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1.              Activation energy can be determined experimentally by an Arrhenius plot or by knowing the rate constant at two different temperatures.

a.       Write the Arrhenius equation, and draw an Arrhenius plot (linear, negative slope) with labelled axes. Briefly explain the determination of activation energy and frequency factor A from the plot. *(5 marks)*

### a. Arrhenius Equation and Plot

The **Arrhenius equation** is used to describe how the rate constant (\(k\)) of a reaction depends on the temperature (\(T\)). The equation is given by:

\[
k = A e^{-\frac{E_a}{RT}}
\]

Where:
- \(k\) is the rate constant,
- \(A\) is the frequency factor (also known as the pre-exponential factor),
- \(E_a\) is the activation energy,
- \(R\) is the gas constant, and
- \(T\) is the absolute temperature in Kelvin.

### Arrhenius Plot

To determine the activation energy (\(E_a\)) and frequency factor (\(A\)), we can take the natural logarithm of both sides of the Arrhenius equation:

\[
\ln k = \ln A - \frac{E_a}{R} \frac{1}{T}
\]

This equation is of the form:

\[
y = mx + c
\]

Where:
- \(y = \ln k\),
- \(x = \frac{1}{T}\),
- \(m = -\frac{E_a}{R}\), and
- \(c = \ln A\).

Therefore, a plot of \(\ln k\) versus \(\frac{1}{T}\) gives a **straight line** with:
- **Slope** (\(m\)) = \(-\frac{E_a}{R}\), from which the activation energy \(E_a\) can be determined.
- **Y-intercept** (\(c\)) = \(\ln A\), from which the frequency factor \(A\) can be calculated.

### Diagram

Here’s a labeled diagram based on the description:

- **Y-axis:** \(\ln k\)
- **X-axis:** \(\frac{1}{T}\)
- **Slope:** \(-\frac{E_a}{R}\)
- **Y-intercept:** \(\ln A\)

![Arrhenius Plot](https://imgur.com/EuDFgLs.png)

#### Determination Process:
1. **Activation Energy (\(E_a\))**: The slope of the line, \(m = -\frac{E_a}{R}\), can be calculated. Multiply the slope by \(-R\) (where \(R = 8.314 \, \text{J/mol K}\)) to find \(E_a\).
2. **Frequency Factor (\(A\))**: The y-intercept gives \(\ln A\). Taking the exponential of the intercept gives the value of \(A\).

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Do you want further details or have any questions?

### Related Questions:
1. How does temperature affect the rate constant according to the Arrhenius equation?
2. What are the typical units for the activation energy and the frequency factor?
3. Can the Arrhenius equation be applied to all types of chemical reactions?
4. What is the significance of a higher or lower activation energy in a chemical reaction?
5. How can you experimentally determine the rate constant at different temperatures?

### Tip:
To reduce errors in determining \(E_a\) and \(A\), it's crucial to accurately measure the rate constant \(k\) at different temperatures, especially over a wide range.

Learn how to determine activation energy and frequency factor using an Arrhenius plot. Understand the Arrhenius equation and its application in chemical kinetics. Suitable for university-level chemistry students and researchers.

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