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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