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The rate constant for a reaction at 25 °C is 0.010 s⁻¹, and its activation energy is 35.8 kJ. Find the rate constant at 50.0 °C. Write the numerical value in the blank, but do not include units.

Answer :

Final answer:

The rate constant at 50.0 °C is approximately 0.0114 s-1.

Explanation:

To find the rate constant at 50.0 °C, we need to use the Arrhenius equation:

[tex]k = A * e^(-Ea/RT)[/tex]

Given:

  • Rate constant at 25 °C (k1) = 0.010 s-1
  • Activation energy (Ea) = 35.8 kJ
  • Temperature at 25 °C (T1) = 25 + 273 = 298 K
  • Temperature at 50.0 °C (T2) = 50 + 273 = 323 K

Let's substitute the values into the equation:

[tex]k2 = A * e^(-Ea/RT2)[/tex]

Since we are looking for the rate constant at 50.0 °C (k2), we can rearrange the equation:

[tex]k2 = k1 * e^((Ea/R) * (1/T1 - 1/T2))[/tex]

Now, let's substitute the given values:

[tex]k2 = 0.010 s-1 * e^((35.8 kJ / (8.314 J/(mol·K))) * (1/298 K - 1/323 K))[/tex]

Simplifying the equation:

[tex]k2 = 0.010 s-1 * e^(0.135 mol-1)[/tex]

Calculating the value:

k2 ≈ 0.010 s-1 * 1.144

k2 ≈ 0.0114 s-1

Learn more about calculating rate constant at a different temperature here:

https://brainly.com/question/14776335

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