Changes in Internal Energy
221
2. If there are fewer moles of gaseous products than gaseous reactants in
the balanced chemical equation, then the atmospheric pressure will do
work on the reaction mixture as it contracts due to the diminished
number of gaseous moles, and this work energy will be added to the
heat that is liberated. A larger amount of heat will be liberated than if
the reaction had occurred at constant volume.
3. If there are the same number of gaseous moles of products as reactants, there will be no contraction or expansion of the reaction mixture.
The heat liberated at constant pressure will be the same as at constant
volume.
We next offer a simple way to calculate the heat effect at constant pressure
from that observed at constant volume, or vice versa. First, note that the product of P and V always has the units of energy. A simple bit of evidence for this
observation comes from the ideal gas law, using the value of 1.987 cal/mole K
forfl:
PV = (n moles) ( 1.987
C
.
al .. W
K ) = l-987(n7) calories
\
mole Ky
It is said that every substance has an internal energy (designated as E), and
that the heat effect associated with a change at a constant volume and temperature is AE. As the molecules go from "state 1" to "state 2," AE = E 2 - E l .
This effect is exactly analogous to the heat effect that is associated with a
change at constant pressure and temperature: A// = H 2 - HI. The variables//
and E are related by the potential of the system to expand or contract — that is,
to the potential to be affected by PV work — by the explicit function
H = E + PV
For a change,
A// = AE + A(/
J V)
If the change is a chemical reaction at constant temperature and pressure,
A(PV) becomes PAV because the pressure remains constant, and it comes as a
result of the difference in the number of gaseous moles of products and reactants in the balanced chemical equation:
I
A(/>V) = PAV = (kn)RT
where An = n 2 (gaseous moles of products) - n 1 (gaseous moles of reactants).
For chemical reactions, then,
A// = AE + (bn)RT
221
2. If there are fewer moles of gaseous products than gaseous reactants in
the balanced chemical equation, then the atmospheric pressure will do
work on the reaction mixture as it contracts due to the diminished
number of gaseous moles, and this work energy will be added to the
heat that is liberated. A larger amount of heat will be liberated than if
the reaction had occurred at constant volume.
3. If there are the same number of gaseous moles of products as reactants, there will be no contraction or expansion of the reaction mixture.
The heat liberated at constant pressure will be the same as at constant
volume.
We next offer a simple way to calculate the heat effect at constant pressure
from that observed at constant volume, or vice versa. First, note that the product of P and V always has the units of energy. A simple bit of evidence for this
observation comes from the ideal gas law, using the value of 1.987 cal/mole K
forfl:
PV = (n moles) ( 1.987
C
.
al .. W
K ) = l-987(n7) calories
\
mole Ky
It is said that every substance has an internal energy (designated as E), and
that the heat effect associated with a change at a constant volume and temperature is AE. As the molecules go from "state 1" to "state 2," AE = E 2 - E l .
This effect is exactly analogous to the heat effect that is associated with a
change at constant pressure and temperature: A// = H 2 - HI. The variables//
and E are related by the potential of the system to expand or contract — that is,
to the potential to be affected by PV work — by the explicit function
H = E + PV
For a change,
A// = AE + A(/
J V)
If the change is a chemical reaction at constant temperature and pressure,
A(PV) becomes PAV because the pressure remains constant, and it comes as a
result of the difference in the number of gaseous moles of products and reactants in the balanced chemical equation:
I
A(/>V) = PAV = (kn)RT
where An = n 2 (gaseous moles of products) - n 1 (gaseous moles of reactants).
For chemical reactions, then,
A// = AE + (bn)RT