Problem PageQuestionThe rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy =Ea27.0/kJmol. If the rate constant of this reaction is ×1.8103·M−1s−1 at 24.0°C, what will the rate constant be at −35.0°C?Round your answer to 2 significant digits.
Question
Problem PageQuestionThe rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy =Ea27.0/kJmol. If the rate constant of this reaction is ×1.8103·M−1s−1 at 24.0°C, what will the rate constant be at −35.0°C?Round your answer to 2 significant digits.
Solution
The Arrhenius equation is given by:
k = A * exp(-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 in Kelvin.
We are given: Ea = 27.0 kJ/mol = 27000 J/mol, k1 = 1.81 x 10^3 M^-1 s^-1 at T1 = 24.0°C = 297.15 K, and we are asked to find k2 at T2 = -35.0°C = 238.15 K.
We can use the two-point form of the Arrhenius equation, which is:
ln(k2/k1) = -Ea/R * (1/T2 - 1/T1)
We can rearrange this to solve for k2:
k2 = k1 * exp[-Ea/R * (1/T2 - 1/T1)]
Substituting the given values and using R = 8.314 J/mol*K, we get:
k2 = 1.81 x 10^3 * exp[-27000/(8.314) * (1/238.15 - 1/297.15)]
After calculating the above expression, we get:
k2 = 1.81 x 10^3 * exp[-3.25] = 1.81 x 10^3 * 0.038 = 68.78 M^-1 s^-1
Rounding to 2 significant digits, the rate constant at -35.0°C is 69 M^-1 s^-1.
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