Question

For a particular reaction, the rate constant is 2.40 ✕ 10−3 m/s at 185°c and 3.84 ✕ 10−3 m/s at 235°c. what is the activation energy for this reaction?

Answer 1

The activation energy of the reaction can be calculated using the Arrhenius equation and the given rate constants and temperatures. The calculation results in an activation energy of approximately 54212.8 J/mol or 54.2 kJ/mol.

Step-by-step explanation:

The activation energy for a reaction can be estimated from temperature and reaction rate data using the Arrhenius equation: k = Ae^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature. Over a small temperature range, the equation simplifies to: ln(k2/k1) = Ea/R(1/T1 - 1/T2). Plugging in given values (with temperatures converted to Kelvin) gives us Ea = R * ln(k2/k1) / (1/T1 - 1/T2), which turns into Ea = 8.314 * ln(3.84 ✕ 10−3 / 2.40 ✕ 10−3) / (1/458.15 - 1/508.15). Evaluating this gives us an activation energy approximately equal to 54212.8 J/mol or 54.2 kJ/mol.

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