The rate constant for the first order decomposition of H$_2$O$_2$ is given by the equation: $$\log k = 14.2 - \frac{1.0\times10^{4}\,\mathrm{K}}{T}$$ Calculate E$_a$ for this reaction, and the rate constant k if its half-life period is 200 minutes. (R = 8.314 J K$^{-1}$ mol$^{-1}$)

CBSE Class 12 · 2016 · All India · Chemical KineticsShort Answer

The rate constant for the first order decomposition of H

_{2}

_{2}

is given by the equation:

lo g k = 14.2 - \frac{1.0 \times 1 0 ^{4} K}{T}

Calculate E

_{a}

for this reaction, and the rate constant k if its half-life period is 200 minutes. (R = 8.314 J K

^{- 1}

mol

^{- 1}

)

Answer: E_a ≈ 191.5 kJ mol⁻¹; k = 0.693/200 ≈ 3.47 × 10⁻³ min⁻¹ (= 5.78 × 10⁻⁵ s⁻¹).

Comparing with the Arrhenius form

lo g k = lo g A - \frac{E _{a}}{2.303 R T}

\frac{E _{a}}{2.303 R} = 1.0 \times 1 0^{4} K

E_{a} = 1.0 \times 1 0^{4} \times 2.303 \times 8.314

E_{a} = 1.915 \times 1 0^{5} J mo l^{- 1} = 191.5 kJ mo l^{- 1}

Rate constant from the half-life (first order):

k = \frac{0.693}{t _{1/2}} = \frac{0.693}{200}

k = 3.47 \times 1 0^{- 3} mi n^{- 1} = 5.78 \times 1 0^{- 5} s^{- 1}

CBSE Class 12 Board · 2016 · All India · Subjective