Since we have the grams of the sample of gas, we need to calculate the number of moles of the gas in order to figure out the molecular weight. We can do this using the gas law equation PV=nRT.
T=91 C = 364 K
n = (2*1)/(0.0821*364) = 0.0669 moles
We divide the mass by the moles to get the molecular weight.
6.13 g/0.0669 moles = 91.6 g/mole
We know that the gas is composed of about 2/3 O and 1/3 N. If this were NO2, the proportions would fit but the molecular weight is too small. If we double that formula we get N2O4. The molecular weight of this is approximately 14*2 + 16*4 = 92 so this fits what we calculated above. We can also check the percent compositions:
64/92 = 69.5% O
28/92 = 30.4% N
This fits with the information above. So the molecular formula of the gas is N2O4.