# Kinetic and Thermodynamic Studies in Batch Reactor

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Kinetic and Thermodynamic Studies in Batch Reactor

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

Prepare aqueous solutions of 0.1, and 0.2 molar NaOH.
Prepare a molar solution of phenolphthalein in a mixture of ethanol and water (2:98 by volume M). 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. The experiment is repeated at several temperatures (50, 40, and 30C).

Fj0 = Fj =0 . Material Balance on perfect mix Batch Reactor
Input rate – Output rate – Disappearance rate = Accumulation rate 1 A batch reactor has neither inflow nor outflow of reactants or products while the reaction is being carried out. Fj0 = Fj =0 . 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

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-order Measuring 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.

The system reach to Equilibrium [P]= [P]e [POH] = [POH]e
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
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

Plot A vs t and use nonlinear regression to find Ae, b, c, and Ao
For simulation Assume b = Ao – Ae c = k’ +k2 Plot A vs t and use nonlinear regression to find Ae, b, c, and Ao Ao =b+Ae