A 100 L sample of chlorine gas at 100 atm and 298 K reacts c

A 1.00 L sample of chlorine gas at 1.00 atm and 298 K reacts completely with 1.00 L of nitrogen gas and 2.00 L of oxygen gas at the same temperature and pressure. There is a single gaseous product, which fills a 2.00 L flask at 1.00 atm and 298 K. Use this information to determine thefollowing characteristics of the product:

(a) Its empirical formula. (b) Its molecular formula.

The answer in my book is A) ClNO2 B) ClNO2

I just needed help on how to work the full problem out.

Solution

from PV=nRT

We get 1*1=n*0.0821*298=0.04 moles of chlorine

similarly 0.04 moles of nitrogen

and 0.08 moles of oxygen so ratio of no of moles for cl:n:o=1:1:2

so empirical is ClNO2

product is also 0.08 moles so its molecular formula should be ClNO2