The rate constant, k, for a reaction varies with temperature as shown by the equation $$k = Ae^{-E_a/RT}$$ For this reaction, at 25 °C, k = 3.46 × 10⁻⁵ s⁻¹ The activation energy $E_a = 96.2 \, kJ \ mol^{-1}$ The gas constant $R = 8.31 \, J \ K^{-1} \ mol^{-1}$ Calculate a value for the Arrhenius constant, A, for this reaction - AQA - A-Level Chemistry - Question 5 - 2019 - Paper 2

We start with the Arrhenius equation:

$k = Ae^{-E_a/RT}$

To find A, we rearrange the equation:

$A = k e^{E_a/RT}$

Now we plug in the values:

1. Convert activation energy $E_a$ to J/mol: $E_a = 96.2 \, kJ \ mol^{-1} = 96200 \, J \ mol^{-1}$

2. Convert temperature from Celsius to Kelvin: $T = 25 °C = 298 \ K$

3. Plug in the values to find A:

   • Using $k = 3.46 × 10^{-5} \, s^{-1}$ and $R = 8.31 \, J \ K^{-1} \ mol^{-1}$:

   $A = 3.46 \times 10^{-5} \, s^{-1} \times e^{\frac{96200}{8.31 imes 298}}$

   • Calculate the exponent:

   $e^{\frac{96200}{(8.31)(298)}} = e^{39.07} \approx 4.32 \times 10^{17}$

   • Thus,

   $A = 3.46 \times 10^{-5} \times 4.32 \times 10^{17} \approx 1499785600 \approx 1.5 \times 10^{9} \, s^{-1}$