Kinetics

Kinetics of a pseudo first order reaction for dehydrogenation of Isopropanol THEORY The rate at which a chemical reaction occurs depends on several factors: the nature of the reaction, the concentrations of the reactants, the temperature, and the presence of possible catalysts. All of these factors can markedly influence the observed rate of reaction. In this experiment, we will study a reaction which, proceeds under moderate temperature (350°C), at a relatively easily measured rate. For the first order irreversible reaction, (CH3)2CHOH

(CH3)3CO + H2

Isopropanol

Acetone

Hydrogen

the rate can be expressed by the following equation, which is called the rate law, rate = k*C(CH3)2CHOH where, k is the specific rate constant for the reaction. As with the concentration, there is a quantitative relationship between reaction rate and temperature. This relation is based on the idea that in order to react, the reactant species must have a certain minimum amount of energy present at the time the reactants collide in the reaction step. This amount of energy, which is typically furnished by the kinetic energy of the species present, is called the activation energy of the reaction. The first order reaction equation for comp A, Rate = -rA= -

dCA 𝑑𝑡

= k*CA

-----(1)

When the volume of reaction system mixture changes linearly with conversion, we have V = Vo(1+ƐA*XA) 𝐶𝐴 𝐶𝐴𝑜

1−XA

= (1+ƐA∗XA)

------(2)

Put equation (2) in equation (1) -rA= We have, space time equation

dCA 𝑑𝑡

1−XA

= k*CAo*(1+ƐA∗XA)

𝑋𝐴 𝑑𝑋𝐴

τ = CAo*∫0

−𝑟𝐴

Substituting for (--rA) gives, 𝑋𝐴

τ= CAo*∫0

𝑑𝑋𝐴 1−XA (1+ƐA∗XA)

k∗CAo∗

Rearranging yields, 𝑋𝐴 (1+ƐA∗XA)∗𝑑𝑋𝐴

τ *k = ∫0

(1−XA)

𝑋𝐴 𝑑𝑋𝐴

= ∫0

𝑋𝐴 (XA)∗𝑑𝑋𝐴

+ƐA ∫0 (1−XA)

τ *k = -ln(1-XA) + ƐA*I1

(1−XA)

------(3)

Where, 𝑋𝐴 (XA)∗𝑑𝑋𝐴

I1 = ∫0 Put,

(1−XA)

(1- XA) = Y

At, XA = 0; Y = 1 At, XA = 1; Y = 1- XA And,

XA = 1- Y 𝑋𝐴 (XA)∗𝑑𝑋𝐴

I1 = ∫0

(1−XA) 1−𝑋𝐴 𝑑𝑌

I1 = − ∫0

1

𝑋𝐴 (1−Y)∗𝑑𝑌

= -∫0

Y

1−𝑋𝐴 𝑑𝑦

+ ∫0

𝑌

I1 = -ln(1-XA) + (1- XA-1) I1 = -ln(1-XA) + XA Substituting for I1 in equation (3) gives, τ *k = -ln(1+XA) - ƐA*ln(1-XA) - XA τ *k = - (1+ƐA)*ln(1-XA) - ƐA* XA

------(5)

Equation (5) is the integrated rate equation for first order reaction for variable density system. From the kinetics expression, at a reactor temperature of 350C, we have: k=k0exp[-Ea/RT] =3.51×105exp[72,380/ (8.314)(273+350)] =..........m3gas/m3bulk catalyst ԑA= (number of mole if completely reacted – number of moles initially)/ number of moles initially

from reaction, = (2-1)/(1)=1