So p= K-K1/2/ (K-1) (where K is the equilibriu constant)
Than says: X_n= 1/1-p so X_n= K-1/K1/2-1
Brackets! You are saying something other than what you intend to say!
It is simpler to say p = K
1/2/(K
1/2-1) and X
n = K
1/2+1
let me think that is only corret to predict the avarage lenght of (only) the Polyemer chains (so the degree of polymerization Xn) only when all monomer has reacted...
When all monomer has reacted, p = 1 and you get X
n = ∞. Theoretically (you never achieve it in practice) you would have a single polymer molecule of infinite length. If you have an equilibrium, p will never be 1.
For any p < 1, there is a broad, approximately exponential distribution of chain lengths, in which monomer is the most numerous kind of molecule present (highest number fraction, but not weight fraction). This is an important fact about condensation polymerisation, and justifies the use of the formula X
n = 1/(1-p), which includes monomer. For some other types of polymerisation, e.g. living polymerisation, there are relatively few growing polymer chains and a large excess of monomer (until you reach high p). That formula then does not give a good description of the degree of polymerisation of the polymer chains themselves.