The rate constant of a reaction is 4.7*10-3 s-1 at 25°C, and the activation energy is 33.6 kJ/mol. What is k at 75°C?

k is 3,18*10⁻² s⁻¹ at 75°C

Explanation:

following Arrhenius equation:

k = k₀*e^ (-Ea/RT)

where k = rate constant, k₀ = frequency factor, Ea = activation energy, R = universal gas constant T=absolute temperature

then for T₁=25°C = 298 K

k₁ = k₀*e^ (-Ea/RT₁)

and for T₁=75°C = 348 K

k₂ = k₀*e^ (-Ea/RT₂)

dividing both equations

k₂/k₁ = e^ (-Ea/RT₂+Ea/RT₁)

k₂ = k₁*e^[-Ea/R * (1/T₂-1/T₁) ]

replacing values

k₂ = k₁*e^[-Ea/R * (1/T₂-1/T₁) ] = 4,7*10⁻³ s⁻¹ * e^[-33.6*1000 J/mol / 8.314 J/molK * (1 / 348 K - 1/298 K) ] = 3,18*10⁻² s⁻¹

thus k is 3,18*10⁻² s⁻¹ at 75°C