The rate constant for the decomposition of acetaldehyde, CH₃CHO, to methane, CH₄, and carbon monoxide, CO, in the gas phase is 1.10 × 10² m⁻¹ s⁻¹ at 703.7 k and 4.90 x 10⁻² m⁻¹ s⁻¹ at 865 k.The activation energy for this decomposition in KJ/mole is 154.303
To determine the activation energy of a reaction (Ea) from two reaction rates (k₁ and k₂) at two different temperatures (T₁ and T₂).
we use the equation -
<u>k₂</u> = <u>Eₐ </u> x ( <u>1 </u> - <u>1 )</u>
k₁ R T₁ T₂
Where,
R is the gas constant (8.3145 J/mol.K).
We have -
k₁= 1.10 x 10⁻² m⁻¹ s⁻¹
T₁= 703.7 K
k₂= 4.90 x 10⁻² m⁻¹ s⁻¹
T₂= 865 K
Putting the values in the equation -
<u>4.90 x 10⁻² m⁻¹ s¹</u> =<u> Ea </u> x ( <u> 1 </u> - <u> 1 )</u>
1.10 x 10⁻² m⁻¹ s⁻¹ (8.3145 J/K.mol) 703.7 K 865 K
Ea = (4<u>.90 x 10⁻² m⁻¹ s⁻¹</u>) / ( <u> 1 </u> - <u> 1 </u> <u>)</u> x (8.3145 J/K.mol)
1.10 x 10⁻² m⁻¹ s⁻¹ 703.7 K 851 K
Ea = 154303 J/mol
When divided by 1000,
Ea in KJ/mol = 154.303 KJ/mol
To learn more about activation energy,
brainly.com/question/8911926
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