[hmok]

Mechanism:
(1) For the first step of an anionic addition polymerization, say, (C4H9-)(Li+) + (Styrene monomer) -> Propagating species, why is the electron lone pair (of C4H9-) attacking the double of Styrene monomer?

Isnt the double bond rich in electron? why are they attacked by nucleophile? is the drop in free energy one of the reason?

Kinetics:
(2) Seeing the rate of propagation , I would like to ask the original calculation of propagation rate. Is it K(prop.)*[input]? or is it K(prop.)*[input]/[output]? I am wondering whether the amount of reaction product will affect the rate.
Besides, I am confused when I see the reaction rate when we take termination due to impurities into account:
any step before this final equation that would help me understand?

[pgk]

The so formed Bu-styrene and polystyrene anions are stabilized by the aromatic conjugation.
Rate(prop.) = K(prop.)*[input]
However, impurities react with anions and stop the anionic polymerization. Therefore, impurities concentration must be taken in account, together with the termination rate constant, in regards to the propagation kinetics.