The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy E = 5.0 kJ/mol. If the rate constant of this reaction is 1.9 × 107 M¹-s Round your answer to 2 significant digits. -1 at 89.0 °C, what will the rate constant be at 121.0 °C?​

Answer 1

The Arrhenius equation is given by:

k = A * exp(-E/(R*T))

where k is the rate constant, A is the pre-exponential factor, E is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

To find the rate constant k at a different temperature, we can use the ratio of the Arrhenius equation at the two temperatures:

k2 / k1 = exp(E/(R*T1) - E/(R*T2))

We are given k1 = 1.9 × 10^7 M^-1 s^-1, E = 5.0 kJ/mol = 5000 J/mol, T1 = 89.0 °C = 362.15 K, and T2 = 121.0 °C = 394.15 K. The gas constant R = 8.314 J/mol*K.

Now we can solve for k2:

k2 = k1 * exp(E/(R*T1) - E/(R*T2))

k2 = (1.9 × 10^7 M^-1 s^-1) * exp(5000/(8.314*362.15) - 5000/(8.314*394.15))

k2 = (1.9 × 10^7 M^-1 s^-1) * exp(1.7083 - 1.5468)

k2 = (1.9 × 10^7 M^-1 s^-1) * exp(0.1615)

k2 ≈ 2.3 × 10^7 M^-1 s^-1

So, the rate constant at 121.0 °C is approximately 2.3 × 10^7 M^-1 s^-1.