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The rate constant for a first-order reaction is 2.4 x 10-4 L/(mol's) at 600 K and 6.2 x 10-4L/(mol · s) at 900 K.
Calculate the activation energy. (R = 8.31 J/mol · K))
O 1.04 x 103 J/mol
O 1.42 x 104 J/mol
O 0.88 x 104 J/mol
O 1.42 x 10J/mol
O 2.55 x 109 J/mol

Respuesta :

onyebuchinnaji

The activation energy for the first-order reaction is determined as 0.62 x 10⁴ J/mol.

Activation energy of the reaction

The activation energy of the reaction is calculated as follows;

[tex]log(\frac{K_2}{K_1} ) = \frac{E_a}{R} (\frac{1}{T_1} - \frac{1}{T_2} )\\\\[/tex]

where;

  • Ea is he activation energy
  • K1 and K2 are the two rates
  • T1 and T2 are the two temperatures
  • R is gas constant

[tex]log(\frac{6.2 \times 10^{-4}}{2.4 \times 10^{-4}}) = \frac{E_a}{8.31} (\frac{1}{600} - \frac{1}{900} )\\\\0.412 = \frac{E_a}{8.31} (5.556 \times 10^{-4})\\\\0.412 = 6.685 \times 10^{-5} E_a\\\\E_a = 0.62 \times 10^4 \ J/mol[/tex]

Thus, the activation energy for the first-order reaction is determined as 0.62 x 10⁴ J/mol.

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