Molar Balance for Reactor Systems - Reaction Engineering

Molar balance is very important concept for chemical engineering undergraduate students. For reactor systems in chemical engineering, this phenomenon is widely applied. This theory is helped to calculate flow rates, reaction rates in industrial applications.

Types of Reactor systems

  1. Batch reactor
  2. Continuous stirred tank reactor ( CSTR )
  3. Plug flow (tubular) reactor (PFR)
Reactor system types

Molar balance equation

There may be a inflow and a outflow in a reactor and reactions are happening inside the reactor (but batch reactor do not contain inflow and outflow. In batch reactor, reactants are filled and products are taken after the reaction). Therefore molar balance equation includes several terms to describe each of those processes. General molar balance equation is written below.

In + Generation = Out + Consumption + Accumulation + Loss

All parameters are in moles and if time basis is used, units are taken as mol hr-1 or mol s-1.

In most of our calculations, we assume that losses are negligible. So we can remove 'Loss' term from molar balance equation.

In + Generation = Out + Consumption + Accumulation

In the molar balance equation, there are two terms such as molar generation and molar consumption. Both of them exists in opposite directions in the equations. Instead of both of them we only use molar generation which represent both generation and consumption together.

Generation means, a species is being produced from a reaction (products). Consumption means, a species is being spent in a reaction (reactants).

We represent
Generation as + Generation
Consumption as - Generation

Now our equation is reduced as below.

In + Generation = Out + Accumulation

Below figure shows us reactor system with inflow and outflow (remember that, there is no inflow or outflow in a batch reactor). We choose one species A for our demonstration.

Reaction system inflow outflow

First, A enters into the system through inflow. Then one or several reactions happen in the system (reactor). Finally remaining A comes out from the reactor. Also there may be no remaining A if all reactants are consumed.

For calculating generation term, we consider small part of volume in the system.

rate of reaction in dv

Generation in the reactor

If A is disappearing/ reducing / consumption (due to reacting), Generation term become negative.

negative generation rate

Accumulation in the reactor

Assume that there are NA moles at time t in the reactor. We can write the accumulation rate as below. Accumulation units can be mol s-1 or kmol h-1.

accumulation term

Molar balance equation for any reactor

Finally, we write the general equation for any reactor system as below.

general molar balance equation for any reactor

Molar balance for continuous stirred tank reactor (CSTR)


If rate of reaction (rA) is same in everywhere in the reactor (no spatial variation), rA becomes a constant in a instant time.

reacton rate constant

If process is at steady state, there is no accumulation. So accumulation is zero.

steady state equation

According to those assumptions, molar balance equation for continuous stirred tank reactor is written as below.

molar balance for continuous stirred tank reactor

Molar balance for plug flow reactor (PFR)

Conditions of the PFR change along the reactor.

plug flow reactor

Select a small volume part and we take our selected specie as A. Lets take inflow of reactor is FA|V and outflow is FA|V+ ΔV


He we consider steady state. ( dNA/dt = 0)

According to those assumptions out molar balance equation for continuous stirred tank reactor.

Molar balance for plug flow reactor

Molar balance for batch reactor

There are no inflow or outflow in the batch reactor. Initially, we filled the reactor by reactants and take out products (reactants may be present in products if reaction or reactions had not been completed. ) after the reaction. Therefore FA = 0 and FAO = 0

We assume that reaction rate (rA) is constant in everywhere in the reactor.

Molar balance for batch reactor

Summary of molar balance equations of reactors

summary of Reactor systems

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