# Calculate Reaction Time & Vol for 90% Conversion in Reactor

• gfd43tg
In summary: This leads to the following equations:In summary, for a batch reactor filled to the brim, it will take 230.3 minutes to reach 90% conversion for a first order reaction with respect to A and B. For a CSTR, the necessary reactor volume is 22,500 L and for a PFR, the necessary reactor volume is 2,250 L. For a first order reaction with respect to B and zero order in A with a specific reaction rate of 0.01/min, the necessary reactor volume for a CSTR is 11,250 L and for a PFR, it is 1,125 L. For a reversible reaction with a Keq of 2 L/mol, the equilibrium conversion is
gfd43tg
Gold Member

## Homework Statement

The elementary liquid phase reaction
$$A + B \rightarrow C$$
is carried out in a 500 L reactor. The entering concentrations of streams A and B are both 2 M and the specific reaction rate is 0.01 L/(mol min).

(a) Calculate the time to reach 90% conversion if the reactor is a batch reactor filled to the brim

Assuming a stoichiometric feed (10 mol A/min) to a continuous-flow reactor, calculate the reactor volume and space-time to achieve 90% conversion if the reactor is
(b) a CSTR (Ans.: V = 22,500 L)
(c) a PFR (Ans: V = 2,250 L)
(d) redo (a) through (c) assuming the reaction is first order in B and zero order in A with k = 0.01/min.
(e) Assume the reaction is reversible with ##K_{e} = 2 \frac {L}{mol}##. Calculate the equilibrium conversion and the CSTR and PFR volumes necessary to achieve 98% of the equilibrium conversion.

## The Attempt at a Solution

(a)
I use the equation ##t = N_{A0} \int_0^X \frac {dX}{-r_{A}V} ##
$$t = C_{A0} \int_0^X \frac {dX}{-r_{A}}$$
I assume this is a first order reaction with respect to A, ##-r_{A} = kC_{A}##, and I know for a liquid phase reaction, ##C_{A} = C_{A0}(1 - X)##. Therefore, ##-r_{A} = kC_{A0}(1-X)##.
$$t = C_{A0} \int_0^X \frac {dX}{kC_{A0}(1-X)}$$
$$t = \frac {1}{k} \int_0^X \frac {dX}{1-X}$$
$$t = - \frac {1}{k} ln(1 - X) = - \frac {1}{0.01} ln(1 - 0.9) = 230.3 \hspace{0.05 in} min$$

(b) This is where I get stuck, I use the equation ##V = \frac {F_{A0}X}{-r_{A}}##
$$V = \frac {F_{A0}X}{kC_{A0}(1-X)}$$
$$V = \frac {10(0.9)}{0.01(2)(1-0.9)} = 4,500 \hspace{0.05 in} L$$
But this is not the answer given in the textbook, 22,500 L and I haven't figured out why.
For the space time,
$$\tau = \frac {V}{v_{0}}$$
where ##v_{0}## is the initial volumetric flow rate. ##F_{A0} = C_{A0}v_{A0}##, so ##10 = 2v_{A0}##, therefore the volumetric flow rate for A is 5 L/min, and since this is a stoichiometric feed, the total volumetric flow rate is 10 L/min, so the space time is 4,500 L/10 = 450 min.

Last edited:
My problem was my assumption, I should have said that ##-r_{A} = kC_{A}C_{B}##, since this reaction is elementary.

Last edited:

## 1. How do you calculate reaction time for 90% conversion in a reactor?

The reaction time for 90% conversion in a reactor can be calculated using the following formula: t = 0.693/k, where t is the reaction time and k is the reaction rate constant. The reaction rate constant can be determined through experiments or by using mathematical models.

## 2. What factors affect the reaction time in a reactor?

The reaction time in a reactor can be affected by various factors such as temperature, pressure, concentration of reactants, presence of catalysts, and the type of reaction. These factors can alter the reaction rate and therefore, impact the reaction time required for 90% conversion.

## 3. How do you determine the volume needed for 90% conversion in a reactor?

The volume needed for 90% conversion in a reactor can be determined by considering the stoichiometry of the reaction, the initial concentration of reactants, and the desired conversion percentage. This can be calculated using the volume equation V = n/C, where V is the volume, n is the number of moles of reactants, and C is the concentration.

## 4. Can the reaction time and volume needed for 90% conversion be predicted accurately?

Yes, the reaction time and volume needed for 90% conversion in a reactor can be predicted accurately using mathematical models and simulations. However, experimental data is still necessary to validate these predictions and account for any unforeseen factors that may impact the reaction.

## 5. How can the reaction time and volume needed for 90% conversion be optimized?

The reaction time and volume needed for 90% conversion can be optimized by adjusting the reaction conditions, such as temperature, pressure, and concentration, to maximize the reaction rate. The use of catalysts and efficient mixing techniques can also help to reduce the reaction time and volume required for 90% conversion in a reactor.

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