Equilibrium Constants

1
Equilibrium Constants Chlorofluorocarbons,
haloalkanes, or FreonsTM, a Dupont trademark for
which they were a 5 billon dollar business, are
alkanes in which all the hydrogens have been
replaced by fluorine and chlorine atoms. FreonTM
12, CF2Cl2, is an example of a halomethane. How
many different halomethanes are there? They are
unreactive gases under ordinary conditions and
are ideal for use as propellants in pressurized
products such as hair sprays, shaving creams,
etc. They are also non-inflammable compounds
with high heat capacities and have found wide use
in halon fire extinguishers and as coolants in
refrigerators and air conditioning
systems. Because they are unreactive these gases
eventually mix into the stratosphere where they
are subject to photodecomposition by ultraviolet
light CF2Cl2 (g) hn (l lt 220 nm) ------gt
CF2Cl (g) Cl (g) The neutral radical
chlorine atoms formed in this decomposition are
very reactive (why?) and react readily with ozone
in the two step mechanism Cl (g) O3 (g)
------gt ClO (g) O2 (g) Kp1 1.1 x 1023
ClO (g) O (g) ------gt O2 (g) Cl
(g) Kp2 7.7 x 1045 to give a net reaction
involving oxygen atoms in which a molecule of
ozone is converted to 2 molecules of oxygen O3
(g) O (g) ------gt 2 O2 (g) Kp, net ?
What role do the Cl (g) atoms play in this
mechansim? What role do the ClO (g) molecules
play?
2
We can begin the calculation of Kp, net by
writing out in detail the equilibrium constant
expression for the net reaction Kp, net
(PO2)2 / ( PO3 PO ) PClO PO2 / (PCl PO3)
PCl PO2 / (PClO PO) How did we accomplish this
last step? Kp1 Kp2 (1.1 x 1023) (7.7 x
1045) 8.5 x 1068 In general, when reactions
are added to give some net reaction, how are the
equilibrium constants of the individual reactions
related to the equilibrium constant of the net
reaction? At equilibrium is oxygen or ozone the
favored molecular species in the reaction O3 (g)
O (g) ------gt 2 O2 (g) ? The chemistry that
we have just described is cause for some concern,
since the stratospheric ozone that is removed as
a result of these reactions absorbs much of the
short wavelength solar ultraviolet light and
protects us from this energetic radiation. The
WEB site http//www.epa.gov/Ozone/science/
provides a good discussion of the causes and
dynamics of ozone depletion in the
stratosphere. Ozone levels are often measured in
Dobson units. One Dobson unit, DU, corresponds
to the ozone that would be present in a column of
the atmosphere if it were compressed to a height
of 0.0100 mm at STP. A hole in the ozone is
said to occur when the ozone has fallen below 220
DU. How many ozone molecules are present in a
column of the atmosphere 1.00 mm2 in area that
has an ozone level of 220 DU?
3
What is Kp for the reaction 1/2 O3 (g) 1/2 O
(g) ------gt O2 (g) Kp ? in which the net
ozone depletion reaction that we just discussed
is scaled by a factor of 1/2? In general,
when a reaction is scaled by some common factor,
how is the equilibrium constant of the scaled
reaction related to the equilibrium constant of
the original reaction? What is Kp for the
reaction 2 O2 (g) ------gt O3 (g) O (g)
Kp ? in which net ozone depletion
reaction that we previously discussed is
reversed? In general, when a reaction is
reversed, how is the equilibrium constant of the
reversed reaction related to the equilibrium
constant of the original reaction?
4
Sulfur dioxide, SO2, formed during the combustion
of sulfur containing fossil fuels, reacts with
atmospheric oxygen and water droplets to form an
areosol of sulfuric acid, i.e., acid rain SO2
(g) 1/2 O2 (g) H2O (l) ------gt H2SO4
(aq) K ? Calculate the equilibrium
constant for this reaction at 25.0 oC, using the
known equilibrium constants for the reactions 2
SO2 (g) O2 (g) ------gt 2 SO3 (g) K1
6.8 x 1024 H2SO4 (aq) ------gt SO3 (g) H2O
(l) K2 2.1 x 10-53
5
During World War I Fritz Haber, a German
scientist, developed a method of synthezing
ammonia from atmospheric nitrogen and hydrogen
known as the Haber synthesis of ammonia N2 (g)
3 H2 (g) ------gt 2 NH3 (g) This reaction is
an example of the chemical fixation of nitrogen
in which normally unreactive molecular nitrogen
is incorporated into a chemical compound. The
ammonia was used produce ammonium nitrate for use
in munitions. In the long run this chemistry has
had a much greater impact in the peacetime
production of fertilizer and has contributed
greatly to feeding the worlds population.
While the equilibrium constant for this
reaction, Kp 821 atm-2, is favorable for the
production of ammonia at 25.0 oC, unfavorable
kinetics requires that the reaction be run at
substantially higher and more costly
temperatures. Mimicking the cheap room
temperature biological fixation of nitrogen by
plant enzymes is still an active and unrealized
goal of biochemists. The equilibrium constant
based on concentration is defined for this
reaction as Kc NH3e2 / ( N2e H2e3
) Assuming that the gases can be treated as
ideal, we can express the gas concentrations in
terms of their partial pressures, e.g., for
ammonia NH3 PNH3 / R T Could you
write similar relations for N2 and H2?
6
These relations allows us to relate Kc to Kp
Kc NH3e2 / ( N2e H2e3 )
(PNH3, e / R T)2 / (PN2, e / R T) (PH2, e / R
T)3 ) Kp (R T)2 (821 atm-2)
(0.008205 L atm / mole K) (298.2 K)2 4.91
x 103 L2 / mole2 4.91 x 103 M-2 Could you
write a general equation describing the relation
between Kc and Kp for any reaction involving
ideal gases? An equilibrium constant based on
mole fractions, Kx, can also be defined using the
relation between mole fractions and partial
pressures that exists for ideal gases Xi Pi
/ Ptotal What is the value of Kx for the Haber
synthesis of ammonia? Do any of the equilibrium
constants K, Kc, Kp, or Kx depend on
pressure? Two likely structures for fulminic
acid, HCNO, are C N - O - H and H - C
? N O Use thermodynamics to argue which one of
these structures is expected to be the most
stable at 25 oC. You will have to look up data
to answer this question.