Let (A,phi) be the reduced free product of infinitely many pairs (A_i,phi_i)
of C*-algebras with faithful states. Assume that the A_i are not too small, in
a specific sense. It is shown that if phi is a trace then K_0(A) is determined
entirely by K_0(phi). If, furthermore, the image of K_0(phi) is dense in the
reals then A has real rank zero. On the other hand, if phi is not a trace then
A is simple and purely infinite
