The rate constant reaction is 0.01439 mim*-1 at 298k and its activation energy is 70000 mol *-1. What is the value rate constant at 313k

To calculate the rate constant at 313 K, we can again use the Arrhenius equation in its comparative form:

\[
\ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)
\]

Given:
- \( k_1 = 0.01439 \, \text{min}^{-1} \) (rate constant at 298 K),
- \( T_1 = 298 \, \text{K} \),
- \( T_2 = 313 \, \text{K} \),
- \( E_a = 70000 \, \text{J/mol} \) (activation energy),
- \( R = 8.314 \, \text{J/mol·K} \).

### Step 1: Calculate the term \(\frac{E_a}{R}\)

\[
\frac{E_a}{R} = \frac{70000 \, \text{J/mol}}{8.314 \, \text{J/mol·K}} = 8418.32 \, \text{K}
\]

### Step 2: Calculate \(\frac{1}{T_2} - \frac{1}{T_1}\)

\[
\frac{1}{T_2} - \frac{1}{T_1} = \frac{1}{313 \, \text{K}} - \frac{1}{298 \, \text{K}} = \frac{298 - 313}{298 \times 313} \, \text{K}^{-1} = -\frac{15}{93274} \, \text{K}^{-1} \approx -0.0001608 \, \text{K}^{-1}
\]

### Step 3: Calculate \(\ln\left(\frac{k_2}{k_1}\right)\)

\[
\ln\left(\frac{k_2}{k_1}\right) = -8418.32 \, \text{K} \times -0.0001608 \, \text{K}^{-1} \approx 1.353
\]

### Step 4: Solve for \( k_2 \)

\[
\frac{k_2}{k_1} = e^{1.353} \approx 3.869
\]

\[
k_2 = k_1 \times 3.869 = 0.01439 \, \text{min}^{-1} \times 3.869 \approx 0.0557 \, \text{min}^{-1}
\]

So, the rate constant of the reaction at 313 K is approximately \( 0.0557 \, \text{min}^{-1} \).

Would you like further details or have any other questions?

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Here are some related questions:
1. How does the activation energy affect the rate constant at different temperatures?
2. What are some methods to experimentally determine the activation energy of a reaction?
3. How does the Arrhenius equation apply to non-ideal systems?
4. What happens to the rate constant if the temperature increases by a larger amount, say to 350 K?
5. Can the Arrhenius equation be used to predict reaction behavior at very low temperatures?

**Tip:** Always check the consistency of your units when using the Arrhenius equation, especially when switching between time units like minutes and seconds.

Learn how to calculate the rate constant of a reaction at 313 K using the Arrhenius equation. Detailed step-by-step solution provided with specific data points: activation energy of 70000 J/mol, rate constant at 298 K of 0.01439 min^-1. Suitable for undergraduate students studying chemical kinetics.

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