# 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

- Due to constant temperature, reaction rate constant (K) is constant.
- Due to liquid phase reaction, we can assume total volume of liquid (which reaction occurs) is constant (V = constant).
- 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.

Answer

- r
_{A} - reaction rate
- V - total volume of liquid
- t - time
- C - concentration
- N
_{A} - 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.

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