What is the rate constant at 250K? Please Help?

2020-09-02 12:44 pm

The gas phase reaction

2 N2O5(g) → 4 NO2(g) + O2(g)

has an activation energy of 103 kJ/mol, and the first order rate constant is
7.97×10-10 min-1 at 220 K. What is the rate constant at 250 K?

I'm not understanding how to find k2 but I know how to set it up.

回答 (1)

老爺子

2020-09-02 1:01 pm

Activation energy, Eₐ = 103 kJ/mol = 103000 J/mol
Gas constant, R = 8.314 J mol⁻¹ K⁻¹
At T₁ = 220 K, k₁ = 7.97 × 10⁻¹⁰ min⁻¹
At T₂ = 250 K. k₂ = ?

Arrhenius equation:
ln(k₁/k₂) = (Ea/R) [(1/T₂) - (1/T₁)]
ln[(7.97 × 10⁻¹⁰)/k₂) = (103000/8.314) [(1/250) - (1/220)]
ln[(7.97 × 10⁻¹⁰)/k₂) = -6.7575
(7.97 × 10⁻¹⁰)/k₂ = e⁻⁶·⁷⁵⁷⁵
k₂/(7.97 × 10⁻¹⁰) = e⁶·⁷⁵⁷⁵
k₂ = (7.97 × 10⁻¹⁰) × e⁶·⁷⁵⁷⁵
Rate constant at 250 K, k₂ = 6.86 × 10⁻⁷ min⁻¹

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