11.3.1 Dissecting the Steady-State Molar Flow Rates to Obtain the Heat of Reaction

To begin our journey, we start with the energy balance equation (11-9) and then proceed to finally arrive at the equations given in Table 11-1 by first dissecting two terms:

  1. The molar flow rates, Fi and Fi0
  2. The molar enthalpies, Hi, Hi0[HiHi(T), and Hi0Hi(T0)]

An animated version of what follows for the derivation of the energy balance can be found in the reaction engineering games “Heat Effects 1” and “Heat Effects 2” on the DVD-ROM. Here, equations move around the screen, making substitutions and approximations to arrive at the equations shown in Table 11-1. Visual learners find these two ICGs a very useful resource.

image

We will now consider flow systems that are operated at steady state. The steady-state energy balance is obtained by setting (dÊsys/dt) equal to zero in Equation (11-9) in order to yield

11-10

image

Steady-state energy balance

To carry out the manipulations to write Equation (11-10) in terms of the heat of reaction, we shall use the generalized reaction

2-2

image

The inlet and outlet summation terms in Equation (11-10) are expanded, respectively, to

11-11

image

and

11-12

image

where the subscript I represents inert species.

We next express the molar flow rates in terms of conversion.

In general, the molar flow rate of species i for the case of no accumulation and a stoichiometric coefficient υi is

image

Specifically, for Reaction (2-2), image, we have

image

Steady-state operation

We can substitute these symbols for the molar flow rates into Equations (11-11) and (11-12), then subtract Equation (11-12) from (11-11) to give

11-13

image

The term in parentheses that is multiplied by FA0X is called the heat of reaction at temperature T and is designated ΔHRx(T).

11-14

image

Heat of reaction at temperature T

All enthalpies (e.g., HA, HB) are evaluated at the temperature at the outlet of the system volume, and, consequently, [ΔHRx(T)] is the heat of reaction at a specific temperature T. The heat of reaction is always given per mole of the species that is the basis of calculation [i.e., species A (joules per mole of A reacted)].

Substituting Equation (11-14) into (11-13) and reverting to summation notation for the species, Equation (11-13) becomes

11-15

image

Combining Equations (11-10) and (11-15), we can now write the steady-state [i.e., image] energy balance in a more usable form:

11-16

image

One can use this form of the steady-state energy balance if the enthalpies are available.

If a phase change takes place during the course of a reaction, this form of the energy balance [i.e., Equation (11-16)] that must be used.

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset
44.220.182.198