Experiment 14 Kinetics of first order reactions

Objective

To follow the reaction by a titrimetric method and determination of the first order rate constant by a graphical treatment of the data.

Introduction

When an ester (such as ethyl acetate) is mixed with water it is converted into alcohol and acid according to the following equation: 
                     H+
CH3CO2C2H5  +  H2O   <-->  CH3CO2H  +  C2H5OH  (1)
When the amount of water is relatively large, the reaction goes practically to completion (the equilibrium shifts to the right) and the rate is first order with respect to the ester. The hydrolysis takes place slowly with pure water and is catalyzed by acids.

The elementary step in a first order reaction is represented by the following equation

                        k1
    A (reactant)    --------->   P (product)   (2)
where k1 is the first order rate constant.
By definition, the rate of a first order reaction is equal to the rate of loss of product or the rate of formation of product and is proportional to the concentration of reactant,

i.e.     -d[A]/dt  =  +d[P]/dt   α  [A]   (3)

or       -d[A]/dt  =  k1 [A]              (4)
Rearranging equation 4 and integrating gives

           ln[A]   =   -k t  +  const     (5)
if at time t = 0 and time t = t, the concentration of A is [A]o and [A]t respectively, the constant of integration is found to be ln[A]o, and equation 5 becomes

           ln[A]t  =   -k1t  +  ln[A]     (6)

and a plot of ln[A] against 't' should give a slope of -k1.

Materials
25 cm3 and 5 cm3 pipettes, 0.5 M HCl, 0.1 M NaOH, ethyl acetate, crushed ice, potassium hydrogen phthalate, stop watch.

Experimental
  1. Pipette 100.0 cm3 of 0.5 M HCl into a conical flask (labeled A) and a further 20.0 cm3 into a second conical flask (labeled B).
  2. Prepare 25 cm3 of crushed-ice/water. Pipette 5.0 cm3 of ethyl acetate into flask A, shake well, start the stop watch and immediately withdraw 5.0 cm3 of the solution. Immediately, run this into the crushed-ice water mixture, and swirl to 'stop' the reaction, and as soon as possible titrate with the NaOH solution. Without ever stopping the watch, note the time to the nearest second at which the solution is run into the ice/water mixture. This is the first time, t1, of the series.
  3. About 10 min after the first withdrawal, pipette another 5.0 cm3 of the reaction mixture from the flask and titrate as before, again noting the exact time, t2, that the reaction is 'stopped'.
  4. Further titrations are made at times of about 20, 30, 40, 60, 80, 100 and 120 min.
  5. The reaction is accelerated to completion by heating to 70�C for � hr. During this time the flask must be stoppered to avoid changes in concentration due to evaporation. Cool to room temperature, pipette 5.0 cm3 and add to 25 cm3 of water and titrate as before.
  6. For a control, take flask B and add 1 cm3 of water, pipette 5.0 cm3 and titrate as before.
Calculation

The initial ethyl acetate concentration is proportional to (V∞ - Vo), where V∞ is the final titre volume for flask A and Vo is the titre volume for flask B. The concentration of ethyl acetate at time t is proportional to (V∞ - Vt) where Vt is the titre volume of the sample at time t. Plot ln(V∞ - Vt) against time. Hence determine the value of k1 (in s-1) and the half-life of the reaction.


Exercise

  1. If the temperature of the reaction increased by about 2�C during the course of the reaction, what effect would this have on the points plotted?
  2. Assume the activation energy, Ea, to be about 11 kJ mol-1, calculate the fractional variation in the rate constant that would result from this increase in temperature.
  3. What is the significance of the titration value obtained from flask B.
  4. Would you expect the first titration value for flask A to be zero? Why?
  5. Find the error in the slope of the graph using the “box” method described in the lab talk, and so determine the uncertainty in k1.(See Appendix 6).

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