It seems ok to me. Remember that Molar mass: M = m * N
A. Insert that and k=R/N
A in v
p and the 2 equations are the same.
The last two equations implies that N*k = n*R which at first glance looks wrong. But N is not Advogadros constant it is the actual number of molecules:
http://en.wikipedia.org/wiki/Ideal_gas_law
So N = n*N
A, and if you insert above:
n*N
A*k = n*R or k = R/N
A , which is the defenition of k.
Edit: Ops I was too slow :)