the rate constant of first order reaction at 7°C& 57°C are 7.0*10^-7 & 9.0*10^-4 mole / litresecond calculate value of rate const at127°C?

When T₁ = (273 + 7) K = 280 K, k₁ = 7.0 × 10⁻⁷ mol/(L s)
When T₂ = (273 + 57) K = 330 K, k₂ = 9.0 × 10⁻⁴ mol/(L s)
When T₃ = (273 + 127) K = 400 K, k₃ = ? mol/(L s)

By Arrhenius equation :
ln(k₁/k₂) = -(Eₐ/R)[(1/T₁) - (1/T₂)]
ln[(7.0 × 10⁻⁷)/(9.0 × 10⁻⁴)] = -(Eₐ/R)[(1/280) - (1/330)] …… {1}

Also :
ln(k₁/k₃) = -(Eₐ/R)[(1/T₁) - (1/T₃)]
ln[(7.0 × 10⁻⁷)/k₃] = -(Eₐ/R)[(1/280) - (1/400)] …… {2}

{2}/{1} :
ln[(7.0 × 10⁻⁷)/k₃] / ln[(7.0 × 10⁻⁷)/(9.0 × 10⁻⁴)] = [(1/280) - (1/400)] / [(1/280) - (1/330)]
ln[(7.0 × 10⁻⁷)/k₃] = ln[(7.0 × 10⁻⁷)/(9.0 × 10⁻⁴)] × [(1/280) - (1/400)] / [(1/280) - (1/330)]
[(7.0 × 10⁻⁷)/k₃] = e^{ln[(7.0 × 10⁻⁷)/(9.0 × 10⁻⁴)] × [(1/280) - (1/400)] / [(1/280) - (1/330)]}
k₃ = (7.0 × 10⁻⁷) / e^{ln[(7.0 × 10⁻⁷)/(9.0 × 10⁻⁴)] × [(1/280) - (1/400)] / [(1/280) - (1/330)]}
k₃ = 1.00 mol/L s