To use the Arrhenius equation to calculate the activation energy. As temperature

Question

To use the Arrhenius equation to calculate the activation energy. As temperature rises, the average kinetic energy of molecules increases. In a chemical reaction, this means that a higher percentage of the molecules possess the required activation energy, and the reaction goes faster. This relationship is shown by the Arrhenius equation k=Ae^-E_1/RT where k is the rate constant. A is the frequency factor. A is the activation energy. R = 8.3145 J/(K. mol) is the gas constant, and T is the Kelvin temperature. The following rearranged version of the equation is also useful: IN (k_1/K_2)=(E_a/R) (1/T_2 - 1/T_1) where k_1 is the rate constant at temperature T_1. and K_2 is the rate constant at temperature T_2. Calculate the value of IN(k_1/k_2) where k-1 and k_2 correspond to the rate constants at the initial and the final temperatures as defined in part A. What is the activation energy of the reaction?

Explanation / Answer

rate constant of chemical reaction increase from 0.100 s-1 to 2.90 s-1

raising the temperature 25.00C to 53.00C

1. (1/T2 - 1/T1) = (1/326 - 1/298 ) = -0.000288 { t1 = 25+ 273 K = 298 K, T2 = 53 +273 = 326 K)

2. ln (k1/k2) = ln(0.10 / 2.90) = -3.367

3. ln(k1/k2) = (Ea/R) (1/T2 - 1/T1) { R = 8.314 jmol-1 K-1}

Ea =  (-3.367 x 8.314 ) / (-0.000288) = 97124.5387 J/mol = 97.124 KJ/mol

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