Geoscience Reference
In-Depth Information
■
EXAMPLE 3.4
Problem:
Again, consider a system at 1000.0 K, where 0.250 atm of oxygen is mixed with 0.500 atm
of hydrogen and 2000 atm of water.
Solution
: Again, the equilibrium constant is very large and the concentration of least reactants must
be reduced to a very small value.
[H
2
O] = 2.000 + 0.500 = 2.500 atm
In this case, oxygen and hydrogen are present in a 1:2 ratio, the same ratio given by the stoichiomet-
ric coefficients. Neither reactant is in excess, and the equilibrium concentrations of both will be very
small values. We have two unknowns but they are related by stoichiometry. Because neither product
is in excess and one molecule of oxygen is consumed for two of hydrogen, the ratio [H2]/[O2] = 2/1
is preserved during the entire reaction and [H
2
] = 2[O
2
]:
1.15 × 10
10
= 2.500
2
/(2[O
2
])
2
[O
2
]
[O2] = 5.14 × 10
-4
atm and [H2] = 2[O2] = 1.03 × 10
-3
atm
3.6.2 l
aWs
oF
e
quilibrium
Some of the laws essential for modeling the fate and transport of chemicals in natural and engi-
neered environmental system include the following:
• Ideal gas law
• Dalton's law
• Raoult's law
• He n r y's l aw
3.6.2.1 Ideal Gas Law
An ideal gas
is defined as one in which all collisions between atoms or molecules are perfectly
elastic and in which there are no intermolecular attractive forces. One can visualize it as collec-
tions of perfectly hard spheres that collide but otherwise do not interact with each other. In such a
gas, all the internal energy is in the form of kinetic energy and any change in the internal energy is
accompanied by a change in temperature. An ideal gas can be characterized by three state variables:
absolute pressure (
P
), volume (
V
), and absolute temperature (
T
). The relationship between them
may be deduced from kinetic theory and is called the
ideal gas law
:
P
×
V
=
n
×
R
×
T
=
N
×
k
×
T
(3.13)
where
P
= Absolute pressure.
V
= Volume.
n
= Number of moles.
R
= Universal gas constant = 8.3145 J/mol⋅K or 0.821 L⋅atm/mol⋅K.
T
= Temperature.
N
= Number of molecules.
k
= Boltzmann constant = 1.38066 × 10
-23
J/K =
R
/
N
A
, where
N
A
is Avogadro's number (6.0221
× 10
23
).
Note:
At standard temperature and pressure (STP), the volume of 1 mol of ideal gas is 22.4 L, a
volume called the
molar volume of a gas
.
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