Page 166 - Modern physical chemistry

158 Relationships among Reactants

Equation (7.65) now assumes the fonn

_ (c+xXd+x)IV2
X ) ,
Kc - ( a-x b-x IV2 [7.67]

which reduces to

[7.68]

Note that here Kc = Kp since An = O.
Secondly, consider the dissociation of phosphorus pentachloride gas

PCL 5 (g) ( ) PCLs (g) + C1 2 (g). [7.69]

In a container of volume V, a moles PCls, _ moles PCls, and c moles C12 are mixed. On
going to equilibrium, x moles PC15 dissociate. If no is a + b + c, the number of moles in
the beginning, the number at the end is

[7.70]

One may organize the pertinent expressions as in table 7.B.

TABLE 7.B

Moles Equilibrium Equilibrium
Con.stituent at Start Moles Mole Fraction
a-x
PCl 6 a a-x --
no+x
b+x
PCla b b+x --
no+x
Cl2 c c+x c+x
no+ x

With these, equation (7.65) takes on the fonn

_ (b+X c+x IV2 _ (b+X
Kc - a _ x I V - ->"""'('a--'-'x"""v--'- [7.71]

In fonnula (7.61), the partial pressure of each constituent equals its mole fraction times
the total pressure P; so here
(b+XXC+X)p2

(no +xt _ (b+XXc+X)p [7.72]
a-x - (a-xXno + x)'
--p
no+x