In the case of a 741 op-amp with R2 = 100k and R1 = 1k the gain should be -100. The output voltage should then be 101 times whatever the input is. I understand that given a large input voltage to the non-inverting terminal, the output should be saturated to the positive rail, but in both simulations and in the experimental procedure I have found that leaving the input open causes the output to be around -8V when my saturation is +-10V. I know leaving the terminal open is not a practical implementation of the op-amp, but theoretically, I would like to know what causes this output voltage to be driven the way it is.
The input bias current for a 741 is about 80 nA: every second, the chip is pulling a (tiny) bit of charge from that input pin.
If there’s a resistive path, it can provide that current.
But if the pin is open-circuited, it acts as a small capacitor. The removed charge drives the voltage at that point more and more negative. That drives the output negative.
Eventually, all those voltages get negative enough that the op amp becomes internally unbalanced, and the output sits down near the rail.