What is the activation energy of a chemical reaction if the reaction rate triples when the temperature goes from 10°C to 30°C? A) 5.5 × 10⁻²⁰ J B) 6.0 × 10⁻²⁰ J C) 6.5 × 10⁻²⁰ J D) 7.0 × 10⁻²⁰ J E) 7.5 × 10⁻²⁰ J

Question

Quizplus · Accepted Answer

According to the Arrhenius equation, the reaction rate constant (k) is proportional to the exponential of the activation energy divided by the product of the gas constant (R) and the temperature in Kelvin (T):
k = A * exp(-Ea/RT)
Taking the ratio of two rate constants at two different temperatures gives:
k2/k1 = (A * exp(-Ea/RT2))/(A * exp(-Ea/RT1))
k2/k1 = exp(Ea/R * (1/T1 - 1/T2))
Since the reaction rate triples when the temperature goes from 10°C (283K) to 30°C (303K), we have:
k2/k1 = 3
303/283 = 1.071
Solving for Ea, we get:
ln(3) = Ea/(8.3145 J/mol*K) * (-1/T1 + 1/T2)
Ea = -ln(3) * 8.3145 J/mol*K * (-1/283K + 1/303K) = 6.5 × 10^20 J. 
Therefore, the answer is choice C.

What Is the Activation Energy of a Chemical Reaction If