Question

In the 1860's the Central Pacific Railroad company employed the chemist James Howden to make an explosive capable of blasting through the granite mountains of the Sierras. The railroad needed tunnels for their train to pass through. James Howden built a nitroglycerin producing lab on Donner Pass where he would make the explosive compound on command. Nitroglycerin has the chemical formula C3H5N3O9. When it is detonated, it decomposes into carbon dioxide, water, oxygen and nitrogen. What is the theoretical yield for moles of nitrogen gas produced upon detonation of 1.320 tons of nitroglycerin? There are 907185 grams in 1 ton and nitroglycerin has a molar mass of 227 g/mol. Do not include decimals in your answer.

Answer 1

8 × 10³ mol N₂

Step-by-step explanation:

Step 1: Write the balanced equation

2 C₃H₅N₃O₉ ⇒ 6 CO₂ + 5 H₂O + 0.5 O₂ + 3 N₂

Step 2: Convert the mass of C₃H₅N₃O₉ from tons to grams

We will use the conversion factor 1 t = 907185 g.

1.320 t × 907185 g/1 t = 1.197 × 10⁶ g

Step 3: Calculate the moles corresponding to 1.197 × 10⁶ g of C₃H₅N₃O₉

The molar mass of C₃H₅N₃O₉ is 227 g/mol.

1.197 × 10⁶ g × 1 mol/227 g = 5.27 × 10³ mol

Step 4: Calculate the moles of N₂ formed from 5.27 × 10³ moles of C₃H₅N₃O₉

The molar ratio of C₃H₅N₃O₉ to N₂ is 2:3.

5.27 × 10³ mol C₃H₅N₃O₉ × 3 mol N₂/2 mol C₃H₅N₃O₉ = 7.91 × 10³ mol N₂ ≈ 8 × 10³ mol N₂