Answer:
Explanation:The rate constant, k, is related to the activation energy, Ea, by the Arrhenius equation:
k = Ae^(-Ea/RT)
where A is the pre-exponential factor, R is the gas constant, and T is the absolute temperature in Kelvin.
To compare the relative rates of reactions A and B, we can calculate the ratio of their rate constants:
k(A) / k(B) = [Ae^(-Ea(A)/RT)] / [Be^(-Ea(B)/RT)]
where A and B are the pre-exponential factors for reactions A and B, respectively.
Taking the natural logarithm of both sides and rearranging gives:
ln(k(A) / k(B)) = ln(A) - ln(B) - [(Ea(A) - Ea(B)) / (RT)]
Plugging in the given values, we get:
ln(k(A) / k(B)) = ln(1) - ln(1) - [(87.00 kJ/mol - 74.30 kJ/mol) / (8.314 J/mol·K × 298 K)] = -1.98
Solving for k(A) / k(B), we get:
k(A) / k(B) = e^(-1.98) = 0.136
Therefore, reaction B is faster than reaction A by a factor of 1 / 0.136 = 7.35.