Answer:
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
