The question got bumped and I looked at it. The OP seems to use the two terms coefficient of ionization and ionization coefficient interchangeably and assigns the variable $\alpha$. The problem is in part asking about the pH of a 0.1 molar ammonia solution.
Am I correct to assume that the ionization coefficient is the fraction of the ammonia that has ionized?
My google foo is off today. I couldn't find a formula anywhere where the context made sense. The problem in question has nothing to do with a plasma.