Kinetic and Thermodynamic Studies in Batch Reactor

Saddawi

The Goal of the Experiment

The goal of this experiment is to determine kinetic and thermodynamic parameters for the alkaline fading of phenolphthalein (Organic Dye) in aqueous solution.

The reaction is carried out in an isothermal stirred batch reactor, at various temperatures and concentrations.

Reaction

In this experiment, phenolphthalein reacts with Sodium hydroxyl in an isothermal continuous stirred batch reactor.

The fading of phenolphthalein in basic solution is an excellent example of second order reversible reaction kinetics

Where the structure of phenolphthalein at pH 8 or lower is colorless and at pH range 8-10 gives a pink color.

Experimental Setup

1. Prepare aqueous solutions of 0.1, and 0.2 molar NaOH. 2. Prepare a 0.0002 molar solution of phenolphthalein in

a mixture of ethanol and water (2:98 by volume 0.0002 M).

3. Approximately 50 ml of the NaOH solution is mixed with about 25 ml of the phenolphthalein solution mixed in a 2:1 ratio. The solution absorbance is monitored with an immersed colorimeter probe until equilibrium is attained.

4. The experiment is repeated at several temperatures (50, 40, and 30C).

Material Balance on perfect mix Batch Reactor

Input rate – Output rate – Disappearance rate = Accumulation rate

2- Assume the batch reactor is perfectly mixed, there are no concentration gradients in the reactor volume

3- the reactor volume is constant and equal to the reactants volume

1 A batch reactor has neither inflow nor outflow of reactants or products while the reaction is being carried out.

Fj0

= Fj

=0 .

For Reversible Second order Reaction like in Phenolphthalein fading color

The kinetics of the reaction obey the rate law:

where: k1 is the rate coefficient for the reaction that consumes P and OH-, and k2 is the rate coefficient for the backwards reaction, which consumes the product POH and produces P and OH-

At Equilibrium the forward reaction rate will equal backward reaction rat

Pseudo-first-orderMeasuring a second-order reaction rate with reactants P and OH- can be problematic: The concentrations of the two reactants must be followed simultaneously, which is more difficult; or measure one of them and calculate the other as a difference, which is less precise. A common solution for that problem is the pseudo-first-order

Therefore you should keep the concentration of one of a reactants e.g. NaOH constant by supplying it in great excess, its concentration can be absorbed within the rate constant, obtaining a pseudo first-order reaction constant.

At time =0[P] = [P]0

[POH] = 0

At t=t[P]=[P]t[POH]=[POH]t

At t= ∞The system reach to Equilibrium [P]= [P]e

[POH] = [POH]e

And the rate of forward reaction will equal to rate of backward reaction

By simplifying the rate equation you will end to the following equation

Where

Diluted concentrations less than 0.01are obeying Beer’s Law, the absorbance (A) can be related to the concentration of the Phenolphthalein

To find k’&k2 Let (k’+k2)= kc

And knowing that Ke=k1/k2

From thermodynamic we know that

The standard enthalpy of the reaction ∆H, can be found from the following relation

By plotting natural log of Kepseudo versus 1/T temperature, ∆H can be foundfrom the

slope.

And ∆S the entropy can be find from

From Arrhenious law, the activation energy (E) and the pre-exponential factor k0 can be found for the reaction

Van’t Hoff Equation

For simulation

Plot A vs t and use nonlinear regression to find Ae, b, c, and Ao

Ao =b+Ae

Assume b = Ao – Ae

c = k’ +k2