Question

The maximum allowable temperature for a reactor is 800 K. At present our operating set point is 780 K, the 20 -K margin of safety to account for fluctuating feed, sluggish controls, etc. Now, with a more sophisticated control system we would be able to raise our set point to 792 K with the same margin of safety that we now have. By how much can the reaction rate, hence, production rate, be raised by this change if the reaction taking place in the reactor has an activation energy of 175 kJ/mol?

Answer 1

The reaction rate can be raised by approximately 1.075 times due to the increase in set point temperature in the reactor.

Step-by-step explanation:

The activation energy of a reaction determines how the reaction rate changes with temperature. By raising the set point temperature in the reactor, the reaction rate can be increased. The activation energy of the reaction is 175 kJ/mol.

To calculate the change in reaction rate, we can use the Arrhenius equation. The equation relates the rate constant of a reaction (k) to the activation energy (Ea) and temperature (T). The equation is as follows:

k = A * exp(-Ea/RT)

Where A is the pre-exponential factor, R is the gas constant, and T is the temperature in Kelvin.

By plugging in the values for the old and new set point temperatures, and solving for the ratio of the rate constants, we can determine the change in reaction rate:

(k2/k1) = exp((Ea/R) * ((1/T1) - (1/T2)))

Substituting the values, we get:

(k2/k1) = exp((175000/(8.314*780))(1/780 - 1/792))

Simplifying and calculating the ratio, we find that the reaction rate can be raised by approximately 1.075 times due to the increase in set point temperature.