Hello,
Depending on the connection between the two vessels it can be complicated.
In case of very thin/long tube between the vessels, it can be a laminar or turbulent flow in a pipe problem. But most formulas assume incompressible fluid. In case of large pressure drop across the pipe between the vessels, these formulas do not apply (as in your case).
Assuming that the process takes short time, you may assume adiabatic or isentropic expansion/compression. That means that after some time, your 50psi will drop due to heat exchange.
When pipe friction is low (large diameter, short connection between vessels), you may have a choked flow (flow limited by speed of sound). Looking to your pressure ratio 151psi/1psi initial, 150/50 final, you will very likely have a choked flow over the complete air transfer process.
In a choked flow, the low-pressure side doesn't influence the mass flow through the orifice as speed of sound avoids pressure disturbances to be transmitted from the low-pressure side to the high-pressure side. The mass flow from the large vessel to the small vessel depends only on the diameter of the orifice/pipe and input conditions (pressure, density, Cp/Cv ratio). When you assume your main vessel very large, you may assume that the pressure in the main vessel is constant during the filling of the small vessel. This eases the calculation or setting up a simulation model, as you have a constant mass flow during the fill period.
Best is to search for "choked flow" (for example wikipedia).