The acid catalyzed irreversible liquid phase reaction

A B

is carried out adiabatically in a CSTR. The reaction is
second order in A. The feed, which is equal molar in water (which contains the
catalyst) and A, enters the reactor at a temperature of 52˚C and a total
volumetric flow rate of 10 dm^{3}/min. The concentration of A entering
the reactor is 4 molar.

a) What is the reactor volume to achieve 80% conversion

b) What conversion
can be achieved in a 1000 dm^{3} CSTR? What is the exit temperature?

Hint 1: What is the combined mole balance, rate law and stoichiometry that gives the reactor value as a function of temperature and conversion?

Hint 2: What is the equation that gives
X, solely as a function of t, k, and C_{A0}?

Hint 3: What is the equation that one obtains from the energy balance that gives X as a function of T?

Hint 4: What is the specific reaction rate 3?

Hint 5: What CSTR reactor volume is necessary to achieve 80% conversion?

Hint 1: Sketch the conversion obtained from the mole balance and energy balance as a function of T.

Hint 2: Write a Polymath program to obtain
the exit conversion and temperature. Use the output to plot X_{EB} and
E_{MB}.

Mole Balance

Let

Energy Balance

For 80% conversion T = 325 + 72.7 = 397.7

Part (b) What conversion can be achieved in a 1000
dm^{3} CSTR?

The exit temperature and conversion are determined from
the intersection of X_{EB} and X_{MB}

We can
generate X_{EB} and X vs. T curves by incrementing T and calculating
the conversion.

Equation for Figure