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