Pressure increase on rate of reaction
There is probably going to be a separate reaction rate law for each phase, assuming that the reaction even occurs in other phases.  Of course, in liquid and solid phases, the pressure is going to have much less of an effect than in a gas phase.  Another consideration is that there may be interphase mass transport between the various phases (at their interfaces), and this may have to be taken into account in the chemical species mass balances for the individual phases.