Which of the following is correct

Options

A. `log.K_2/K_1=E_a/2.303[(DeltaT)/(T_1T_2)]`
B. For zero order `t_(1//2)` is inversely proportional to initial concentration
C. Catalyst decreases the activation energy
D. All of these

Answer

To solve the question "Which of the following is correct?", we will analyze each of the options provided and determine their validity based on chemical kinetics principles.

### Step-by-Step Solution:

1. **Analyze the First Option:**
- The first option states:
\[ \log \frac{k_2}{k_1} = \frac{E_a}{2.303 \cdot \Delta t} \cdot \frac{1}{T_1 \cdot T_2} \]
- This equation resembles the Arrhenius equation, which is:
\[ \log \frac{k_2}{k_1} = \frac{E_a}{2.303R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \]
- The correct form includes the gas constant \( R \), which is missing in the first option. Therefore, this option is **incorrect**.

2. **Analyze the Second Option:**
- The second option states:
"For zero-order reactions, \( t_{1/2} \) is inversely proportional to the initial concentration."
- For zero-order reactions, the half-life is given by:
\[ t_{1/2} = \frac{[A]_0}{2k} \]
- This indicates that \( t_{1/2} \) is **directly proportional** to the initial concentration \([A]_0\), not inversely. Therefore, this option is also **incorrect**.

3. **Analyze the Third Option:**
- The third option states:
"A catalyst decreases the activation energy."
- This statement is true. Catalysts provide an alternative pathway for the reaction with a lower activation energy, thus facilitating the reaction. Therefore, this option is **correct**.

4. **Analyze the Fourth Option:**
- The fourth option states:
"All of these."
- Since the first two options are incorrect and only the third option is correct, this option is also **incorrect**.

### Conclusion:
The only correct statement among the options provided is that a catalyst decreases the activation energy. Therefore, the correct answer is:

**Correct Option: Third Option (C)**

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