# Batch Reactor Solved Problems | Examples

Here, we are going to use molar balance, energy balance, reaction rate equationand more theories to solve a batch reactor problem. This will helpful to understand fundamentals of batch reactor.

Problem

Consider the elementary reaction A → B + C which occurs in liquid state and ideal batch reactor at constant temperature. Determine the time required for the concentration of A to become half of the its initial concentration.
reaction rate constant,K = 0.1 /sec

Assumptions made to simplify the problem

1. Due to constant temperature, reaction rate constant (K) is constant.
2. Due to liquid phase reaction, we can assume total volume of liquid (which reaction occurs) is constant (V = constant).
3. No loses in the reactor

You should know how molar balance is applied to batch reactor. See how molar balance is applied to batch reactor.

• rA - reaction rate
• V - total volume of liquid
• t - time
• C - concentration
• NA - moles of A

In this problem, they ask the required time for the concentration of A to become half of the its initial concentration. So we should build a relationship between concentration and time variable (C and t).

In the reaction rate equation, there is a direct relationship between concentration and time. So we are going to use that.

From reaction rate equation and molar balance equation we can obtain first order differential equation.

Then differential equation is integrated to find time. #### sizing a batch reactor without rate constant

Reaction rate is not a constant in a batch reactor with time. So you have to write the reaction rate as a function of time. When, reaction rate equation is written, reaction rate constant is used.

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