Since #n_"moles of stuff"# is presumed to be constant; i.e. we reasonably assume that you have not added any more solute to the solution, then:
#C_1V_1=C_2V_2#, each side of the equation has units #molxxL^-1xxL=mol#, so this is consistent dimensionally. Is this what you want? Someone here will be happy to expand if I have missed the point of your question.
See here for a pertinent example.