The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy =Ea45.0/kJmol. If the rate constant of this reaction is ×1.9102·M−1s−1 at 76.0°C, what will the rate constant be at 30.0°C?Round your answer to 2 significant digits.
Question
The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy =Ea45.0/kJmol. If the rate constant of this reaction is ×1.9102·M−1s−1 at 76.0°C, what will the rate constant be at 30.0°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.
Given: Ea = 45.0 kJ/mol = 45000 J/mol k1 = 1.91 x 10^2 M^-1 s^-1 at T1 = 76.0°C = 76.0 + 273.15 = 349.15 K We need to find k2 at T2 = 30.0°C = 30.0 + 273.15 = 303.15 K
We can use the two-point form of the Arrhenius equation, which is:
ln(k2/k1) = -Ea/R * (1/T2 - 1/T1)
Rearranging for k2 gives:
k2 = k1 * exp[-Ea/R * (1/T2 - 1/T1)]
Substituting the given values and using R = 8.314 J/mol*K, we get:
k2 = 1.91 x 10^2 * exp[-45000/(8.314) * (1/303.15 - 1/349.15)]
Calculating the above expression will give the value of k2. Remember to round your answer to 2 significant digits.
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