The role of multi-10 TW chirped laser pulses interacting with N2 gas jet targets, as a test case for multi-electron targets, is experimentally examined. Complementary measurements using He gas jet targets, which are fully ionized well before the laser pulse peak, are also presented for comparison with the measurements for the multi-electron N2 targets. It is found that for both gases positively chirped laser pulses accelerate electrons more efficiently compared to the Fourier transform-limited and negatively chirped pulses. Furthermore, multi-electron targets offer additional electron injection mechanisms for efficient electron acceleration as a function of the chirp, due to the dynamic ionization of inner-shell electrons near the peak of the laser pulse. Finally, we show that the background plasma density value plays a critical role in the efficient acceleration of positively chirped pulses as well as in the tuning of the positive chirp value for maximizing the electron energy. We clearly observe that larger plasma density values require higher positive chirp values for efficient electron acceleration.