Catalyst increses the rate of reaction

Options

A. by decreasing `E_(a)`
B. by increasing `E_(a)`
C. by decreasing A
D. by increasing entropy

Explanation

**Step-by-Step Text Solution:**

1. **Understanding the Role of a Catalyst:**
A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process. It achieves this by providing an alternative pathway for the reaction with a lower activation energy.

2. **Graphical Representation:**
To visualize this, we can plot a graph with potential energy on the y-axis and the reaction coordinate on the x-axis. The graph will show the energy changes as reactants convert to products.

3. **Identifying Activation Energy:**
In the absence of a catalyst, the reactants need to overcome a certain amount of energy, known as the activation energy (Ea), to reach the transition state. This is represented as the peak of the curve on the graph.

4. **Effect of Catalyst on Activation Energy:**
When a catalyst is introduced, it lowers the activation energy required for the reaction. This means that the energy barrier that the reactants must overcome to form products is reduced.

5. **Comparing Reaction Pathways:**
The reaction pathway with the catalyst will show a lower peak (lower activation energy) compared to the pathway without the catalyst. This indicates that the reactants can convert to products more easily and quickly when a catalyst is present.

6. **Mathematical Representation:**
The rate of a reaction can be expressed by the equation:
\[ k = A \cdot e^{-\frac{E_a}{RT}} \]
where \(k\) is the rate constant, \(A\) is the pre-exponential factor, \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature. A decrease in \(E_a\) (due to the catalyst) leads to an increase in the rate constant \(k\), thereby increasing the reaction rate.

7. **Conclusion:**
In summary, a catalyst increases the rate of a reaction by lowering the activation energy, which allows the reactants to convert to products more quickly.

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