Answer:
67.017 dm³
Step-by-step explanation:
Data given:
amount of C₃H₅N₃O₉ = 452.36 g
volume of N₂ = ?
Solution:
First we look at the decomposition reaction of C₃H₅N₃O₉
2 C₃H₅N₃O₉ ----------> 6 CO₂ + 3 N₂ + 5 H₂O + O₂
2 mol 3 mol
So, 2 mole of C₃H₅N₃O₉ gives 3 moles of nitrogen on decomposition.
now convert mole of C₃H₅N₃O₉ to mass
Formula used
mass in grams = no. of moles x molar mass . . . . . . (1)
molar mass of C₃H₅N₃O₉ = 227 g/mol
put values in equation 1
mass in grams = 2 mol x 227 g/mol
Mass in grams = 454 g
So, it means that 454 g of C₃H₅N₃O₉ gives 3 moles of nitrogen on decomposition then how many moles of Nitrogen (N₂) will produce by 452.36 g of C₃H₅N₃O₉
Apply unity formula
454 g of C₃H₅N₃O₉ ≅ 3 moles of N₂
452.36 g of C₃H₅N₃O₉ ≅ X moles of N₂
Do cross multiplication
X moles of N₂ = 3 moles x 452.36 g / 454 g
X moles of N₂ = 2.989 moles
So,
no. of moles of N₂ = 2.989 moles
To find volume formula will be used
no. of moles = volume of gas/ molar volume . . . . . (2)
Rearrange the above equation 2
volume of gas = no. of moles x molar volume . . . . . (3)
Molar volume = 22.42 dm³/mol
Put values in above equation 3
volume of gas = 2.989 mol x 22.42 (dm³/mol)
volume of gas = 67.017 dm³
So, volume of N₂ = 67.017 dm³