For an inert real gas, if you were to reduce the pressure to half of its original value, then what would the final volume (Vf) relative to the initial volume (Vi) be?

A. 1/2 Vi - a little bit

B. 1/2 Vi + a little bit

C. 2 Vi - a little bit

D. 2 Vi + a little bit

The answer is C.

So, I understand that A and B are first eliminated, because of the inverse relationship between pressure and volume, as derived by the ideal gas law. I think I understand the rationale for C, which is that in an ideal situation if you were to compare to ideal gases, then 1/2 the pressure, should double the volume. The second part would be to then factor in the volume that the gas particles occupy, would lead to a final volume = 2 Vi - a little bit.

Here are my two questions:

1. If we are compareing the final volume (Vf) relative to the initial volume (Vi), since we are dealing with a real gas in both the initial and final volumes, wouldn't the ratio be...

Volume initial = Videal - a little bit (the volume occupied by the gas particles) : Volume final = Videal - a little bit (the volume occupied by the gas particles) ?

Wouldn't that mean that, Vf = 2 Vo, since we factored in the volume occupied by the gas particles in both scenarios?

2. The final few sentences in the rationale state, "If the pressure were double [instead], the volume wouldn't be reduced by exactly one-half, either. The new volume would be 1/2 Vi + a little bit."

I thought we always subtracted the ideal gas volume - the volume occupied by the gas. Could someone explain the plus sign?