Question

Given that the initial rate constant is 0.0180s−1 at an initial temperature of 30 ∘C , what would the rate constant be at a temperature of 180. ∘C for the same reaction described in Part A?

Express your answer with the appropriate units.

(I solved this and got 2.01, which is wrong, but I'm not exactly sure why).

(Reaction A was: The activation energy of a certain reaction is 44.3 kJ/mol . At 30 ∘C , the rate constant is 0.0180s−1 . At what temperature in degrees Celsius would this reaction go twice as fast?) I already solved Part A, so I do not need the answer to this. I am also confused about the units for this equation. What would the units be, and why?

Answer 1

Rate constant at temperature 180.^oC = 6.08 s^-1

Explanation

According to Arrhenius law,

ln(k₂ / k₁) = (E_a / R) * (1/T₁ - 1/T₂)

where

k₁ = initial rate constant = 0.0180 s^-1

T₁ = initial temperature = 30 ^oC = 303 K

k₂ = final rate constant

T₂ = final temperature = 180. ^oC = 453 K

E_a = activation energy = 44.3 kJ/mol = 44.3 x 10³ J/mol

R = constant = 8.314 J/mol-K

Substituting the values,

ln(k₂ / 0.0180 s^-1) = [(44.3 x 10³ J/mol) / (8.314 J/mol-K)] * (1/303 K - 1/453 K)

ln(k₂ / 0.0180 s^-1) = 5.823

k₂ / 0.0180 s^-1 = e^5.823

k₂ / 0.0180 s^-1 = 338

k₂ = (0.0180 s^-1) * (338)

k₂ = 6.08 s^-1