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

Answer:

$k(75.0^0C)=2.65 x 10^4 s^{-1}$

Explanation:

Hello,

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

$\frac{k(75.0^0C)}{k(25.0^0C)} =exp[-\frac{\Delta Ea}{R}(\frac{1}{T_{k(75.0^0C)}}-\frac{1}{T_{k(25.0^0C)}} )]$

Thus, the rate constant results:

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

Best regards.