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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

Question 5

$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.png$

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 act... show full transcript

Worked Solution & Example Answer: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

Step 1

Calculate A using the Arrhenius equation

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Answer

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:

Convert activation energy $E_a$ to J/mol: $E_a = 96.2 \, kJ \ mol^{-1} = 96200 \, J \ mol^{-1}$
Convert temperature from Celsius to Kelvin: $T = 25 °C = 298 \ K$
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,
$A = 3.46 \times 10^{-5} \times 4.32 \times 10^{17} \approx 1499785600 \approx 1.5 \times 10^{9} \, s^{-1}$

Step 2

Give the units for A

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Answer

The units for the Arrhenius constant A can be derived from the rate constant, k. Since k has the units of $s^{-1}$ , and we multiplied it by a dimensionless exponential term, the units for A remain the same:

$\text{Units of A} = s^{-1}$

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Calculate A using the Arrhenius equation

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