You could perhaps consider to apply Mass Flow Controllers (MFC) for both air and the other gas: https://www.researchgate.net/post/How_do_I_calibrate_a_mass_flow_controller_for_ammonia_gas_For_other_gases_I_normally_use_a_bubble_meter https://www.researchgate.net/post/Is_it_possible_to_use_Nitrogen_MFC_of_200_bar_for_Hydrogen_flow_of_the_same_pressure_What_order_of_error_is_expected
I haven't taken a detailed look at the differential equation. You want to calculate the gas concentration at the outlet of the mixing chamber. First, we would have to make an assumption, e.g. that mixing is perfect within the chamber. Then, I assume, we are looking at a PT1-element (first order low-pass). When you adjust the gas flow in the two inlets, the concentration is moving from the initial concentration towards the equilibrium.
Consequently, in order to calculate the concentration in the outlet at a given time, you need to know the two flow rates, the size of the chamber and the initial concentration.
the dimensions of the chamber are (h=10 and D=20) cm , the flow rate of gas is 2L/min and the air flow is 12 L/min. the chamber is contacted with rotary pump.