Question

A particular first-order reaction has a rate constant of 1.35 × 102 s-1 at 25.0°C. What is the magnitude of k at 75.0°C if Ea = 91.0 kJ/mol? A particular first-order reaction has a rate constant of 1.35 × 102 s-1 at 25.0°C. What is the magnitude of k at 75.0°C if Ea = 91.0 kJ/mol? 4.10 × 106 s-1 713 s-1 1.36 × 102 s-1 2.65 × 104 s-1 3.69 × 104 s-1

Answer 1

`k(75.0^0C)=2.65 x 10^4 s^(-1)`

Step-by-step explanation:

Hello,

In this case, based on the given information, the Arrhenius equation is used to predict k at 75.0 °C as:

`(k(75.0^0C))/(k(25.0^0C)) =exp[-(\Delta Ea)/(R)((1)/(T_(k(75.0^0C)))-(1)/(T_(k(25.0^0C))) )]`

Thus, the rate constant results:

`k(75.0^0C)=k(25.0^0C)exp[-(\Delta Ea)/(R)((1)/(T_(k(75.0^0C)))-(1)/(T_(k(25.0^0C))) )]\\\\k(75.0^0C)=1.35x10^2s^(-1)exp[-(91000J/mol)/(8.314J/(mol*K))((1)/(348.15K)-(1)/(298.15K) )]\\\\k(75.0^0C)=2.65 x 10^4 s^(-1)`

Best regards.