A particular reaction has an activation energy, Ea, of 117 kJ/mol. If the rate constant for the reaction is 0.00289 s −1 at 590 °C, at what temperature(in°C) would the rate constant be 0.492 s −1?

The temperature is 1259.4 K (986.4°C)

Explanation:

Step 1: Data given

The activation energy Ea, = 117 kJ/mol

the rate constant for the reaction is 0.00289 s −1 at 590 °C

The new rate constant = 0.492 s −1

Step 2: Calculate the temperature

ln(kX / k 590°C)  =  Ea/R * (1/T1 - 1/T2)

⇒with kX is the rate constant at the new temperature = 0.492 /s

⇒with k 590 °C = the rate constant at 590 °C = 0.00289 /s

⇒with Ea = the activation energy = 117000 J/mol

⇒with R = the gas constant = 8.314 J/mol*K

⇒with T1 = 590 °C = 863 K

⇒ with T2 = the new temperature

ln (0.492 / 0.00289) = 117000/8.314 *(1/863 - 1/T2)

5.137 =14072.6 * (1/863 - 1/T2)

3.65*10^-4 = (1/863 - 1/T2)

3.65*10^-4 = 0.001159 - 1/T2

0,000794‬ = 1/T2

T2 = 1259.4 K

The temperature is 1259.4 K or 986.4 °C

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