Question 33 of 37intermediate🔧 ApplyNumerical2 marks

The decomposition of hydrocarbon follows the equation k=(4.5×1011s−1)e−28000K/Tk = (4.5 \times 10^{11} \text{s}^{-1}) e^{-28000K/T}. Calculate EaE_a.

Correct Answer

The activation energy EaE_a is 232.8 kJ/mol.

Exercise: EXERCISES | Q: 3.26 | (Page 27)
For More Understanding

Explanation

This question tests the student's understanding of the Arrhenius equation form. By comparing the given equation with the standard Arrhenius equation, students can directly extract the activation energy. The key insight is recognizing that the exponent in the given equation contains the term 28000K, which equals Ea/RE_a/R.

Solution Steps

  1. Step 1: Write the standard Arrhenius equation: k=Ae−Ea/RTk = Ae^{-E_a/RT}

  2. Step 2: Compare with the given equation: k=(4.5×1011s−1)e−28000K/Tk = (4.5 \times 10^{11} \text{s}^{-1}) e^{-28000K/T}

  3. Step 3: Equate the exponents: EaRT=28000KT\frac{E_a}{RT} = \frac{28000K}{T}

  4. Step 4: Simplify to get: Ea=28000K×RE_a = 28000K \times R

  5. Step 5: Substitute R = 8.314 J K⁻¹ mol⁻¹: Ea=28000×8.314=232792E_a = 28000 \times 8.314 = 232792 J/mol

  6. Step 6: Convert to kJ/mol: Ea=232.8E_a = 232.8 kJ/mol

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