Page 72 - The engineering of chemical reactions

56 Reaction Rates, the Batch Reactor, and the Real World

This problem actually should be calculated for AU = 0 rather than AH = 0 for
a constant-volume process, and at these temperatures there are many additional
products because CO2 and Hz0 will dissociate significantly at this temperature.
However, the final result would not make much difference, especially if you were
in the room.

Recompute the final temperature and pressure if the methane were 5% in air.

This mixture has l/2 the stoichiometric amount of CH4, so the products will be 1
mole of COz, 2 moles of HzO, 2 moles of 02 remaining, and 16 moles of Nz, for a
total of 21 moles. The final temperature rise will therefore be approximately half
of that above, but you will still leave the room very quickly.

Recompute the final temperature and pressure if the methane were 3% in air.

A mixture of methane in air is flammable only between 5 and 15%; so no reaction
occurs and the temperature and pressure are unchanged. You might ask the person
who turned on the lights to open the window because the room seems a bit stuffy.
We will discuss combustion processes and explosions more in Chapter 10.

We usually estimate the adiabatic temperature changes for exothermic reactions
by assuming AHR evaluated at 298 K and C, for air at 298 K. These are calculated
with stoichiometric reactant mixtures assuming complete reaction. Even mildly exother-
mic reactions have adiabatic temperature rises much above 100 K, and total combustion
processes for stoichiometric mixtures in air have adiabatic temperatures above 2000 K.
These are not accurate calculations for high final temperatures because properties vary with
temperature and because of other reactions that will occur at high temperatures. Note that
large N produces a smaller AT, and thus AT will be larger for pure 02 instead of air
and smaller if the reactant mixture is diluted with an inert. While these calculations give
only approximate final temperatures because we assumed constant heat capacities, they
indicate the size of the thermal hazard of exothermic chemical reactions from a very simple
calculation.
For reactions in liquid solution we write an enthalpy balance on a 1 liter volume of
the liquid
T
Q = AH,(C,, - C,) + PC, dT = 0
s
10
where now each term has units of calories/liter. If this reaction goes to completion, CA = 0
and the equation becomes
-AHR
T=T,+ - CAo
PC,