To find the volume of O2 required, we first need to balance the chemical equation:

CH4 + 2O2 = CO2 + 2H2O

From the balanced equation, we can see that 1 mole of CH4 reacts with 2 moles of O2 to produce 1 mole of CO2 and 2 moles of H2O.

Given that V(CH4) = 5000 L, we need to find the volume of O2 required. Since the volume ratios in a chemical reaction are directly proportional to the coefficients in the balanced equation, we can say that the ratio of volumes of O2 to CH4 is 2:1.

Therefore, the volume of O2 required can be calculated as follows:
V(O2) = (5000 L) * (2/1) = 10000 L

So, the volume of O2 required for the complete combustion of 5000 L of CH4 is 10000 L.