Molar mass of C₃H₅N₃O₉ = (12.0×3 + 1.0×5 + 14.0×3 + 16.0×9) g/mole = 227.0 g/mole

No. of moles of C₃H₅N₃O₉ decomposed = (75.0 × 1000 g) / (227.0 g/mole) = 330.4 mole

C₃H₅N₃O₉(l) → 12 CO₂(g) + 6 N₂(g) + 10 H₂O(g) + O₂(g)

Mole ratio C₃H₅N₃O₉ : (mixture of gases ) = 4 : (12+6+10+1) = 4 : 29

No. of moles of mixture of gases generated = (330.4 mole) × (29/4) mole = 2,395 mole

For the mixture of gases generated :

Pressure, P = 755/760 atm

Volume, V = ? L

No. of moles, n = 2395 mole

Gas constant, R = 0.0821 L atm / (mole K)

Absolute temperature, T = (273 + 530) K = 803 K

Gas law : PV = nRT

Then, V = nRT/P

Volume of the mixture of gases generated, V = 2,395 × 0.0821 × 803 / (755/760) L = 159,000 L