Question 27

The rate constant for the first order decomposition of H₂O₂is given by the following equation:

log k = 14.34 - 1.25 x 10⁴K/T

Calculate E_afor this reaction and at what temperature will its half-period be 256 minutes?

Answer

Arrhenius equation is given by,

k= Ae ^-E_a/RT

⇒In k = In A - E_a/RT

⇒In k = Log A - E_a/RT

⇒ Log k = Log A - E_a/2.303RT (i)

The given equation is

Log k = 14.34 - 1.25 10⁴ K/T (ii)

From equation (i) and (ii), we obtain

E_a/2.303RT = 1.25 10⁴ K/T

⇒ E_a=1.25 × 10⁴K × 2.303 × R

= 1.25 × 10⁴K × 2.303 × 8.314 J K^{- 1}mol^{- 1}

= 239339.3 J mol^{- 1} (approximately)

= 239.34 kJ mol - 1

Also, when t_1/2= 256 minutes,

k = 0.693 / t_1/2

= 0.693 / 256

= 2.707 × 10^{- 3}min ^{- 1}

= 4.51 × 10^{- 5}s^{- 1}

It is also given that, log k= 14.34 - 1.25 × 10⁴K/T

= 668.95 K

= 669 K (approximately)

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