Question

For the decomposition reaction CH_3​3​​COH (g) → CH_4​4​​(g) + CO(g), the second order rate constant changes from 0.105 M^{-1}​−1​​s^{-1}​−1​​ at 759 K to 0.343 M^{-1}​−1​​s^{-1}​−1​​ at 791 K. What rate constant is expected at 836 K?

Answer 1

Arhenius equation

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

step 1 : Finding Ea of the reaction

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

k1 = 0.105 M^​-1​​s^-1 , T1 = 759 K

k2 = 0.343 M^​-1​​s^-1 , T2 = 791 K

Ea = 8.314 J/mol.K * ln ( 0.343 / 0.105) / ( 1/759 - 1/791) K^-1

Ea = 9.8418 J/mol / ( 0.0013175 - 0.001264)

Ea = 9.8418 J/mol / 0.0000535

Ea = 183958 J/mol or 183.9 kJ/mol

step 2 : calculating rate constant at 836 K

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

k1 = 0.105 M^​-1​​s^-1 , T1 = 759 K

k2 = x M^​-1​​s^-1 , T2 = 836 K

ln k2 - lnk1 = Ea/R * ( 1/T1 - 1/T2)

ln k2 - ln (0.105 M^​-1​​s^-1 ) = 183958 J/mol / 8.314 J/mol.K * ( 1/759 - 1/836 ) K^-1

ln k2 + 2.2537 M^​-1​​s^-1 = 22126.29 ( 0.0013175 - 0.00119617)

ln k2 + 2.2537 M^​-1​​s^-1 = 2.6845

ln k2 = (2.6845 - 2.2537) M^​-1​​s^-1

ln k2 = 0.4308

k2 = 1.538 M^​-1​​s^-1   is the rate constant at 836 K