time intervals so that you can check the assumption of isothermality and get an estimate of experimental errors.
  
  
• Charge the reactor with a fresh batch of KOH, increase the temperature to about 35 deg.C and repeat the experiment.
  
  
• Make a final run at about 40 deg.C. Remember that the time to reach equilibrium will decrease drastically with increasing temperature. Make sure you have enough measurements to determine the slope S accurately !

E. Report Preparation

• Give a short presentation of the problem and derive equation (6).
  
  
• Compute the values of the kinetic constants k₁ and k₂ at the three temperatures using the method outlined above. You will notice that the initial absorbance A₀ cannot be accurately measured. Thus A₀ must be estimated from the experimental data by an iterative procedure.
• Guess a value for A₀, plot
  
  

  vs. time

  
  and fit a straight line through the points.
  
  According to equation (11), the intercept of this line with the vertical axis should be equal to zero. If this is not true, obtain a better guess for A₀ and continue to iterate. You may want to write a simple computer program to do that.
• Include all plots with your report.
  
• Determine the activation energies E₁ and E₂ for the forward and reverse reactions.
  
• Determine the heat of reaction.
  
• Write a short discussion of your results.
  
  • Do they show that the assumed kinetic expression for reaction (R-2) is valid ?
  • Were your runs carried out under isothermal conditions ? If not, how did this affect the computed values of kinetic constants and activation energies ?
  • Estimate the maximum error in the computed activation energies.
  • Use your data to check the validity of the assumption that the concentration c₂ of OH^- remained constant during your runs.
    
• Attach all your raw data to the report.

Top

Return to Zygourakis Teaching page