The rate constant of a chemical reaction increased from 0.100 s^-1 to 2.70 s^-1

Question

The rate constant of a chemical reaction increased from 0.100 s^-1 to 2.70 s^-1 upon raising the temperature from 25.0 degree C to 47.0 degree C. 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 = Adele, not where k is the rate constant., 4 is the frequency factor. Ea. is the activation energy. R = 8.3145 J/(K middot moll) is the gas constant, and T is the Kelvin temperature. The following rearranged version of the equation is also useful: LN (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 (1/t_2 - 1/t_1 where T_1 is the initial temperature and T_2 is the final temperature. Express your answer numerically. Calculate the value of In where k_1 and k_2 correspond to the rate constants at the initial and the final temperatures as defined in part A.

Explanation / Answer

Part A ) (1/T2 - 1/T1)

Temperatures in K

So,

(1/T2 - 1/T1) = (1/320 - 1/298) = -2.31 x 10^-4

Part B ) ln(k1/k2)

taking values from above,

ln(k1/k2) = ln(0.1/2.70) = -3.30

Part C ) energy of activation Ea

ln(k1/k2) = -Ea/R[1/T2 - 1/T1]

R = gas constant

So,

Ea = -3.30 x 8.314/-2.31 x 10^-4 x 1000 = 118.7 kJ/mol

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