If 452.36 g of c3h5n3o9 decompose what volume of n2 will be produced

67.017 dm³

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