In the water and ammonia
syntheses just discussed, the numbers of molecules of reactants
and products in the equation were different, so
was not a unitless quantity. The conversion of units from atmospheres
to moles per liter is a simple one involving the ideal gas law,
PV = nRT, which we discussed in Chapter 2. In this expression
Pis the pressure in atmospheres, V is the volume in liters, n
is the number of moles, T is the absolute temperature, and R is
the gas constant expressed in units of liter atm per deg per mole:
R = 0.08205
liter atm deg
mole
For the jth component in a mixture of gases,
p
V = n
RT
p
= (n
/ V) RT = RT
in which p
is the partial pressure and
is the concentration of the jth gas in moles per liter.
Equilibrium constants with concentrations expressed as partial pressures
in atmospheres are designated by ,
and constants in units of moles per liter are designated by .
For the water formation reaction that we have just seen, these constants
can be written as


To obtain ,
from , one need
only substitute p
= RT for each
chemical substance, reactant and product:
=
RT = 1.35 x 10
atm
(mole / liter)
= 1.35 x 10
x 0.08205 x 298 liter
= 3.31
x 10
liter
Only if the number of moles of reactants and products is the same,
will and Kc
be the same unitless number. In general, if the balanced chemical
equation shows an increase of n
in the number of moles of gas in the products as compared with reactants,
then
