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For the decomposition of gaseous dinitrogen pentoxide, 2 N₂O₅(g) → 4 N₂(g) + O₂(g) the rate constant is k = 2.8X10⁻³ s⁻1 at 60°C. The initial concentration of N₂O₅ is 1.58 mol/L. (b) What fraction of the N₂O₅ has decomposed after 5.00 min?

Respuesta :

The fraction of the N₂O₅ has decomposed after 5.00 min is 0.387.

Calculation of fraction of N₂O₅:

Rate constant k = 2.8X10⁻³ s⁻1 at 60°C

Initial concentration of N₂O₅ = 1.58 mol/L

For the first order reaction

Rate = k[A]

[tex][A] = [A_{o} ] e^{-kt} [A] = 1.58 mol/L * e^{(-2.8*10^-3/s * 300s)} [A] = 0.967 mol/L[/tex]

Concentration of N₂O₅ decomposed = 1.58 - 0.967 = 0.613 mol/L

Fraction of N₂O₅ decomposed after 5.00 min = 0.613/1.58 = 0.387

Hence, the fraction of the N₂O₅ has decomposed after 5.00 min is 0.387.

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