How many liters of oxygen are needed to react with 6.00 L of nitrogen at the same temperature and pressure according
to the following reaction? 2N2(g) + 5O2(g) --> 2N2O5(g)

Hi Vinay
You know that equal volumes have equal number of moles at the same temperature and pressure (Avogadro's law)
So you just need to read this equation in terms of volumes
From balanced equation we know
2 L of N2 reacting with 5L of O2
Now you can use simple mathematics to calculate volume of O2 required to react with 6L of N2