Question

It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be _______kJ mol⁻¹. [nearest integer]

(Given In10=2.3, R=8.3 J K⁻¹ mol⁻¹, log 2=0.30)
A. 59.00
B. 59.0
C. 59

Answer 1

The activation energy (Ea) for the reaction at 300 K is determined using the Arrhenius equation and the temperature dependence of the rate constant. The value of the activation energy is calculated to be 59 kJ mol⁻¹, corresponding to option C.

Step-by-step explanation:

The question pertains to the calculation of the activation energy (Ea) for a chemical reaction using the temperature dependence of the rate constant. According to the Arrhenius equation, the rate constant k doubles when the temperature is increased by 9 K. Using the given data, we are asked to find the value of activation energy in kJ mol⁻¹ at 300 K. The Arrhenius equation is = ln k = ln A - (Ea/RT).

Where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in kelvins. After taking the natural log of the ratio between the doubled rate constant (k2) and the initial rate constant (k1), and using the provided logarithmic conversions, we can solve for the activation energy Ea. Substituting the given value for R and computing, we find that the activation energy for the reaction is 59 kJ mol⁻¹, which corresponds to answer option C.